% Encoding: ISO-8859-1
@Article{0,
author = {and Thiele, U.},
title = {x},
journal = {x},
year = {2019},
volume = {x},
pages = {x},
abstract = {x},
doi = {x},
note = {(submitted)},
eprint = {http://arxiv.org/abs/},
}
@InCollection{EGUW2019springer,
author = {S. Engelnkemper and Gurevich, S.V. and H. Uecker and D. Wetzel and U. Thiele},
title = {Continuation for thin film hydrodynamics and related scalar problems},
booktitle = {Computational Modeling of Bifurcations and Instabilities in Fluid Mechanics},
publisher = {Springer},
year = {2019},
editor = {Gelfgat, A.},
series = {Computational Methods in Applied Sciences, vol 50},
pages = {459-501},
abstract = {This chapter illustrates how to apply continuation techniques in the analysis of a particular class of nonlinear kinetic equations that describe the time evolution of a single scalar field like a density or interface profiles of various types. We first systematically introduce these equations as gradient dynamics combining mass-conserving and nonmass-conserving fluxes followed by a discussion of nonvariational amendmends and a brief introduction to their analysis by numerical continuation. The approach is first applied to a number of common examples of variational equations, namely, Allen-Cahn- and Cahn-Hilliard-type equations including certain thin-film equations for partially wetting liquids on homogeneous and heterogeneous substrates as well as Swift-Hohenberg and Phase-Field-Crystal equations. Second we consider nonvariational examples as the Kuramoto-Sivashinsky equation, convective Allen-Cahn and Cahn-Hilliard equations and thin-film equations describing stationary sliding drops and a transversal front instability in a dip-coating. Through the different examples we illustrate how to employ the numerical tools provided by the packages auto07p and pde2path to determine steady, stationary and time-periodic solutions in one and two dimensions and the resulting bifurcation diagrams. The incorporation of boundary conditions and integral side conditions is also discussed as well as problem-specific implementation issues.},
doi = {10.1007/978-3-319-91494-7_13},
eprint = {http://arxiv.org/abs/1808.02321},
file = {:EGUW2019springer.pdf:PDF},
}
@Article{EnTh2019el,
Abstract = {Employing a long-wave mesoscopic hydrodynamic model for the film height evolution we study ensembles of pinned and sliding drops of a volatile liquid that continuously condense onto a chemically heterogeneous inclined substrate. Our analysis combines, on the one hand, path continuation techniques to determine bifurcation diagrams for the depinning of single drops of nonvolatile liquid on single hydrophilic spots on a partially wettable substrate and, on the other hand, time simulations of growth and depinning of individual condensing drops as well as of the long-time behaviour of large ensembles of such drops. Pinned drops grow on the hydrophilic spots, depin and slide along the substrate while merging with other pinned drops and smaller drops that slide more slowly, and possibly undergo a pearling instability. As a result, the collective behaviour converges to a stationary state where condensation and outflow balance. The main features of the emerging drop size distribution can then be related to single-drop bifurcation diagrams.},
Author = {S. Engelnkemper and Thiele, U. },
DOI = {10.1209/0295-5075/127/54002},
Eprint = {http://arxiv.org/abs/1901.10235},
Journal = {Europhys. Lett.},
Pages = {54002},
Title = {The collective behaviour of ensembles of condensing liquid drops on heterogeneous inclined substrates},
Volume = {127},
file = {:EnTh2019el.pdf:PDF; EnTh2019arxiv.pdf:PDF},
Year = {2019}
}
@Article{LTCG2019pre,
Abstract = {The influence of a temporal forcing on the pattern formation in Langmuir-Blodgett transfer is studied employing a generalized Cahn-Hilliard model. The occurring frequency-locking effects allow for controlling the pattern formation process. In the case of one-dimensional (i.e., stripe) patterns one finds various synchronization phenomena such as entrainment between the distance of deposited stripes and the forcing frequency. In two dimensions, the temporal forcing gives rise to the formation of intricate complex patterns such as vertical stripes, oblique stripes, and lattice structures. Remarkably, it is possible to influence the system in the spatial direction perpendicular to the forcing direction leading to synchronization in two spatial dimensions.},
Author = {Ly, P.-M. T. and Thiele, U. and Chi, L. and Gurevich, S. V.},
DOI = {10.1103/PhysRevE.99.062212},
Eeprint = {http://arxiv.org/abs/1902.05825},
Journal = {Phys. Rev. E},
Pages = {062212},
Title = {Effects of time-periodic forcing in a {C}ahn-{H}illiard model for {L}angmuir-{B}lodgett transfer},
Volume = {99},
file = {:LTCG2019pre.pdf:PDF},
Year = {2019}
}
@Article{TALT2019arxiv,
Note = {(submitted)},
Abstract = {x},
Author = {D. Tseluiko and M. Alesemi and Lin, T.-S. and Thiele, U. },
DOI = {x},
Eprint = {http://arxiv.org/abs/1905.13396},
Journal = {x},
Pages = {x},
Title = {Effect of driving on coarsening dynamics in phase-separating systems},
Volume = {x},
file = {:TALT2019arxiv.pdf:PDF},
Year = {2019}
}
@Article{TFEK2019njp,
author = {U. Thiele and T. Frohoff-H\"ulsmann and S. Engelnkemper and E. Knobloch and Archer, A. J.},
title = {First order phase transitions and the thermodynamic limit},
journal = {New J. Phys.},
year = {2019},
volume = {21},
pages = {123021},
abstract = {We consider simple mean field continuum models for first order liquid-liquid demixing and solid-liquid phase transitions and show how the Maxwell construction at phase coexistence emerges on going from finite-size closed systems to the thermodynamic limit. The theories considered are the Cahn-Hilliard model of phase separation, which is also a model for the liquid-gas transition, and the phase field crystal model of the solid-liquid transition. Our results show that states comprising the Maxwell line depend strongly on the mean density with spatially localized structures playing a key role in the approach to the thermodynamic limit.},
doi = {10.1088/1367-2630/ab5caf},
eeprint = {http://arxiv.org/abs/1908.11304},
}
@Article{ThHa2019arxiv,
author = {U. Thiele and S. Hartmann},
title = {Gradient dynamics model for drops spreading on polymer brushes},
journal = {x},
year = {2019},
volume = {x},
pages = {x},
abstract = {x},
doi = {x},
file = {:ThHa2019arxiv.pdf:PDF},
note = {(submitted)},
eprint = {http://arxiv.org/abs/1910.10582},
}
@Article{TSJT2020preprint,
author = {S. Trinschek and F. Stegemerten and K. John and Thiele, U.},
title = {Thin-Film Modelling of Resting and Moving Active Droplets},
journal = {x},
year = {2019},
volume = {x},
pages = {x},
abstract = {x},
doi = {x},
note = {(submitted)},
eprint = {http://arxiv.org/abs/1911.08258},
}
@Article{TWGT2019prf,
author = {Tewes, W. and Wilczek, M. and Gurevich, S. V. and Thiele, U.},
title = {Self-organised dip-coating patterns of simple, partially wetting, nonvolatile liquids},
journal = {Phys. Rev. Fluids},
year = {2019},
volume = {4},
pages = {123903},
abstract = {When a solid substrate is withdrawn from a bath of simple, partially wetting, nonvolatile liquid, one typically distinguishes two regimes, namely, after withdrawal the substrate is macroscopically dry or homogeneously coated by a liquid film. In the latter case, the coating is called a Landau-Levich film. Its thickness depends on the angle and velocity of substrate withdrawal. We predict by means of a numerical and analytical investigation of a hydrodynamic thin-film model the existence of a third regime. It consists of the deposition of a regular pattern of liquid ridges oriented parallel to the meniscus. We establish that the mechanism of the underlying meniscus instability originates from competing film dewetting and Landau-Levich film deposition and argue that the mechanism also occurs for other combinations of film instability and lateral driving. Our analysis combines a marginal stability analysis, numerical time simulations and a numerical bifurcation study via path-continuation.},
doi = {10.1103/PhysRevFluids.4.123903},
eeprint = {http://arxiv.org/abs/1906.00677},
file = {:TWGT2019prf.pdf:PDF},
}
@Article{AEZT2018l,
Abstract = {We study the deposition mechanisms of polymer from a confined meniscus of volatile liquid. In particular, we investigate the physical processes that are responsible for qualitative changes in the pattern deposition of polymer and the underlying interplay of the state of pattern deposition, motion of the meniscus, and the transport of polymer within the meniscus. As a model system we evaporate a solution of poly(methyl methacrylate) (PMMA) in toluene. Different deposition patterns are observed when varying the molecular mass, the initial concentration of the solute, and temperature; these are systematically presented in the form of morphological phase diagrams. The modi of deposition and meniscus motion are correlated. They vary with the ratio between the evaporation-driven convective flux and the diffusive flux of the polymer coils in the solution. In the case of a diffusion-dominated solute transport, the solution monotonically dewets the solid substrate by evaporation, supporting continuous contact line motion and continuous polymer deposition. However, a convection-dominated transport results in an oscillatory ratcheting dewetting-wetting motion of the contact line with more pronounced dewetting phases. The deposition process is then periodic and produces a stripe pattern. The oscillatory motion of the meniscus differs from the well documented stick-slip motion of the meniscus, observed as well, and is attributed to the opposing influences of evaporation and Marangoni stresses, which alternately dominate the deposition process.},
Author = {Abo Jabal, M. and Egbaria, A. and Zigelman, A. and Thiele, U. and Manor, O.},
DOI = {10.1021/acs.langmuir.8b02268},
Eprint = {http://arxiv.org/abs/1807.03054},
File = {:AEZT2018l.pdf:PDF},
Journal = {Langmuir},
Pages = {11784-11794},
Title = {Connecting monotonic and oscillatory motions of the meniscus of a volatile polymer solution to the transport of polymer coils and deposit morphology},
Volume = {34},
Year = {2018}
}
@Article{BoTH2018jfm,
Abstract = {We consider steady solutions of the Stokes equations for the flow of a film of fluid on the outer or inner surface of a cylinder that rotates with its axis perpendicular to the direction of gravity. We find that previously unobserved stable and unstable steady solutions coexist over an intermediate range of rotation rates for sufficiently high values of the Bond number (ratio of gravitational forces relative to surface tension). Furthermore, we compare the results of the Stokes calculations to the classic lubrication models of Pukhnachev (J. Appl. Mech. Tech. Phys., vol 18, 1977, pp. 344-351) and Reisfeld & Bankoff (J. Fluid Mech., vol. 236, 1992, pp. 167-196); an extended lubrication model of Benilov & O'Brien (Phys. Fluids, vol. 17, 2005, 052106) and Evans et al. (Phys. Fluids, vol. 16, 2004, pp. 2742-2756); and a new lubrication approximation formulated using gradient dynamics. We quantify the range of validity of each model and confirm that the gradient-dynamics model is most accurate over the widest range of parameters, but that the new steady solutions are not captured using any of the simplified models because they contain features that can only be described by the full Stokes equations.},
Author = {von Borries Lopes, A. and Thiele, U. and Hazel, A.L.},
DOI = {10.1017/jfm.2017.756},
Eeprint = {http://arxiv.org/abs/},
File = {:BoTH2018jfm.pdf:PDF},
Journal = {J. Fluid Mech.},
Pages = {540-574},
Title = {On the multiple solutions of coating and rimming flows on rotating cylinders},
Volume = {835},
Year = {2018}
}
@Article{OpGT2018pre,
Abstract = {The conserved Swift-Hohenberg equation (or phase-field-crystal [PFC] model) provides a simple microscopic description of the thermodynamic transition between fluid and crystalline states. Combining it with elements of the Toner-Tu theory for self-propelled particles, Menzel and L\"owen [Phys. Rev. Lett. 110, 055702 (2013)] obtained a model for crystallization (swarm formation) in active systems. Here, we study the occurrence of resting and traveling localized states, i.e., crystalline clusters, within the resulting active PFC model. Based on linear stability analyses and numerical continuation of the fully nonlinear states, we present a detailed analysis of the bifurcation structure of periodic and localized, resting and traveling states in a one-dimensional active PFC model. This allows us, for instance, to explore how the slanted homoclinic snaking of steady localized states found for the passive PFC model is amended by activity. A particular focus lies on the onset of motion, where we show that it occurs either through a drift-pitchfork or a drift-transcritical bifurcation. A corresponding general analytical criterion is derived.},
Author = {L. Ophaus and Gurevich, S.V. and U. Thiele},
DOI = {10.1103/PhysRevE.98.022608},
Eeprint = {http://arxiv.org/abs/1803.08902},
File = {:OpGT2018pre.pdf:PDF},
Journal = {Phys. Rev. E},
Pages = {022608},
Title = {Resting and Traveling Localized States in an Active Phase-Field-Crystal Model},
Volume = {98},
Year = {2018}
}
@Article{Thie2018csa,
Abstract = {We highlight some recent developments that widen the scope and reach of mesoscopic thin-film (or long-wave) hydrodynamic models employed to describe the dynamics of thin films, drops and contact lines of simple and complex liquids on solid substrates. The basis of the discussed developments is the reformulation of various mesoscopic thin-film hydrodynamic models as gradient dynamics on underlying energy functionals. After briefly presenting the general approach, the following sections discuss how to improve these models by amending the energy functional and the mobility function, how to obtain gradient dynamics models for some complex liquids, and how to incorporate processes beyond relaxational dynamics.},
Author = {U. Thiele},
DOI = {10.1016/j.colsurfa.2018.05.049},
Eprint = {http://arxiv.org/abs/1803.05388},
File = {Thie2018csa.pdf:Thie2018csa.pdf:PDF},
Journal = {Colloids Surf. A},
Pages = {487-495},
Title = {Recent advances in and future challenges for mesoscopic hydrodynamic modelling of complex wetting},
Volume = {553},
Year = {2018}
}
@Article{TrJT2018sm,
Abstract = {The spreading of bacterial colonies at solid-air interfaces is determined by the physico-chemical properties of the involved interfaces. The production of surfactant molecules by bacteria is a widespread strategy that allows the colony to efficiently expand over the substrate. On the one hand, surfactant molecules lower the surface tension of the colony, effectively increasing the wettability of the substrate, which facilitates spreading. On the other hand, gradients in the surface concentration of surfactant molecules result in Marangoni flows that drive spreading. These flows may cause an instability of the circular colony shape and the subsequent formation of fingers. In this work, we study the effect of bacterial surfactant production and substrate wettability on colony growth and shape within the framework of a hydrodynamic thin film model. We show that variations in the wettability and surfactant production are sufficient to reproduce four different types of colony growth, which have been described in the literature, namely, arrested and continuous spreading of circular colonies, slightly modulated front lines and the formation of pronounced fingers.},
Author = {S. Trinschek and K. John and U. Thiele},
DOI = {10.1039/c8sm00422f},
Eeprint = {http://arxiv.org/abs/1803.00522},
File = {:TrJT2018sm.pdf:PDF},
Journal = {Soft Matter},
Pages = {4464-4476},
Title = {Modelling of surfactant-driven front instabilities in spreading bacterial colonies},
Volume = {14},
Year = {2018}
}
@Article{TSTJ2018l,
Abstract = {The three-phase contact line of a droplet on a smooth surface can be characterized by the Young-Dupr\'e equation. It relates the interfacial energies with the macroscopic contact angle $\theta_e$. On the mesoscale, wettability is modeled by a film-height-dependent wetting energy $f(h)$. Macro- and mesoscale description are consistent if $\gamma cos(\theta_e) = \gamma+f(h_a)$, where $\gamma$ and $h_a$ are the liquid-gas interface energy and the thickness of the equilibrium liquid adsorption layer, respectively. Here, we derive a similar consistency condition for the case of a liquid covered by an insoluble surfactant. At equilibrium, the surfactant is spatially inhomogeneously distributed implying a non-trivial dependence of $\theta_e$ on surfactant concentration. We derive macroscopic and mesoscopic descriptions of a contact line at equilibrium and show that they are only consistent if a particular dependence of the wetting energy on the surfactant concentration is imposed.This is illustrated by a simple example of dilute surfactants, for which we show excellent agreement between theory and time-dependent numerical simulations.},
Author = {Thiele, U. and Snoeijer, J.H. and Trinschek, S. and John, K.},
DOI = {10.1021/acs.langmuir.8b00513},
Eprint = {http://arxiv.org/abs/1802.04042},
File = {:TSTJ2018l.pdf:PDF},
Journal = {Langmuir},
Pages = {7210-7221},
Title = {Equilibrium contact angle and adsorption layer properties with surfactants},
Volume = {34},
Year = {2018},
note = {Also see Erratum: Langmuir, 35, 4788-4789 (2019), doi:10.1021/acs.langmuir.9b00616}
}
@Article{WTYT2018bj,
Abstract = {Collective cell migration is a fundamental process during embryogenesis and its initial occurrence, called epiboly, is an excellent in vivo model to study the physical processes involved in collective cell movements that are key to understanding organ formation, cancer invasion, and wound healing. In zebrafish, epiboly starts with a cluster of cells at one pole of the spherical embryo. These cells are actively spreading in a continuous movement toward its other pole until they fully cover the yolk. Inspired by the physics of wetting, we determine the contact angle between the cells and the yolk during epiboly. By choosing a wetting approach, the relevant scale for this investigation is the tissue level, which is in contrast to other recent work. Similar to the case of a liquid drop on a surface, one observes three interfaces that carry mechanical tension. Assuming that interfacial force balance holds during the quasi-static spreading process, we employ the physics of wetting to predict the temporal change of the contact angle. Although the experimental values vary dramatically, the model allows us to rescale all measured contact-angle dynamics onto a single master curve explaining the collective cell movement. Thus, we describe the fundamental and complex developmental mechanism at the onset of embryogenesis by only three main parameters: the offset tension strength, α, that gives the strength of interfacial tension compared to other force-generating mechanisms; the tension ratio, δ, between the different interfaces; and the rate of tension variation, λ, which determines the timescale of the whole process.},
Author = {Bernhard Wallmeyer and Sarah Trinschek and Sargon Yigit and Uwe Thiele and Timo Betz},
DOI = {10.1016/j.bpj.2017.11.011},
Eprint = {http://arxiv.org/abs/},
File = {:WTYT2018bj.pdf:PDF},
Journal = {Biophys. J.},
Pages = {213-222},
Title = {Collective cell migration in embryogenesis follows the laws of wetting},
Volume = {114},
Year = {2018}
}
@Article{BTAH2017jcp,
Abstract = {The wetting behavior of a liquid on solid substrates is governed by the nature of the effective interaction between the liquid-gas and the solid-liquid interfaces, which is described by the binding or wetting potential g(h) which is an excess free energy per unit area that depends on the liquid film height h. Given a microscopic theory for the liquid, to determine g(h), one must calculate the free energy for liquid films of any given value of h, i.e., one needs to create and analyze out-of-equilibrium states, since at equilibrium there is a unique value of h, specified by the temperature and chemical potential of the surrounding gas. Here we introduce a Nudged Elastic Band (NEB) approach to calculate g(h) and illustrate the method by applying it in conjunction with a microscopic lattice density functional theory for the liquid. We also show that the NEB results are identical to those obtained with an established method based on using a fictitious additional potential to stabilize the non-equilibrium states. The advantages of the NEB approach are discussed.},
Author = {O. Buller and W. Tewes and Archer, A.J. and A. Heuer and U. Thiele and S. Gurevich},
DOI = {10.1063/1.4990702},
Eprint = {http://arxiv.org/abs/1706.06492},
File = {:BTAH2017jcp.pdf:PDF},
Journal = {J. Chem. Phys.},
Pages = {094704},
Title = {Nudged Elastic Band calculation of the binding potential for liquids at interfaces},
Volume = {147},
Year = {2017}
}
@Article{HuTA2017jcp,
Abstract = {For a film of liquid on a solid surface, the binding potential $g(h)$ gives the free energy as a function of the film thickness h and also the closely related (structural) disjoining pressure $\Pi=\partial g/\partial h$. The wetting behaviour of the liquid is encoded in the binding potential and the equilibrium film thickness corresponds to the value at the minimum of $g(h)$. Here, the method we developed in the work of Hughes \textit{et al.} [J. Chem. Phys. 142, 074702 (2015)], and applied with a simple discrete lattice-gas model, is used with continuum density functional theory (DFT) to calculate the binding potential for a Lennard-Jones fluid and other simple liquids. The DFT used is based on fundamental measure theory and so incorporates the influence of the layered packing of molecules at the surface and the corresponding oscillatory density profile. The binding potential is frequently input in mesoscale models from which liquid drop shapes and even dynamics can be calculated. Here we show that the equilibrium droplet profiles calculated using the mesoscale theory are in good agreement with the profiles calculated directly from the microscopic DFT. For liquids composed of particles where the range of the attraction is much less than the diameter of the particles, we find that at low temperatures $g(h)$ decays in an oscillatory fashion with increasing h, leading to highly structured terraced liquid droplets.},
Author = {Hughes, A. P. and Thiele, U. and Archer, A. J.},
DOI = {10.1063/1.4974832},
Eprint = {http://arxiv.org/abs/1611.06957},
File = {:HuTA2017jcp.pdf:PDF},
Journal = {J. Chem. Phys.},
Pages = {064705},
Title = {Influence of the fluid structure on the binding potential: Comparing liquid drop profiles from density functional theory with results from mesoscopic theory},
Volume = {146},
Year = {2017}
}
@Article{TBHT2017jcp,
Abstract = {We employ kinetic Monte Carlo (KMC) simulations and a thin-film continuum model to comparatively study the transversal (i.e., Plateau-Rayleigh) instability of ridges formed by molecules on pre-patterned substrates. It is demonstrated that the evolution of the occurring instability qualitatively agrees between the two models for a single ridge as well as for two weakly interacting ridges. In particular, it is shown for both models that the instability occurs on well defined length and time scales which are, for the KMC model, significantly larger than the intrinsic scales of thermodynamic fluctuations. This is further evidenced by the similarity of dispersion relations characterizing the linear instability modes.},
Author = {Tewes, W. and Buller, O. and Heuer, A. and Thiele, U. and Gurevich, S. V.},
DOI = {10.1063/1.4977739},
Eprint = {http://arxiv.org/abs/1611.09685},
File = {:TBHT2017jcp.pdf:PDF},
Journal = {J. Chem. Phys.},
Pages = {094704},
Title = {Thin film and kinetic {Monte Carlo} modeling of {P}lateau-{R}ayleigh instabilities of ridges on chemically patterned substrates},
Urrl = {http://aip.scitation.org/doi/full/10.1063/1.4977739},
Volume = {146},
Year = {2017}
}
@Article{TJLT2017prl,
Abstract = {We introduce and analyze a model for osmotically spreading bacterial colonies at solid-air interfaces that includes wetting phenomena, i.e., surface forces. The model is based on a hydrodynamic description for liquid suspensions which is supplemented by bioactive processes. We show that surface forces determine whether a biofilm can expand laterally over a substrate and provide experimental evidence for the existence of a transition between continuous and arrested spreading for Bacillus subtilis biofilms. In the case of arrested spreading, the lateral expansion of the biofilm is confined, albeit the colony is biologically active. However, a small reduction in the surface tension of the biofilm is sufficient to induce spreading. The incorporation of surface forces into our hydrodynamic model allows us to capture this transition in biofilm spreading behavior.},
Author = {S. Trinschek and K. John and S. Lecuyer and U. Thiele},
DOI = {10.1103/PhysRevLett.119.078003},
Eprint = {http://arxiv.org/abs/1612.05450},
File = {:TJLT2017prl.pdf:PDF},
Journal = {Phys. Rev. Lett.},
Pages = {078003},
Title = {Continuous vs. arrested spreading of biofilms at solid-gas interfaces - the role of surface forces},
Volume = {119},
Year = {2017}
}
@Article{WTEG2017prl,
Abstract = {Ensembles of interacting drops that slide down an inclined plate show a dramatically different coarsening behavior as compared to drops on a horizontal plate: As drops of different size slide at different velocities, frequent collisions result in fast coalescence. However, above a certain size individual sliding drops are unstable and break up into smaller drops. Therefore, the long-time dynamics of a large drop ensemble is governed by a balance of merging and splitting. We employ a long-wave film height evolution equation and determine the dynamics of the drop size distribution towards a stationary state from direct numerical simulations on large domains. The main features of the distribution are then related to the bifurcation diagram of individual drops obtained by numerical path continuation. The gained knowledge allows us to develop a Smoluchowski-type statistical model for the ensemble dynamics that well compares to full direct simulations.},
Author = {Wilczek, M. and Tewes, W. and Engelnkemper, S. and Gurevich, S. V. and Thiele, U.},
DOI = {10.1103/PhysRevLett.119.204501},
Eeprint = {http://arxiv.org/abs/1706.00656v1},
File = {:WTEG2017prl.pdf:PDF},
Journal = {Phys. Rev. Lett.},
Pages = {204501},
Title = {Sliding drops - ensemble statistics from single drop bifurcations},
Volume = {119},
Year = {2017}
}
@Article{WZCT2017jpcm,
Abstract = {When a plate is withdrawn from a liquid bath, either a static meniscus forms in the transition region between the bath and the substrate or a liquid film of finite thickness (a Landau-Levich film) is transferred onto the moving substrate. If the substrate is inhomogeneous, e.g. has a prestructure consisting of stripes of different wettabilities, the meniscus can be deformed or show a complex dynamic behavior. Here we study the free surface shape and dynamics of a dragged meniscus occurring for striped prestructures with two orientations, parallel and perpendicular to the transfer direction. A thin film model is employed that accounts for capillarity through a Laplace pressure and for the spatially varying wettability through a Derjaguin (or disjoining) pressure. Numerical continuation is used to obtain steady free surface profiles and corresponding bifurcation diagrams in the case of substrates with different homogeneous wettabilities. Direct numerical simulations are employed in the case of the various striped prestructures. The final part illustrates the importance of our findings for particular applications that involve complex liquids by modeling a Langmuir-Blodgett transfer experiment. There, one transfers a monolayer of an insoluble surfactant that covers the surface of the bath onto the moving substrate. The resulting pattern formation phenomena can be crucially influenced by the hydrodynamics of the liquid meniscus that itself depends on the prestructure on the substrate. In particular, we show how prestructure stripes parallel to the transfer direction lead to the formation of bent stripes in the surfactant coverage after transfer and present similar experimental results.},
Author = {Wilczek, M. and Zhu, J. and Chi, L. and Thiele, U. and Gurevich, S.},
DOI = {10.1088/0953-8984/29/1/014002},
Eprint = {http://arxiv.org/abs/1607.08118},
File = {:WZCT2017jpcm.pdf:PDF},
Journal = {J. Phys.: Condens. Matter},
Nnumber = {1},
Pages = {014002},
Title = {Dip-coating with prestructured substrates: transfer of simple liquids and {L}angmuir-{B}lodgett monolayers},
Uurl = {http://stacks.iop.org/0953-8984/29/i=1/a=014002},
Volume = {29},
Year = {2017}
}
@Article{YSTA2017pre,
Abstract = {We present a study of the spreading of liquid droplets on a solid substrate at very small scales. We focus on the regime where effective wetting energy (binding potential) and surface tension effects significantly influence steady and spreading droplets. In particular, we focus on strong packing and layering effects in the liquid near the substrate due to underlying density oscillations in the fluid caused by attractive substrate-liquid interactions. We show that such phenomena can be described by a thin-film (or long-wave or lubrication) model including an oscillatory Derjaguin (or disjoining or conjoining) pressure and explore the effects it has on steady droplet shapes and the spreading dynamics of droplets on both an adsorption (or precursor) layer and completely dry substrates. At the molecular scale, commonly used two-term binding potentials with a single preferred minimum controlling the adsorption layer height are inadequate to capture the rich behavior caused by the near-wall layered molecular packing. The adsorption layer is often submonolayer in thickness, i.e., the dynamics along the layer consists of single-particle hopping, leading to a diffusive dynamics, rather than the collective hydrodynamic motion implicit in standard thin-film models. We therefore modify the model in such a way that for thicker films the standard hydrodynamic theory is realized, but for very thin layers a diffusion equation is recovered.},
Author = {Yin, H. and Sibley, D.N. and Thiele, U. and Archer, A.J.},
DOI = {10.1103/PhysRevE.95.023104},
Eeprint = {http://arxiv.org/abs/1611.00390},
File = {:YSTA2017pre.pdf:PDF},
Journal = {Phys. Rev. E},
Pages = {023104},
Title = {Films, layers and droplets: {T}he effect of near-wall fluid structure on spreading dynamics},
Volume = {95},
Year = {2017}
}
@InBook{AWTK2016,
Abstract = {We show how deeply quenching a liquid to temperatures where it is linearly unstable and the crystal is the equilibrium phase often produces crystalline structures with defects and disorder. As the solid phase advances into the liquid phase, the modulations in the density distribution created behind the advancing solidification front do not necessarily have a wavelength that is the same as the equilibrium crystal lattice spacing. This is because in a deep enough quench the front propagation is governed by linear processes, but the crystal lattice spacing is determined by nonlinear terms. The wavelength mismatch can result in significant disorder behind the front that may or may not persist in the latter stage dynamics. We support these observations by presenting results from dynamical density functional theory calculations for simple one- and two-component two-dimensional systems of soft core particles. },
Author = {Archer, A.J. and Walters, M.C. and Thiele, U. and Knobloch, E.},
Booktitle = {Mathematical Challenges in a New Phase of Materials Science},
DOI = {10.1007/978-4-431-56104-0_1},
Editor = {Y. Nishiura and M. Kotani},
Eprint = {http://arxiv.org/abs/1505.07976},
File = {AWTK2016chapter.pdf:AWTK2016.pdf:PDF},
ISBN = {978-3-319-28027-1},
Pages = {1--26},
Publisher = {Springer International Publishing},
Series = {Springer Proceedings in Mathematics \& Statistics 166},
Title = {Generation of defects and disorder from deeply quenching a liquid to form a solid},
Uurl = {http://dx.doi.org/10.1007/978-4-431-56104-0_1},
Year = {2016}
}
@Article{ChGT2016el,
Abstract = {We investigate the collective behavior of self-propelled particles (SPPs) undergoing competitive processes of pattern formation and rotational relaxation of their self-propulsion veloc- ities. In full accordance with previous work, we observe transitions between different steady states of the SPPs caused by the intricate interplay among the involved effects of pattern formation, ori- entational order, and coupling between the SPP density and orientation fields. Based on rigorous analytical and numerical calculations, we prove that the rate of the orientational relaxation of the SPP velocity field is the main factor determining the steady states of the SPP system. Further, we determine the boundaries between domains in the parameter plane that delineate qualitatively different resting and moving states. In addition, we analytically calculate the collective velocityv of the SPPs and show that it perfectly agrees with our numerical results. We quantitatively demonstrate that v does not vanish upon approaching the transition boundary between the moving pattern and homogeneous steady states.},
Author = {Chervanyov, A.I. and Gomez, H. and Thiele, U.},
DOI = {10.1209/0295-5075/115/68001},
Eprint = {http://arxiv.org/abs/1611.02140},
File = {:ChGT2016el.pdf:PDF},
Journal = {Europhys. Lett.},
Pages = {68001},
Title = {Effect of the orientational relaxation on the collective motion of patterns formed by self-propelled particles},
Volume = {115},
Year = {2016}
}
@Article{EWGT2016prf,
Abstract = {We study fully three-dimensional droplets that slide down an incline by employing a thin-film equation that accounts for capillarity, wettability, and a lateral driving force in small-gradient (or long-wave) approximation. In particular, we focus on qualitative changes in the morphology and behavior of stationary sliding drops. We employ the inclination angle of the substrate as control parameter and use continuation techniques to analyze for several fixed droplet sizes the bifurcation diagram of stationary droplets, their linear stability, and relevant eigenmodes. The obtained predictions on existence ranges and instabilities are tested via direct numerical simulations that are also used to investigate a branch of time-periodic behavior (corresponding to repeated breakup-coalescence cycles, where the breakup is also denoted as pearling) which emerges at a global instability, the related hysteresis in behavior, and a period-doubling cascade. The nontrivial oscillatory behavior close to a Hopf bifurcation of drops with a finite-length tail is also studied. Finally, it is shown that the main features of the bifurcation diagram follow scaling laws over several decades of the droplet size.},
Author = {Engelnkemper, S. and Wilczek, M. and Gurevich, S. V. and Thiele, U.},
DOI = {10.1103/PhysRevFluids.1.073901},
Eprint = {http://arxiv.org/abs/1607.05482},
File = {:EWGT2016prf.pdf:PDF},
Journal = {Phys. Rev. Fluids},
Pages = {073901},
Title = {Morphological transitions of sliding drops - dynamics and bifurcations},
Urrl = {http://link.aps.org/doi/10.1103/PhysRevFluids.1.073901, http://journals.aps.org/prfluids/supplemental/10.1103/PhysRevFluids.1.073901},
Volume = {1},
Year = {2016}
}
@Article{LRTT2016pf,
Abstract = {We discuss the behavior of partially wetting liquids on a rotating cylinder using a model that takes into account the e ects of gravity, viscosity, rotation, surface tension, and wettability. Such a system can be considered as a prototype for many other systems where the interplay of spatial heterogeneity and a lateral driving force in the proximity of a first- or second-order phase transition results in intricate behavior. So does a partially wetting drop on a rotating cylinder undergo a depinning transition as the rotation speed is increased, whereas for ideally wetting liquids, the behavior only changes quantitatively. We analyze the bifurcations that occur when the rotation speed is increased for several values of the equilibrium contact angle of the partially wetting liquids. This allows us to discuss how the entire bifurcation structure and the ow behavior it encodes change with changing wettability. We employ various numerical continuation techniques that allow us to track stable/unstable steady and time-periodic lm and drop thickness pro les. We support our ndings by time-dependent numerical simulations and asymptotic analyses of steady and time-periodic pro les for large rotation numbers.},
Author = {Lin, T.-S. and Rogers, S. and Tseluiko, D. and Thiele, U.},
DOI = {10.1063/1.4959890},
Eprint = {http://arxiv.org/abs/1511.01167},
File = {:LRTT2016pf.pdf:PDF},
Journal = {Phys. Fluids},
Pages = {082102},
Title = {Bifurcation analysis of the behavior of partially wetting liquids on a rotating cylinder},
Volume = {28},
Year = {2016}
}
@InBook{PoTS2016,
Abstract = {We consider a colony of self-propelled particles (swimmers) in a thin liquid film resting on a solid plate with deformable liquid-gas interface. Individual particles swim along the surface of the film predominantly in circles and interact via a short range alignment and longer-range anti-alignment. The local surface tension of the liquid-gas interface is altered by the local density of swimmers due to the soluto-Marangoni effect. Without the addition of swimmers, the flat film surface is linearly stable. We show that a finite wave length instability of the homogeneous and isotropic state can be induced by the carrier film for certain values of the rotational diffusivity and a nonzero rotation frequency of the circular motion of swimmers. In the nonlinear regime we find square arrays of vortices, stripe-like density states and holes developing in the film.},
Author = {A. Pototsky and U. Thiele and H. Stark},
Booktitle = {Control of Self-Organizing Nonlinear Systems},
DOI = {10.1007/978-3-319-28028-8_20},
Editor = {Sch{\"o}ll, E. and Klapp, S. H. L. and H{\"o}vel, P.},
File = {PoTS2016chapter.pdf:PoTS2016.pdf:PDF},
ISBN = {978-3-319-28027-1},
Pages = {393--412},
Publisher = {Springer International Publishing},
Series = {Understanding Complex Systems},
Title = {Swarming of Self-propelled Particles on the Surface of a Thin Liquid Film},
Uurl = {http://dx.doi.org/10.1007/978-3-319-28028-8_20},
Year = {2016}
}
@Article{PoTS2016epje,
Abstract = {We consider a colony of point-like self-propelled surfactant particles (swimmers) without direct interactions that cover a thin liquid layer on a solid support. The particles predominantly swim normal to the free film surface with only a small component parallel to the film surface. The coupled dynamics of the swimmer density and film height profile is captured in a long-wave model allowing for diffusive and convective transport of the swimmers (including rotational diffusion). The dynamics of the film height profile is determined by i) the upward pushing force of the swimmers onto the liquid-gas interface, ii) the solutal Marangoni force due to gradients in the swimmer concentration, and iii) the rotational diffusion of the swimmers together with the in-plane active motion. After reviewing and extending the analysis of the linear stability of the uniform state, we analyse the fully nonlinear dynamic equations and show that point-like swimmers, which only interact via long-wave deformations of the liquid film, self-organise in highly regular (standing, travelling, and modulated waves) and various irregular patterns.},
Author = {A. Pototsky and U. Thiele and H. Stark},
DOI = {10.1140/epje/i2016-16051-4},
Eprint = {http://arxiv.org/abs/1601.02061},
File = {:PoTS2016epje.pdf:PDF},
Journal = {Eur. Phys. J. E},
Nnote = {First online: 06 May 2016},
Nnumber = {5},
Pages = {1--19},
Title = {Mode instabilities and dynamic patterns in a colony of self-propelled surfactant particles covering a thin liquid layer},
Urrl = {http://dx.doi.org/10.1140/epje/i2016-16051-4},
Volume = {39},
Year = {2016}
}
@Article{ThAP2016prf,
Abstract = {In this paper we propose equations of motion for the dynamics of liquid films of surfactant suspensions that consist of a general gradient dynamics framework based on an underlying energy functional. This extends the gradient dynamics approach to dissipative nonequilibrium thin-film systems with several variables and casts their dynamic equations into a form that reproduces Onsager's reciprocity relations. We first discuss the general form of gradient dynamics models for an arbitrary number of fields and discuss simple well-known examples with one or two fields. Next we develop the three-field gradient dynamics model for a thin liquid film covered by soluble surfactant and discuss how it automatically results in consistent convective (driven by pressure gradients, Marangoni forces, and Korteweg stresses), diffusive, adsorption or desorption, and evaporation fluxes. We then show that in the dilute limit, the model reduces to the well-known hydrodynamic form that includes Marangoni fluxes due to a linear equation of state. In this case the energy functional incorporates wetting energy, surface energy of the free interface (constant contribution plus an entropic term), and bulk mixing entropy. Subsequently, as an example, we show how various extensions of the energy functional result in consistent dynamical models that account for nonlinear equations of state, concentration-dependent wettability, and surfactant and film bulk decomposition phase transitions. We conclude with a discussion of further possible extensions towards systems with micelles, surfactant adsorption at the solid substrate, and bioactive behavior.},
Author = {Thiele, U. and Archer, A.J. and Pismen, L.M.},
DOI = {10.1103/PhysRevFluids.1.083903},
Eprint = {http://arxiv.org/abs/1609.00946},
File = {:ThAP2016prf.pdf:PDF},
Journal = {Phys. Rev. Fluids},
Pages = {083903},
Title = {Gradient dynamics models for liquid films with soluble surfactant},
Volume = {1},
Year = {2016}
}
@Article{TrJT2016ams,
Abstract = {Biofilms are ubiquitous macro-colonies of bacteria that develop at various interfaces (solid- liquid, solid-gas or liquid-gas). The formation of biofilms starts with the attachment of individual bac- teria to an interface, where they proliferate and produce a slimy polymeric matrix - two processes that result in colony growth and spreading. Recent experiments on the growth of biofilms on agar substrates under air have shown that for certain bacterial strains, the production of the extracellular matrix and the resulting osmotic influx of nutrient-rich water from the agar into the biofilm are more crucial for the spreading behaviour of a biofilm than the motility of individual bacteria. We present a model which de- scribes the biofilm evolution and the advancing biofilm edge for this spreading mechanism. The model is based on a gradient dynamics formulation for thin films of biologically passive liquid mixtures and suspensions, supplemented by bioactive processes which play a decisive role in the osmotic spreading of biofilms. It explicitly includes the wetting properties of the biofilm on the agar substrate via a dis- joining pressure and can therefore give insight into the interplay between passive surface forces and bioactive growth processes.},
Author = {S. Trinschek and K. John and U. Thiele},
DOI = {10.3934/matersci.2016.3.1138},
Eprint = {http://arxiv.org/abs/1607.08425},
File = {TrJT2016ams.pdf:TrJT2016ams.pdf:PDF},
Journal = {AIMS Materials Science},
Pages = {1138--1159},
Title = {From a thin film model for passive suspensions towards the description of osmotic biofilm spreading},
Volume = {3},
Year = {2016}
}
@Article{HLHT2015l,
Abstract = {A mesoscopic continuum model is employed to analyze
the transport mechanisms and structure formation
during the redistribution stage of deposition
experiments where organic molecules are deposited on
a solid substrate with periodic stripe-like
wettability patterns. Transversally invariant ridges
located on the more wettable stripes are identified
as very important transient states and their linear
stability is analyzed accompanied by direct
numerical simulations of the fully nonlinear
evolution equation for two-dimensional
substrates. It is found that there exist two
different instability modes that lead to different
nonlinear evolutions that result (i) at large ridge
volume in the formation of bulges that spill from
the more wettable stripes onto the less wettable
bare substrate and (ii) at small ridge volume in the
formation of small droplets located on the more
wettable stripes. In addition, the influence of
different transport mechanisms during redistribution
is investigated focusing on the cases of convective
transport with no-slip at the substrate, transport
via diffusion in the film bulk and via diffusion at
the film surface. In particular, it is shown that
the transport process does neither influence the
linear stability thresholds nor the sequence of
morphologies observed in the time simulation, but
only the ratio of the time scales of the different
process phases.},
Author = {Honisch, C. and Lin, T.-S. and Heuer, A. and Thiele, U. and Gurevich, S. V.},
DOI = {10.1021/acs.langmuir.5b02407},
Eeprint = {http://arxiv.org/abs/1506.09078},
File = {HLHT2015l.pdf:HLHT2015l.pdf:PDF},
Journal = {Langmuir},
Pages = {10618--10631},
Title = {Instabilities of layers of deposited molecules on chemically stripe patterned substrates: {R}idges vs.\ drops},
Urrl = {http://pubs.acs.org/doi/abs/10.1021/acs.langmuir.5b02407},
Volume = {31},
Year = {2015}
}
@Article{HuTA2015jcp,
Abstract = {The contribution to the free energy for a film of liquid of thickness h on a solid surface due to the interactions between the solid-liquid and liquid-gas interfaces is given by the binding potential, g(h). The precise form of g(h) determines whether or not the liquid wets the surface. Note that differentiating g(h) gives the Derjaguin or disjoining pressure. We develop a microscopic density functional theory (DFT) based method for calculating g(h), allowing us to relate the form of g(h) to the nature of the molecular interactions in the system. We present results based on using a simple lattice gas model, to demonstrate the procedure. In order to describe the static and dynamic behaviour of non-uniform liquid films and drops on surfaces, a mesoscopic free energy based on g(h) is often used. We calculate such equilibrium film height profiles and also directly calculate using DFT the corresponding density profiles for liquid drops on surfaces. Comparing quantities such as the contact angle and also the shape of the drops, we find good agreement between the two methods. We also study in detail the effect on g(h) of truncating the range of the dispersion forces, both those between the fluid molecules and those between the fluid and wall. We find that truncating can have a significant effect on g(h) and the associated wetting behaviour of the fluid.},
Author = {Hughes, A. P. and Thiele, U. and Archer, A. J.},
DOI = {10.1063/1.4907732},
Eprint = {http://arxiv.org/abs/1501.07046},
File = {HuTA2015jcp.pdf:HuTA2015jcp.pdf:PDF},
Journal = {J. Chem. Phys.},
Pages = {074702},
Title = {Liquid drops on a surface: using density functional theory to calculate the binding potential and drop profiles and comparing with results from mesoscopic modelling},
Volume = {142},
Year = {2015}
}
@Article{STBT2015sm,
Abstract = {We show that a film of a suspension of polymer
grafted nanoparticles on a liquid substrate can be
employed to create two-dimensional nanostructures
with a remarkable variation in the pattern length
scales. The presented experiments also reveal the
emergence of concentration-dependent bimodal
patterns as well as re-entrant behaviour that
involves length scales due to dewetting and
compositional instabilities. The experimental
observations are explained through a gradient
dynamics model consisting of coupled evolution
equations for the height of the suspension film and
the concentration of polymer. Using a Flory-Huggins
free energy functional for the polymer solution, we
show in a linear stability analysis that the thin
film undergoes dewetting and/or compositional
instabilities depending on the concentration of the
polymer in the solution. We argue that the formation
via hierarchical self-assembly of various
functional nanostructures observed in different
systems can be explained as resulting from such an
interplay of instabilities.},
Author = {Sarika, C. K. and Tomar, G. and Basu, J. K. and Thiele, U.},
DOI = {10.1039/c5sm02108a},
File = {STBT2015sm.pdf:STBT2015sm.pdf:PDF},
Journal = {Soft Matter},
Pages = {8975--8980},
Title = {Bimodality of hierarchical self-assembly of polymeric nanoparticles},
Volume = {11},
Year = {2015}
}
@Article{WTGK2015mmnp,
Abstract = {We briefly review selected mathematical models that describe the dynamics of pat- tern formation phenomena in dip-coating and Langmuir-Blodgett transfer experiments, where solutions or suspensions are transferred onto a substrate producing patterned deposit layers with structure length from hundreds of nanometres to tens of micrometres. The models are presented with a focus on their gradient dynamics formulations that clearly shows how the dynamics is governed by particular free energy functionals and facilitates the comparison of the models. In particular, we include a discussion of models based on long-wave hydrodynamics as well as of more phenomenological models that focus on the pattern formation processes in such systems. The models and their relations are elucidated and examples of resulting patterns are discussed before we conclude with a discussion of implications of the gradient dynamics formulation and of some related open issues.},
Author = {Wilczek, M. and Tewes, W. B. H. and Gurevich, S. V. and K{\"o}pf, M. H. and Chi, L. and Thiele, U.},
DOI = {10.1051/mmnp/201510402},
Eeprint = {http://arxiv.org/abs/1502.03632},
File = {WTGK2015mmnp.pdf:WTGK2015mmnp.pdf:PDF;:WTGK2015mmnp.pdf:PDF},
Journal = {Math. Model. Nat. Phenom.},
Pages = {44--60},
Title = {Modelling Pattern Formation in Dip-Coating Experiments},
Volume = {10},
Year = {2015}
}
@Article{XuTQ2015jpcm,
Abstract = {In order to model the dynamics of thin films of mixtures, solutions, and suspensions, a thermodynamically consistent formulation is needed such that various coexisting dissipative processes with cross couplings can be correctly described in the presence of capillarity, wettability, and mixing effects. In the present work, we apply Onsager's variational principle to the formulation of thin film hydrodynamics for binary fluid mixtures. We first derive the dynamic equations in two spatial dimensions, one along the substrate and the other normal to the substrate. Then, using long-wave asymptotics, we derive the thin film equations in one spatial dimension along the substrate. This enables us to establish the connection between the present variational approach and the gradient dynamics formulation for thin films. It is shown that for the mobility matrix in the gradient dynamics description, Onsager's reciprocal symmetry is automatically preserved by the variational derivation. Furthermore, using local hydrodynamic variables, our variational approach is capable of introducing diffusive dissipation beyond the limit of dilute solute. Supplemented with a Flory-Huggins-type mixing free energy, our variational approach leads to a thin film model that treats solvent and solute in a symmetric manner. Our approach can be further generalized to include more complicated free energy and additional dissipative processes.},
Author = {Xu, X. and Thiele, U. and Qian, T.},
DOI = {10.1088/0953-8984/27/8/085005},
File = {XuTQ2015jpcm.pdf:XuTQ2015jpcm.pdf:PDF},
Journal = {J. Phys.: Condens. Matter},
Pages = {085005},
Title = {A Variational Approach to Thin Film Hydrodynamics of Binary Mixtures},
Volume = {27},
Year = {2015}
}
@Article{AWTK2014pre,
Abstract = {Using dynamical density functional theory we calculate the speed of solidification fronts advancing into a quenched two-dimensional model fluid of soft-core particles. We find that solidification fronts can advance via two different mechanisms, depending on the depth of the quench. For shallow quenches, the front propagation is via a nonlinear mechanism. For deep quenches, front propagation is governed by a linear mechanism and in this regime we are able to determine the front speed via a marginal stability analysis. We find that the density modulations generated behind the advancing front have a characteristic scale that differs from the wavelength of the density modulation in thermodynamic equilibrium, i.e., the spacing between the crystal planes in an equilibrium crystal. This leads to the subsequent development of disorder in the solids that are formed. In a one-component fluid, the particles are able to rearrange to form a well-ordered crystal, with few defects. However, solidification fronts in a binary mixture exhibiting crystalline phases with square and hexagonal ordering generate solids that are unable to rearrange after the passage of the solidification front and a significant amount of disorder remains in the system.},
Author = {Archer, A.J. and Walters, M.C. and Thiele, U. and Knobloch, E.},
DOI = {10.1103/PhysRevE.90.042404},
File = {AWTK2014pre.pdf:AWTK2014pre.pdf:PDF},
Journal = {Phys. Rev. E},
Pages = {042404},
Title = {Solidification in soft-core fluids: disordered solids from fast solidification fronts},
Volume = {90},
Year = {2014}
}
@Article{DWCD2014ccp,
Abstract = {We provide an overview of current techniques and
typical applications of numerical bifurcation
analysis in fluid dynamical problems. Many of these
problems are characterized by high-dimensional
dynamical systems which undergo transitions as
parameters are changed. The computation of the
critical conditions associated with these
transitions, popularly referred to as tipping
points, is important for understand- ing the
transition mechanisms. We describe the two basic
classes of methods of nu- merical bifurcation
analysis, which differ in the explicit or implicit
use of the Jacobian matrix of the dynamical
system. The numerical challenges involved in both
methods are mentioned and possible solutions to
current bottlenecks are given. To demonstrate that
numerical bifurcation techniques are not restricted
to relatively low-dimensional dynamical systems, we
provide several examples of the application of the
modern techniques to a diverse set of fluid
mechanical problems.},
Author = {Dijkstra, H. A. and Wubs, F. W. and Cliffe, A. K. and E. Doedel and Dragomirescu, I. F. and B. Eckhardt and Gelfgat, A. Y. and A. Hazel and V. Lucarini and Salinger, A. G. and Phipps, E. T. and J. Sanchez-Umbria and H. Schuttelaars and Tuckerman, L. S. and U. Thiele},
DOI = {10.4208/cicp.240912.180613a},
File = {DWCD2014ccp.pdf:DWCD2014ccp.pdf:PDF},
Journal = {Commun. Comput. Phys.},
Pages = {1--45},
Title = {Numerical Bifurcation Methods and their Application to Fluid Dynamics: {A}nalysis beyond Simulation},
Volume = {15},
Year = {2014}
}
@Article{GTLT2014prl,
Abstract = {When a plate is withdrawn from a liquid bath a coating layer is deposited whose thickness and homogeneity depend on the velocity and the wetting properties of the plate. Using a long-wave mesoscopic hydrodynamic description that incorporates wettability via a Derjaguin (disjoining) pressure we identify four qualitatively different dynamic transitions between microscopic and macroscopic coatings that are out-of-equilibrium equivalents of known equilibrium unbinding transitions. Namely, these are continuous and discontinuous dynamic wetting and emptying transitions. Several of their features have no equivalent at equilibrium.},
Author = {M. Galvagno and D. Tseluiko and Lopez, H. and U. Thiele},
DOI = {10.1103/PhysRevLett.112.137803},
Eprint = {http://arxiv.org/abs/1311.6994},
File = {GTLT2014prl.pdf:GTLT2014prl.pdf:PDF},
Journal = {Phys. Rev. Lett.},
Pages = {137803},
Title = {Continuous and discontinuous dynamic unbinding transitions in drawn film flow},
Volume = {112},
Year = {2014}
}
@Article{HuTA2014ajp,
Abstract = {Classical density functional theory (DFT) is a statistical mechanical theory for calculating the density profiles of the molecules in a liquid. It is widely used, for example, to study the density distribution of the molecules near a confining wall, the interfacial tension, wetting behavior, and many other properties of nonuniform liquids. DFT can, however, be somewhat daunting to students entering the field because of the many connections to other areas of liquid-state science that are required and used to develop the theories. Here, we give an introduction to some of the key ideas, based on a lattice-gas (Ising) model fluid. This approach builds on knowledge covered in most undergraduate statistical mechanics and thermodynamics courses, so students can quickly get to the stage of calculating density profiles, etc., for themselves. We derive a simple DFT for the lattice gas and present some typical results that can readily be calculated using the theory.},
Author = {Hughes, A. P. and Thiele, U. and Archer, A. J.},
DOI = {10.1119/1.4890823},
Eprint = {http://arxiv.org/abs/1311.1964},
File = {HuTA2014ajp.pdf:HuTA2014ajp.pdf:PDF},
Journal = {Am. J. Phys.},
Pages = {1119--1129},
Title = {An introduction to inhomogeneous liquids, density functional theory, and the wetting transition},
Volume = {82},
Year = {2014}
}
@Article{KoTh2014n,
Abstract = {We explore the bifurcation structure of a modified
Cahn-Hilliard equation that describes a system that
may undergo a first-order phase transition and is
kept permanently out of equilibrium by a lateral
driving. This forms a simple model, e.g., for the
deposition of stripe patterns of different phases of
surfactant molecules through Langmuir-Blodgett
transfer. Employing continuation techniques the
bifurcation structure is numerically investigated
using the non-dimensional transfer velocity as the
main control parameter. It is found that the snaking
structure of steady front states is intertwined with
a large number of branches of time-periodic
solutions that emerge from Hopf or period-doubling
bifurcations and end in global bifurcations (sniper
and homoclinic). Overall the bifurcation diagram has
a harp-like appearance. This is complemented by a
two-parameter study in non-dimensional transfer
velocity and domain size (as a measure of the
distance to the phase transition threshold) that
elucidates through which local and global
codimension 2 bifurcations the entire harp-like
structure emerges.},
Author = {K{\"o}pf, M. H. and Thiele, U.},
DOI = {10.1088/0951-7715/27/11/2711},
Eprint = {http://arxiv.org/abs/1405.2117},
File = {KoTh2014n.pdf:KoTh2014n.pdf:PDF},
Journal = {Nonlinearity},
Pages = {2711--2734},
Title = {Emergence of the bifurcation structure of a {L}angmuir-{B}lodgett transfer model},
Volume = {27},
Year = {2014}
}
@Article{PoTA2014pre,
Abstract = {There are two modes by which clusters of aggregating
particles can coalesce: The clusters can merge
either (i) by the Ostwald ripening process, in which
particles diffuse from one cluster to the other
while the cluster centers remain stationary, or (ii)
by means of a cluster translation mode, in which the
clusters move toward each other and join. To
understand in detail the interplay between these
different modes, we study a model system of hard
particles with an additional attraction between
them. The particles diffuse along narrow channels
with smooth or periodically corrugated walls, so
that the system may be treated as
one-dimensional. When the attraction between the
particles is strong enough, they aggregate to form
clusters. The channel potential influences whether
clusters can move easily or not through the system
and can prevent cluster motion. We use dynamical
density functional theory to study the dynamics of
the aggregation process, focusing in particular on
the coalescence of two equal-sized clusters. As long
as the particle hard-core diameter is nonzero, we
find that the coalescence process can be halted by a
sufficiently strong corrugation potential. The
period of the potential determines the size of the
final stable clusters. For the case of smooth
channel walls, we demonstrate that there is a
crossover in the dominance of the two different
coarsening modes, which depends on the strength of
the attraction between particles, the cluster sizes,
and the separation distance between clusters.},
Author = {A. Pototsky and Thiele, U. and Archer, A.J.},
DOI = {10.1103/PhysRevE.89.032144},
Eprint = {http://arxiv.org/abs/1401.7046},
File = {PoTA2014pre.pdf:PoTA2014pre.pdf:PDF},
Journal = {Phys. Rev. E},
Pages = {032144},
Title = {Coarsening modes of clusters of aggregating particles},
Urrl = {http://link.aps.org/doi/10.1103/PhysRevE.89.032144},
Volume = {89},
Year = {2014}
}
@Article{PoTS2014pre,
Abstract = {We consider a carpet of self-propelled particles at the liquid-gas interface of a liquid film on a solid substrate. The particles exert an excess pressure on the interface and also move along the interface while the swimming direction changes due to rotational diffusion. We study the intricate influence of these self-propelled insoluble surfactants on the stability of the film surface and show that depending on the strength of in-surface rotational diffusion and the absolute value of the in-surface swimming velocity, several characteristic instability modes can occur. In particular, rotational diffusion can either stabilize the film or induce instabilities of different character.},
Author = {A. Pototsky and U. Thiele and H. Stark},
DOI = {10.1103/PhysRevE.90.030401},
File = {PoTS2014pre.pdf:PoTS2014pre.pdf:PDF},
Journal = {Phys. Rev. E},
Pages = {030401(R)},
Title = {Stability of liquid films covered by a carpet of self-propelled surfactant particles},
Volume = {90},
Year = {2014}
}
@Article{TDGR2014l,
Abstract = {During the spreading of a liquid over a solid substrate, the contact line can stay pinned at sharp edges until the contact angle exceeds a critical value. At (or sufficiently near) equilibrium, this is known as Gibbs criterion. Here, we show both experimentally and theoretically that, for completely wetting volatile liquids, there also exists a dynamically-produced contribution to the critical angle for depinning, which increases with the evaporation rate. This suggests that one may introduce a simple modification of the Gibbs criterion for (de)pinning that accounts for the nonequilibrium effect of evaporation.},
Author = {Tsoumpas, Y. and Dehaeck, S. and Galvagno, M. and Rednikov, A. and Ottevaere, H. and Thiele, U. and Colinet, P.},
DOI = {10.1021/la502708f},
Eprint = {http://arxiv.org/abs/1410.6783},
File = {TDGR2014l.pdf:TDGR2014l.pdf:PDF},
Journal = {Langmuir},
Pages = {11847--11852},
Title = {Non Equilibrium Gibbs Criterion for Completely Wetting Volatile Liquids},
Volume = {30},
Year = {2014}
}
@Article{Thie2014acis,
Abstract = {When a simple or complex liquid recedes from a
smooth solid substrate it often leaves a homogeneous
or structured deposit behind. In the case of a
receding non-volatile pure liquid the deposit might
be a liquid film or an arrangement of droplets
depending on the receding speed of the meniscus and
the wetting properties of the system. For complex
liquids with volatile components as, e.g., polymer
solutions and particle or surfactant suspensions,
the deposit might be a homogeneous or structured
layer of solute with structures ranging from line
patterns that can be orthogonal or parallel to the
receding contact line via hexagonal or square
arrangements of drops to complicated hierarchical
structures. We review a number of recent experiments
and modelling approaches with a particular focus on
mesoscopic hydrodynamic long-wave models. The
conclusion highlights open question and speculates
about future developments.},
Author = {Thiele, U.},
DOI = {10.1016/j.cis.2013.11.002},
Eprint = {http://arxiv.org/abs/1307.0958},
File = {Thie2014acis.pdf:Thie2014acis.pdf:PDF},
Journal = {Adv. Colloid Interface Sci.},
Pages = {399--413},
Title = {Patterned deposition at moving contact line},
Volume = {206},
Year = {2014}
}
@Article{TsGT2014epje,
Abstract = {A liquid film is studied that is deposited onto a flat plate that is inclined at a constant angle to the horizontal and is extracted from a liquid bath at a constant speed. We analyse steady-state solutions of a long-wave evolution equation for the film thickness. Using centre manifold theory, we first obtain an asymptotic expansion of solutions in the bath region. The presence of an additional temperature gradient along the plate that induces a Marangoni shear stress significantly changes these expansions and leads to the presence of logarithmic terms that are absent otherwise. Next, we numerically obtain steady solutions and analyse their behaviour as the plate velocity is changed. We observe that the bifurcation curve exhibits collapsed (or exponential) heteroclinic snaking when the plate inclination angle is above a certain critical value. Otherwise, the bifurcation curve is monotonic. The steady profiles along these curves are charac- terised by a foot-like structure that is formed close to the meniscus and is preceded by a thin precursor film further up the plate. The length of the foot increases along the bifurcation curve. Finally, we prove with a Shilnikov-type method that the snaking behaviour of the bifurcation curves is caused by the existence of an infinite number of heteroclinic orbits close to a heteroclinic chain that connects in an appropriate three-dimensional phase space the fixed point corresponding to the precursor film with the fixed point corresponding to the foot and then with the fixed point corresponding to the bath.},
Author = {D. Tseluiko and M. Galvagno and U. Thiele},
DOI = {10.1140/epje/i2014-14033-2},
Eprint = {http://arxiv.org/abs/1307.4618},
File = {TsGT2014epje.pdf:TsGT2014epje.pdf:PDF},
Journal = {Eur. Phys. J. E},
Pages = {33},
Title = {Collapsed heteroclinic snaking near a heteroclinic chain in dragged meniscus problems},
Volume = {37},
Year = {2014}
}
@Article{AOAT2013l,
Abstract = {The stability of thin
poly(methyl-methacrylate) (PMMA) films of low
molecular weight on a solid substrate is controlled
by the areal coverage of gold nanoparticles (NPs)
present at the air-polymer interface. As the polymer
becomes liquid the Au NPs are free to diffuse,
coalesce, and aggregate while the polymer film can
change its morphology through viscous flow. These
processes lead at the same time to the formation of
a fractal network of Au NPs and to the development
of spinodal instabilities of the free surface of the
polymer films. For thinner films a single wavelength
is observed, while for thicker films two wavelengths
compete. With continued heating the aggregation
process results in a decrease in coverage, the
networks evolve into disordered particle assemblies,
while the polymer films flatten again. The
disordering occurs first on the smallest scales and
coincides (in thicker films) with the disappearance
of the smaller wavelength. The subsequent
disordering on larger scales causes the films to
flatten.},
Author = {G. Amarandei and O'Dwyer, C and A. Arshak and U. Thiele and U. Steiner and D. Corcoran},
DOI = {10.1021/la400659q},
File = {AOAT2013l.pdf:AOAT2013l.pdf:PDF},
Journal = {Langmuir},
Pages = {6706--6714},
Title = {The effect of {Au} nanoparticles spatial distribution on stability of thin polymer films},
Volume = {29},
Year = {2013}
}
@Article{BrMT2013epjst,
Abstract = {We present 2D steady concentration profiles of
confined lay- ers of off-critical polymer
blends. The layer rests on a solid substrate and has
a flat free surface due to very high surface
tension. The profiles correspond to non-linear
steady solutions of the Cahn-Hilliard equation in a
rectangular domain. The free polymer-gas interface
is considered to be sharp, while the internal
interfaces are diffuse. We explore the rich solution
structure (including laterally structured layers,
stratified lay- ers, checkerboard structures,
oblique states and droplets) as a function of mean
concentration.},
Author = {Bribesh, F. and Madruga, S. and Thiele, U.},
DOI = {10.1140/epjst/e2013-01775-5},
File = {BrMT2013epjst.pdf:BrMT2013epjst.pdf:PDF},
Journal = {Eur. Phys. J. Special Topics},
Pages = {3--12},
Title = {Two-dimensional steady states in off-critical mixtures with high interface tension},
Volume = {219},
Year = {2013}
}
@Article{JoTh2013pj,
Abstract = {In gesch{\"u}ttelten Fl{\"u}ssigkeiten mit freien
Oberfl{\"a}chen treten interessante Effekte auf, zum
Beispiel dynamische Oberfl{\"a}chenmuster und
gerichteter Transport. Tropfen k{\"o}nnen auf der
Oberfl{\"a}che einer gesch{\"u}ttelten Fl{\"u}ssigkeit h{\"u}pfend
mit selbst erzeugten Oberfl{\"a}chenwellen wechselwirken
und sich dadurch gerichtet bewegen, oder sie
klettern eine gesch{\"u}ttelte geneigte feste Oberfl{\"a}che
hinauf. Dieser gerichtete Tropfentransport l{\"a}sst
sich im letzteren Fall durch ein Minimalmodell
verstehen, das einer hydrodynamischen Realisierung
des Ratschenprinzips entspricht.},
Author = {K. John and U. Thiele},
File = {JoTh2013pj.pdf:JoTh2013pj.pdf:PDF},
Journal = {Physik Journal},
Number = {2},
Pages = {33--38},
Title = {Kletternde Tropfen},
Urrl = {http://www.pro-physik.de/details/physikjournalArticle/4270771/Kletternde_Tropfen.html},
Volume = {12},
Year = {2013}
}
@Article{LCAK2013pf,
Abstract = {We discuss the long-wave hydrodynamic model for a
thin film of nematic liquid crystal in the limit of
strong anchoring at the free surface and at the
substrate. We rigorously clarify how the elastic
energy enters the evolution equation for the film
thickness in order to provide a solid basis for
further investigation: several conflicting models
exist in the literature that predict qualitatively
different behaviour. We consolidate the various
approaches and show that the long-wave model derived
through an asymptotic expansion of the full
nemato-hydrodynamic equations with consistent
boundary conditions agrees with the model one
obtains by employing a thermodynamically motivated
gradient dynamics formulation based on an underlying
free energy functional. As a result, we find that in
the case of strong anchoring the elastic distortion
energy is always stabilising. To support the
discussion in the main part of the paper, an
appendix gives the full derivation of the evolution
equation for the film thickness via asymptotic
expansion.},
Author = {Lin, T.-S. and Cummings, L. J. and Archer, A. J. and Kondic, L. and Thiele, U.},
DOI = {10.1063/1.4816508},
Eprint = {http://arxiv.org/abs/1301.4110},
File = {LCAK2013pf.pdf:LCAK2013pf.pdf:PDF},
Journal = {Phys. Fluids},
Pages = {082102},
Title = {Note on the hydrodynamic description of thin nematic films: strong anchoring model},
Volume = {25},
Year = {2013}
}
@Article{LKTC2013jfm,
Abstract = {We study spreading dynamics of nematic liquid crystal droplets within the framework of the long-wave approximation. A fourth-order nonlinear parabolic partial differential equation governing the free surface evolution is derived. The influence of elastic distortion energy and of imposed anchoring variations at the substrate are explored through linear stability analysis and scaling arguments, which yield useful insight and predictions for the behaviour of spreading droplets. This behaviour is captured by fully nonlinear time-dependent simulations of three-dimensional droplets spreading in the presence of anchoring variations that model simple defects in the nematic orientation at the substrate.
},
Author = {Lin, T.-S. and Kondic, L. and Thiele, U. and Cummings, L. J.},
DOI = {10.1017/jfm.2013.297},
Eprint = {http://arxiv.org/abs/1303.5267},
File = {LKTC2013jfm.pdf:LKTC2013jfm.pdf:PDF},
Journal = {J. Fluid Mech.},
Pages = {214--230},
Title = {Modelling spreading dynamics of nematic liquid crystals in three spatial dimensions},
Volume = {729},
Year = {2013}
}
@Article{TARG2013pre,
Abstract = {The conserved Swift-Hohenberg equation with cubic
nonlinearity provides the simplest microscopic
description of the thermodynamic transition from a
fluid state to a crystalline state. The resulting
phase field crystal model describes a variety of
spatially localized structures, in addition to
different spatially extended periodic
structures. The location of these structures in the
temperature versus mean order parameter plane is
determined using a combination of numerical
continuation in one dimension and direct numerical
simulation in two and three dimensions. Localized
states are found in the region of thermodynamic
coexistence between the homogeneous and structured
phases, and may lie outside of the binodal for these
states. The results are related to the phenomenon of
slanted snaking but take the form of standard
homoclinic snaking when the mean order parameter is
plotted as a function of the chemical potential, and
are expected to carry over to related models with a
conserved order parameter.},
Author = {Thiele, U. and Archer, A. J. and Robbins, M. J. and Gomez, H. and Knobloch, E.},
DOI = {10.1103/PhysRevE.87.042915},
Eprint = {http://arxiv.org/abs/1301.4472},
File = {TARG2013pre.pdf:TARG2013pre.pdf:PDF},
Journal = {Phys. Rev. E},
Pages = {042915},
Title = {Localized states in the conserved Swift-Hohenberg equation with cubic nonlinearity},
Volume = {87},
Year = {2013}
}
@Article{ThTL2013prl,
Abstract = {A thermodynamically consistent gradient dynamics
model for the evolution of thin layers of liquid
mixtures, solutions, and suspensions on solid
substrates is presented which is based on a
film-height- and mean-concentration-dependent free
energy functional. It is able to describe a large
variety of structuring processes, including coupled
dewetting and decomposition processes. As an
example, the model is employed to investigate the
dewetting of thin films of liquid mixtures and
suspensions under the influence of effective
long-range van der Waals forces that depend on
solute concentration. The occurring fluxes are
discussed, and it is shown that spinodal dewetting
may be triggered through the coupling of film height
and concentration fluctuations. Fully nonlinear
calculations provide the time evolution and
resulting steady film height and concentration
profiles.},
Author = {Thiele, U. and Todorova, D. V. and Lopez, H.},
DOI = {10.1103/PhysRevLett.111.117801},
Eprint = {http://arxiv.org/abs/1305.3425},
File = {ThTL2013prl.pdf:ThTL2013prl.pdf:PDF},
Journal = {Phys. Rev. Lett.},
Pages = {117801},
Title = {Gradient dynamics description for films of mixtures and suspensions: Dewetting triggered by coupled film height and concentration fluctuations},
Volume = {111},
Year = {2013}
}
@Article{TMTT2013jcp,
Abstract = {We study equilibrium properties of polymer films and
droplets on a solid substrate employing
particle-based simulation techniques (molecular
dynamics) and a continuum description. Parameter-
passing techniques are explored that facilitate a
detailed comparison of the two models. In
particular, the liquid-vapor, solid-liquid, and
solid-vapor interface tensions, and the Derjaguin or
disjoining pressure are determined by molecular
dynamics simulations. This information is then
introduced into continuum descriptions accounting
for (i) the full curvature and (ii) a long-wave
approximation of the curvature (thin film model). A
comparison of the dependence of the contact angle on
droplet size indicates that the theories agree well
if the contact angles are defined in a compatible
manner.},
Author = {Tretyakov, N. and M\"{u}ller, M. and Todorova, D. and Thiele, U.},
DOI = {10.1063/1.4790581},
Eprint = {http://arxiv.org/abs/1209.1008},
File = {TMTT2013jcp.pdf:TMTT2013jcp.pdf:PDF},
Journal = {J. Chem. Phys.},
Pages = {064905},
Title = {Parameter passing between Molecular Dynamics and continuum models for droplets on solid substrates: {T}he static case},
Urrl = {http://jcp.aip.org/resource/1/jcpsa6/v138/i6/p064905_s1},
Volume = {138},
Year = {2013}
}
@Article{TsBT2013ijam,
Abstract = {We consider self-similar solutions related to rupture of thin liquid films on a solid substrate that evolve solely under the stabilizing influence of surface tension and the destabilizing influence of effective van der Waals interactions between the free surface of the film and the substrate. Such solutions have been previously analysed in the literature and various numerical approaches to obtain such solutions have been proposed. Such approaches are based either on shooting or finite-difference schemes and require well-chosen initial guesses for solutions. We propose an alternative numerical method, which is based on a homotopy approach and continuation techniques and allows one to reach self-similar solutions from analytically known small-amplitude steady solutions of the related thin-film equation. We argue that this method is more robust than previously proposed methods and does not require initial guesses to obtain solutions. Although the present study focuses on the particular case of self-similar solutions related to planar rupture that have square-root far-field behaviour, our approach can also be used to obtain planar solutions having a different far-field behaviour and radially symmetric self-similar solutions for the considered thin-film equation. We expect the approach to be also valid for other equations of similar type that show a subcritical primary bifurcation and finite-time singularities.},
Author = {D. Tseluiko and J. Baxter and Thiele, U.},
DOI = {10.1093/imamat/hxt021},
File = {TsBT2013ijam.pdf:TsBT2013ijam.pdf:PDF},
Journal = {IMA J. Appl. Math.},
Pages = {762--776},
Title = {A homotopy continuation approach for analysing finite-time singularities in thin liquid films},
Volume = {78},
Year = {2013}
}
@Article{ABCO2012sm,
Abstract = {Strong electric fields produce forces that can
overcome the surface tension in thin liquid polymer
films and in this way induce an instability of the
free surface of the film, that triggers the
formation of structures on a micrometer length
scale. Here, we study experimentally a
polymer-air-polymer system for several combinations
of polymer films. These results are accompanied by
theoretical considerations based on coupled
long-wave time evolution equations for the two free
surface profiles. The linear stability and nonlinear
time evolution are investigated and compared to the
experimental findings. The prediction that the
instability always evolves through a mirror mode
that couples the two surfaces in an anti-phase
manner agrees well with the experimental
results. The model describes well the linear (early
stage) evolution of the instability. In the
non-linear (later stage) evolution, topographical
differences in the instability pattern occur if the
mobilities of the two layers significantly differ
and an unpredicted acceleration of growth is seen in
thinner less mobile films. Possible reasons for the
mismatch are discussed.},
Author = {G. Amarandei and P. Beltrame and I. Clancy and O'Dwyer, C and A. Arshak and U. Steiner and D. Corcoran and U. Thiele},
DOI = {10.1039/c2sm25273b},
File = {ABCO2012sm.pdf:ABCO2012sm.pdf:PDF},
Journal = {Soft Matter},
Pages = {6333--6349},
Title = {Pattern formation induced by an electric field in a polymer-air-polymer thin film system},
Volume = {8},
Year = {2012}
}
@Article{ARTK2012pre,
URL = {http://link.aps.org/doi/10.1103/PhysRevE.86.031603},
Abstract = {We determine the speed of a crystallization (or,
more generally, a solidification) front as it
advances into the uniform liquid phase after the
system has been quenched into the crystalline region
of the phase diagram. We calculate the front speed
by assuming a dynamical density functional theory
(DDFT) model for the system and applying a marginal
stability criterion. Our results also apply to phase
field crystal (PFC) models of solidification. As the
solidification front advances into the unstable
liquid phase, the density profile behind the
advancing front develops density modulations and the
wavelength of these modulations is a dynamically
chosen quantity. For shallow quenches, the selected
wavelength is precisely that of the crystalline
phase and so well-ordered crystalline states are
formed. However, when the system is deeply quenched,
we find that this wavelength can be quite different
from that of the crystal, so the solidification
front naturally generates disorder in the
system. Significant rearrangement and aging must
subsequently occur for the system to form the
regular well-ordered crystal that corresponds to the
free energy minimum. Additional disorder is
introduced whenever a front develops from random
initial conditions. We illustrate these findings
with simulation results obtained using the PFC
model},
Author = {Archer, A. J. and Robbins, M. J. and Thiele, U. and Knobloch, E.},
DOI = {10.1103/PhysRevE.86.031603},
Eprint = {http://arxiv.org/abs/1206.0902},
File = {ARTK2012pre.pdf:ARTK2012pre.pdf:PDF},
Issue = {3},
Journal = {Phys. Rev. E},
Month = sep,
Numpages = {13},
Pages = {031603},
Publisher = {American Physical Society},
Title = {Solidification fronts in supercooled liquids: {H}ow rapid fronts can lead to disordered glassy solids},
Volume = {86},
Year = {2012}
}
@Article{BrFT2012pf,
Abstract = {We study two-dimensional steady concentration and
film thickness profiles for isothermal free surface
films of a binary liquid mixture on a solid
substrate employ- ing model-H that couples the
diffusive transport of the components of the mixture
(convective Cahn-Hilliard equation) and the
transport of momentum (Navier-Stokes- Korteweg
equations). The analysis is based on minimising the
underlying free energy equivalent to solving the
static limit of model-H. Additionally, the linear
stability (in time) of relevant layered films is
analyzed. This allows for a comparison of the
position of certain branching points in the
bifurcation diagrams of steady solutions with the
value predicted as onset of a linear
instability. Results are presented for the cases of
(i) a flat film without energetic bias at the free
surface, (ii) a flat film with energetic bias, (iii)
a height-modulated film without energetic bias, and
(iv) a height-modulated film with energetic bias. In
all cases we discuss symmetries of the various
steady solutions allowing us to order them and to
infer properties of solution branches and relations
between them.},
Author = {Bribesh, F. A. M. and Frastia, L. and Thiele, U.},
DOI = {10.1063/1.4727888},
File = {BrFT2012pf.pdf:BrFT2012pf.pdf:PDF},
Journal = {Phys. Fluids},
Pages = {062109},
Title = {Decomposition driven interface evolution for layers of binary mixtures: III. Two-dimensional steady film states},
Volume = {24},
Year = {2012}
}
@Article{FrAT2012sm,
Abstract = {When a film of a liquid suspension of nanoparticles
or a polymer solution is deposited on a surface, it
may dewet from the surface and as the solvent
evaporates the solute particles/polymer can be
deposited on the surface in regular line
patterns. In this paper we explore a hydrodynamic
model for the process that is based on a long-wave
approximation that predicts the deposition of
irregular and regular line patterns. This is due to
a self-organised pinning-depinning cycle that
resembles a stick-slip motion of the contact
line. We present a detailed analysis of how the line
pattern properties depend on quantities such as the
evaporation rate, the solute concentration, the
P{\~{A}}{\copyright}clet number, the chemical potential of the ambient
vapour, the disjoining pressure, and the intrinsic
viscosity. The results are related to several
experiments and to depinning transitions in other
soft matter systems.},
Author = {Frastia, L. and Archer, A. J. and Thiele, U.},
DOI = {10.1039/C2SM26574E},
Eeprint = {http://arxiv.org/abs/1208.6127},
File = {FrAT2012sm.pdf:FrAT2012sm.pdf:PDF},
Journal = {Soft Matter},
Pages = {11363--11386},
Title = {Modelling the formation of structured deposits at receding contact lines of evaporating solutions and suspensions},
Volume = {8},
Year = {2012}
}
@Article{HTHB2012el,
Abstract = {We study the depinning and subsequent motion of
two-dimensional droplets with large contact angles
that are driven by a body force on flat substrates
decorated with a sinusoidal wettability pattern. To
this end, we solve the Stokes equation employing a
boundary element method. At the substrate a Navier
slip condition and a spatially varying microscopic
contact angle are imposed. Depending on the
substrate properties, we observe a range of driving
forces where resting and periodically moving
droplets are found, even though inertial effects are
neglected. This is possible in the considered
overdamped regime because additional energy is
stored in the non-equilibrium configuration of the
droplet interfaces. Finally, we present the
dependence of the driving at de- and repinning on
wettability contrast and slip length, complemented
by a bifurcation analysis of pinned-droplet
configurations.},
Author = {Herde, D. and Thiele, U. and Herminghaus, S. and Brinkmann, M.},
DOI = {10.1209/0295-5075/100/16002},
File = {HTHB2012el.pdf:HTHB2012el.pdf:PDF},
Journal = {Europhys. Lett.},
Pages = {16002},
Title = {Driven large contact angle droplets on chemically heterogeneous substrates},
Volume = {100},
Year = {2012}
}
@Article{KGFT2012njp,
Abstract = {The formation of regular stripe patterns during the
transfer of surfactant monolayers from water
surfaces onto moving solid substrates can be
understood as a phase decomposition process under
the influence of the effective molecular interaction
between the substrate and the monolayer, also called
substrate-mediated condensation (SMC). To describe
this phenomenon, we propose a reduced model based on
an amended Cahn-Hilliard equation. A combination of
numerical simulations and continuation methods is
employed to investigate stationary and time-periodic
solutions of the model and to determine the
resulting bifurcation diagram. The onset of
spatiotemporal pattern formation is found to result
from a homoclinic and a Hopf bifurcation at small
and large substrate speeds, respectively. The
critical velocity corresponding to the Hopf
bifurcation can be calculated by means of the
marginal stability criterion for pattern formation
behind propagating fronts. In the regime of low
transfer velocities, the stationary solutions
exhibit snaking behavior.},
Author = {K{\"o}pf, M. H. and Gurevich, S. V. and Friedrich, R. and Thiele, U.},
DOI = {10.1088/1367-2630/14/2/023016},
File = {KGFT2012njp.pdf:KGFT2012njp.pdf:PDF},
Journal = {New J. Phys.},
Pages = {023016},
Title = {Substrate-mediated pattern formation in monolayer transfer: a reduced model},
Volume = {14},
Year = {2012}
}
@Article{RATK2012pre,
Abstract = {A modified phase-field crystal model in which the
free energy may be minimized by an order parameter
profile having isolated bumps is investigated. The
phase diagram is calculated in one and two
dimensions and we locate the regions where modulated
and uniform phases are formed and also regions where
localized states are formed. We investigate the
effectiveness of the phase-field crystal model for
describing fluids and crystals with defects. We
further consider a two-component model and elucidate
how the structure transforms from hexagonal
crystalline ordering to square ordering as the
concentration changes. Our conclusion contains a
discussion of possible interpretations of the order
parameter field.},
Author = {Robbins, M. J. and Archer, A. J. and Thiele, U. and Knobloch, E.},
DOI = {10.1103/PhysRevE.85.061408},
Eprint = {http://arxiv.org/abs/1112.2074},
File = {RATK2012pre.pdf:RATK2012pre.pdf:PDF},
Journal = {Phys. Rev. E},
Pages = {061408},
Title = {Modelling fluids and crystals using a two-component modified phase field crystal model},
Volume = {85},
Year = {2012}
}
@Article{ThAP2012pf,
Abstract = {In this paper, we propose several models that
describe the dynamics of liquid films which are
covered by a high concentration layer of insoluble
surfactant. First, we briefly review the "classical"
hydrodynamic form of the coupled evolution equations
for the film height and surfactant concentration
that are well established for small
concentrations. Then we re-formulate the basic model
as a gradient dynamics based on an underlying free
energy functional that accounts for wettability and
capillarity. Based on this re-formulation in the
framework of nonequilibrium thermodynamics, we
propose extensions of the basic hydrodynamic model
that account for (i) nonlinear equations of state,
(ii) surfactant-dependent wettability, (iii)
surfactant phase transi- tions, and (iv)
substrate-mediated condensation. In passing, we
discuss important differences to most of the models
found in the literature.},
Author = {Thiele, U. and Archer, A. J. and Plapp, M.},
DOI = {10.1063/1.4758476},
Eprint = {http://arxiv.org/abs/1202.1688},
File = {ThAP2012pf.pdf:ThAP2012pf.pdf:PDF},
Journal = {Phys. Fluids},
Pages = {102107},
Title = {Thermodynamically consistent description of the hydrodynamics of free surfaces covered by insoluble surfactants of high concentration},
Volume = {24},
Year = {2012}
}
@Misc{Thie2012b,
Note = {Set of Auto tutorials and ready-to-run files for sitting and sliding drop solutions of thin film equations. To be obtained from u.thiele{\@}lboro.ac.uk.},
Author = {Thiele, U.},
Title = {Auto tutorial for thin film equations},
Year = {2012}
}
@InBook{Thie2012chapter,
URL = {https://doi.org/10.1007/978-3-7091-1227-4_3},
Abstract = {We provide a brief account of recent studies of dewetting films of simple and some complex liquids. First, we review basic models for dewetting onelayer films of simple liquids as they are often employed as reference case for studies of simple liquids in more complex situations or of complex liquids. Then we discuss films of binary mixtures that may undergo dewetting and decomposition processes in parallel, assuming that the films first decompose into stratified (layered) films before they evolve lateral structures. Such a setting is described employing a longwave sharpinterface two-layer model. We also use a onedomain diffuse interface model to analyse the process. After describing the linear stability of stratified films in both cases we lay out some advantages and disadvantages of the two models. We conclude by mentioning some other cases of films of complex liquids, providing references for further study and discussing future challenges.},
Address = {Vienna},
Author = {U. Thiele},
Booktitle = {Multiphase Microfluidics: {T}he Diffuse Interface Model},
DOI = {10.1007/978-3-7091-1227-4_3},
Editor = {R. Mauri},
ISBN = {3709112265},
Pages = {93--127},
Publisher = {Springer Vienna},
Title = {Dewetting and decomposing films of simple and complex liquids},
Year = {2012}
}
@Article{ToTP2012jem,
Abstract = {We discuss a thin film evolution equation for a
wetting evaporating liquid on a smooth solid
substrate. The model is valid for slowly evaporating
small sessile droplets when thermal effects are
insignificant, while wettability and capillarity
play a major role. The model is first employed to
study steady evaporating drops that are fed locally
through the substrate. An asymptotic analysis
focuses on the precursor film and the transition
region towards the bulk drop and a numerical
continuation of steady drops determines their fully
non-linear profiles. Following this, we study the
time evolution of freely evaporating drops without
influx for several initial drop shapes. As a result
we find that drops initially spread if their initial
contact angle is larger than the apparent contact
angle of large steady evaporating drops with
influx. Otherwise they recede right from the
beginning.},
Author = {Todorova, D. and Thiele, U. and Pismen, L. M.},
DOI = {10.1007/s10665-011-9485-1},
File = {ToTP2012jem.pdf:ToTP2012jem.pdf:PDF},
Journal = {J. Eng. Math.},
Pages = {17--30},
Title = {The relation of steady evaporating drops fed by an influx and freely evaporating drops},
Volume = {73},
Year = {2012}
}
@Article{BKHT2011pre,
Abstract = {Depinning of two-dimensional liquid ridges and
three-dimensional drops on an inclined substrate is
studied within the lubrication approximation. The
structures are pinned to wetting heterogeneities
arising from variations of the strength of the
short-range contribution to the disjoining
pressure. The case of a periodic array of
hydrophobic stripes transverse to the slope is
studied in detail using a combination of direct
numerical simulation and branch-following
techniques. Under appropriate conditions the ridges
may either depin and slide downslope as the slope is
increased, or first break up into drops via a
transverse instability, prior to depinning. The
different transition scenarios are examined together
with the stability properties of the different
possible states of the system.},
Author = {Beltrame, P. and Knobloch, E. and H{\"a}nggi, P. and Thiele, U.},
DOI = {10.1103/PhysRevE.83.016305},
File = {BKHT2011pre.pdf:BKHT2011pre.pdf:PDF},
Journal = {Phys. Rev. E},
Pages = {016305},
Title = {{Rayleigh} and depinning instabilities of forced liquid ridges on heterogeneous substrates},
Volume = {83},
Year = {2011}
}
@Article{FrAT2011prl,
Abstract = {We describe the formation of deposition patterns that are observed in many different experiments where a three-phase contact line of a volatile nanoparticle suspension or polymer solution recedes. A dynamical model based on a long-wave approximation predicts the deposition of irregular and regular line patterns due to self-organized pinning-depinning cycles corresponding to a stick-slip motion of the contact line. We analyze how the line pattern properties depend on the evaporation rate and solute concentration.},
Author = {Frastia, L. and Archer, A. J. and Thiele, U.},
DOI = {10.1103/PhysRevLett.106.077801},
Eeprint = {http://arxiv.org/abs/1008.4334},
File = {FrAT2011prl.pdf:FrAT2011prl.pdf:PDF},
Journal = {Phys. Rev. Lett.},
Numpages = {4},
Pages = {077801},
Title = {Dynamical model for the formation of patterned deposits at receding contact lines},
Urrl = {http://link.aps.org/doi/10.1103/PhysRevLett.106.077801},
Volume = {106},
Year = {2011}
}
@Article{FrTP2011mmnp,
Abstract = {We determine the steady-state structures that result
from liquid-liquid demixing in a free surface film
of binary liquid on a solid substrate. The
considered model corresponds to the static limit of
the diffuse interface theory describing the phase
separation process for a binary liquid (model-H),
when supplemented by boundary conditions at the free
surface and taking the influence of the solid
substrate into account. The resulting variational
problem is numerically solved employing a Finite
Element Method on an adaptive grid. The developed
numerical scheme allows us to obtain the coupled
steady-state film thickness profile and the
concentration profile inside the film. As an example
we determine steady state profiles for a
reflection-symmetric two-dimensional droplet for
various surface tensions of the film and various
preferential attraction strength of one component to
the substrate. We discuss the relation of the
results of the present diffuse interface theory to
the sharp interface limit and determine the
effective interface tension of the diffuse interface
by several means.},
Author = {L. Frastia and U. Thiele and Pismen, L. M.},
DOI = {10.1051/mmnp/20116104},
File = {FrTP2011mmnp.pdf:FrTP2011mmnp.pdf:PDF},
Journal = {Math. Model. Nat. Phenom.},
Pages = {62--86},
Title = {Determination of the thickness and composition profiles for a film of binary mixture on a solid substrate},
Volume = {6},
Year = {2011}
}
@Article{KaTh2011epjst,
Author = {Kalliadasis, S. and Thiele, U.},
DOI = {10.1140/epjst/e2011-01458-3},
File = {KaTh11.pdf:KaTh2011epjst.pdf:PDF},
Journal = {Eur. Phys. J. Special Topics},
Pages = {199--200},
Title = {Dynamics of drops and films on heterogeneous substrates},
Volume = {197},
Year = {2011}
}
@Article{MaTh2011epjst,
Author = {Madruga, S. and Thiele, U.},
DOI = {10.1140/epjst/e2011-01364-8},
File = {MaTh11.pdf:MaTh2011epjst.pdf:PDF},
Journal = {Eur. Phys. J. Special Topics},
Pages = {101--108},
Title = {Convective instabilities in films of binary mixtures},
Volume = {192},
Year = {2011}
}
@Article{PAST2011pre,
Abstract = {We consider the unidirectional particle transport in
a suspension of colloidal particles which interact
with each other via a pair potential having a
hard-core repulsion plus an attractive tail. The
colloids are confined within a long narrow channel
and are driven along by a dc or an ac external
potential. In addition, the walls of the channel
interact with the particles via a ratchetlike
periodic potential. We use dynamical density
functional theory to compute the average particle
current. In the case of dc drive, we show that as
the attraction strength between the colloids is
increased beyond a critical value, the stationary
density distribution of the particles loses its
stability leading to depinning and a time-dependent
density profile. Attraction induced symmetry
breaking gives rise to the coexistence of stable
stationary density profiles with different spatial
periods and time-periodic density profiles, each
characterized by different values for the particle
current.},
Author = {A. Pototsky and Archer, A. J. and Savel'ev, S. E. and U. Thiele and F. Marchesoni},
DOI = {10.1103/PhysRevE.83.061401},
Eprint = {http://arxiv.org/abs/1103.2871},
File = {PAST2011pre.pdf:PAST2011pre.pdf:PDF},
Journal = {Phys. Rev. E},
Pages = {061401},
Title = {Ratcheting of driven attracting colloidal particles: {T}emporal density oscillations and current multiplicity},
Volume = {83},
Year = {2011}
}
@Article{RoAT2011jpcm,
Abstract = {Recent experiments have shown that various
structures may be formed during the evaporative
dewetting of thin films of colloidal
suspensions. Nanoparticle deposits of strongly
branched -flower-like-, labyrinthine and network
structures are observed. They are caused by the
different transport processes and the rich phase
behaviour of the system. We develop a model for the
system, based on a dynamical density functional
theory, which reproduces these structures. The model
is employed to determine the influences of the
solvent evaporation and of the diffusion of the
colloidal particles and of the liquid over the
surface. Finally, we investigate the conditions
needed for liquid-particle phase separation to
occur and discuss its effect on the self-organized
nanostructures.},
Author = {Robbins, M. J. and Archer, A. J. and Thiele, U. },
DOI = {10.1088/0953-8984/23/41/415102},
Eprint = {http://arxiv.org/abs/1106.4467},
File = {RoAT2011jpcm.pdf:RoAT2011jpcm.pdf:PDF},
Journal = {J. Phys.: Condens. Matter},
Numpages = {18},
Pages = {415102},
Title = {Modelling the evaporation of thin films of colloidal suspensions using Dynamical Density Functional Theory},
Volume = {23},
Year = {2011}
}
@Article{Thie2011epjst,
Abstract = {This note discusses how one may further develop thin
film evolution equations for solutions and
suspensions. First, we review the time evolution
equation of a film or drop of simple liquid under
the sole influence of wettability and capillarity
and its formulation as a gradient dynamics. Second,
we introduce such a gradient dynamics for a film of
suspension or solution and show that it is
equivalent to thin film equa- tions in the
literature. Finally, the new formulation is used to
discuss extensions towards solute
molecules/particles with net attractive in-
teractions, decomposing solute-solvent systems and a
solute-dependent wettability.},
Author = {Thiele, U.},
DOI = {10.1140/epjst/e2011-01462-7},
File = {Thie2011epjst.pdf:Thie2011epjst.pdf:PDF},
Journal = {Eur. Phys. J. Special Topics},
Pages = {213--220},
Title = {Note on thin film equations for solutions and suspensions},
Volume = {197},
Year = {2011}
}
@Article{Thie2011epjstb,
Author = {Thiele, U.},
DOI = {10.1140/epjst/e2011-01438-7},
File = {Thie11d.pdf:Thie2011epjstb.pdf:PDF},
Journal = {Eur. Phys. J. Special Topics},
Pages = {67--71},
Title = {Thoughts on mesoscopic continuum models},
Volume = {197},
Year = {2011}
}
@Article{Thie2011jfm,
Abstract = {We discuss the analogy of the behaviour of films and drops of liquid on a rotating horizontal cylinder on the one hand and substrates with regular one-dimensional wettability patterns on the other hand. On the basis of the similarity between the respective governing long-wave equations, we show that a drop of partially wetting liquid on a rotating cylinder undergoes a depinning transition when the rotation speed is increased. The transition occurs via a sniper bifurcation, as in a recently described scenario for drops depinning on heterogeneous substrates.},
Author = {Thiele, U.},
DOI = {10.1017/S0022112010005483},
Eeprint = {http://arxiv.org/abs/1010.2920},
File = {Thie2011jfm.pdf:Thie2011jfm.pdf:PDF},
Journal = {J. Fluid Mech.},
Pages = {121--136},
Title = {On the depinning of a drop of partially wetting liquid on a rotating cylinder},
Volume = {671},
Year = {2011}
}
@Article{ArRT2010pre,
Abstract = {Recent experiments have shown that the striking
structure formation in dewetting films of
evaporating colloidal nanoparticle suspensions
occurs in an ultrathin ''postcursor'' layer that is
left behind by a mesoscopic dewetting front. Various
phase change and transport processes occur in the
postcursor layer that may lead to nanoparticle
deposits in the form of labyrinthine, network, or
strongly branched ''finger'' structures. We develop a
versatile dynamical density functional theory to
model this system which captures all these
structures and may be employed to investigate the
influence of evaporation or condensation,
nanoparticle transport, and solute transport in a
differentiated way. We highlight, in particular, the
influence of the subtle interplay of decomposition
in the layer and contact line motion on the observed
particle-induced transverse instability of the
dewetting front.},
Author = {Archer, A. J. and Robbins, M. J. and Thiele, U. },
DOI = {10.1103/PhysRevE.81.021602},
File = {ART10.pdf:ArRT2010pre.pdf:PDF},
Journal = {Phys. Rev. E},
Nnote = {selected for the February 15, 2010 issue of Virtual Journal of Nanoscale Science {\&} Technology},
Number = {2},
Numpages = {5},
Pages = {021602},
Title = {Dynamical density functional theory for the dewetting of evaporating thin films of nanoparticle suspensions exhibiting pattern formation},
Volume = {81},
Year = {2010}
}
@Article{BeTh2010sjads,
Abstract = {Lubrication equations describe many structuring
processes of thin liquid films. We develop and apply
a numerical framework suitable for their analysis
employing a dynamical systems approach. In
particular, we present a time integration algorithm
based on exponential propagation and an algorithm
for steady-state continuation. Both algorithms
employ a Cayley transform to overcome numerical
problems resulting from scale separation in space
and time. An adaptive time-step allows one to study
the dynamics close to hetero- or homoclinic
connections. The developed framework is employed, on
the one hand, to analyze different phases of the
dewetting of a liquid film on a horizontal
homogeneous substrate. On the other hand, we
consider the depinning of drops pinned by a
wettability defect. Time-stepping and path-following
are used in both cases to analyze steady-state
solutions and their bifurcations as well as dynamic
processes on short and long time-scales. Both
examples are treated for two- and three-dimensional
(2d and 3d) physical settings and prove that the
developed algorithms are reliable and efficient for
1d and 2d lubrication equations.},
Author = {Beltrame, P. and Thiele, U.},
DOI = {10.1137/080718619},
Eeprint = {http://arxiv.org/abs/0903.0014},
File = {BeTh10.pdf:BeTh2010sjads.pdf:PDF},
Journal = {SIAM J. Appl. Dyn. Syst.},
Pages = {484--518},
Title = {Time integration and steady-state continuation method for lubrication equations},
Volume = {9},
Year = {2010}
}
@InCollection{BHET2010,
Abstract = {On non-ideal real substrates the onset of droplet
motion under lateral driving is strongly influenced
by substrate defects. A finite driving force is
necessary to overcome the pinning influence of
microscale heterogeneities. The dynamics of
depinning two- and three-dimensional droplets is
studied using a long-wave evolution equation for the
film thickness profile in the case of a localized
hydrophobic wettability defect. It is found that the
nature of the depinning transition explains the
experimentally observed stick-slip motion.},
Address = {Berlin Heidelberg},
Author = {Beltrame, P. and H{\"a}nggi, P. and Knobloch E. and Thiele, U.},
Booktitle = {Progress in Industrial Mathematics at ECMI 2008},
DOI = {10.1007/978-3-642-12110-4_99},
Editor = {Fitt, A. D. and Norbury, J. and Ockendon, H. and Wilson, E.},
File = {BHKT10.pdf:BHET2010.pdf:PDF},
ISBN = {978-3-642-12110-4},
Pages = {623--629},
Publisher = {Springer},
Series = {Mathematics in Industry},
Title = {Depinning of 2d and 3d droplets blocked by a hydrophobic defect},
Urrl = {http://www.springer.com/978-3-642-12109-8},
Year = {2010}
}
@InProceedings{BSPM2010,
Author = {Blunt, M. O. and Stannard, A. and Pauliac-Vaujour, E. and Martin, C. P. and Vancea, I. and Suvakov, M. and Thiele, U. and Tadic, B. and Moriarty, P.},
Booktitle = {The Oxford Handbook on Nanoscience and Technology: {F}rontiers and Advances, Volume 1: Basic aspects},
Editors = {Narlikar, A.V. and Fu, Y.Y.},
File = {Blun10.pdf:BSPM2010.pdf:PDF},
Pages = {214--248},
Publisher = {Oxford University Press},
Title = {Patterns and pathways in nanoparticle self-organisation},
Year = {2010}
}
@Article{JoTh2010prl,
Abstract = {We develop and analyze a minimal hydrodynamic model
to understand why a drop climbs a smooth homogeneous
incline that is harmonically vibrated at an angle
different from the substrate normal [P. Brunet,
J. Eggers, and R.D. Deegan, Phys. Rev. Lett. 99,
144501 (2007)]. We find that the vibration component
orthogonal to the substrate induces a nonlinear
(anharmonic) response in the drop shape. This
results in an asymmetric response of the drop to the
parallel vibration and, as a consequence, in the
observed net motion. In addition to establishing the
basic mechanism, we identify scaling laws valid in a
broad frequency range and a flow reversal at high
frequencies.},
Author = {John, K. and Thiele, U.},
DOI = {10.1103/PhysRevLett.104.107801},
Eeprint = {arXiv:0907.1223v1},
File = {JoTh2010prl.pdf:JoTh2010prl.pdf:PDF},
Journal = {Phys. Rev. Lett.},
Pages = {107801},
Title = {Self-ratcheting {S}tokes drops driven by oblique vibrations},
Volume = {104},
Year = {2010}
}
@Article{SAPS2010l,
Abstract = {We provide compelling evidence that ring formation
in solutions of thiol-passivated Au nanoparticles is
driven by breath figure dynamics. A method for the
controlled placement of rings of nanoparticles on a
solid substrate, which exploits variations in
substrate wettability to fix the positions of the
submicrometer water droplets formed in the breath
figure process, has been developed. This is achieved
by heterogeneously patterning hydrogen-terminated
silicon substrates with oxide regions that act as
adsorption sites for the droplets. The droplets in
turn template the formation of thiol-passivated Au
nanoparticle rings during spin-casting from volatile
solvents.},
Author = {Stannard, A. and Alhummiany, H. and Pauliac-Vaujour, E. and Sharp, J. S. and Moriarty, P. and Thiele, U.},
DOI = {10.1021/la1004787},
File = {Stan10.pdf:SAPS2010l.pdf:PDF},
Journal = {Langmuir},
Pages = {13892--13896},
Title = {Directing the Nucleation of Nanoparticle Rings},
Volume = {26},
Year = {2010}
}
@Article{Thie2010jpcm,
Abstract = {In the present contribution we review basic
mathematical results for three physical systems
involving self-organizing solid or liquid films at
solid surfaces. The films may undergo a structuring
process by dewetting, evaporation/condensation or
epitaxial growth, respectively. We highlight
similarities and differences of the three systems
based on the observation that in certain limits all
of them may be described using models of similar
form, i.e. time evolution equations for the film
thickness profile. Those equations represent
gradient dynamics characterized by mobility
functions and an underlying energy functional. Two
basic steps of mathematical analysis are used to
compare the different systems. First, we discuss the
linear stability of homogeneous steady states,
i.e. flat films, and second the systematics of
non-trivial steady states, i.e. drop/hole states for
dewetting films and quantum-dot states in epitaxial
growth, respectively. Our aim is to illustrate that
the underlying solution structure might be very
complex as in the case of epitaxial growth but can
be better understood when comparing the much simpler
results for the dewetting liquid film. We
furthermore show that the numerical continuation
techniques employed can shed some light on this
structure in a more convenient way than
time-stepping methods. Finally we discuss that the
usage of the employed general formulation does not
only relate seemingly unrelated physical systems
mathematically, but does allow as well for
discussing model extensions in a more unified way. },
Author = {Thiele, U.},
DOI = {10.1088/0953-8984/22/8/084019},
Eeprint = {http://arxiv.org/abs/1010.2928},
File = {Thie10.pdf:Thie2010jpcm.pdf:PDF},
Journal = {J. Phys.: Cond. Mat.},
Pages = {084019},
Title = {Thin film evolution equations from (evaporating) dewetting liquid layers to epitaxial growth},
Volume = {22},
Year = {2010}
}
@Article{ThJo2010cp,
Abstract = {We discuss the usage of ratchet mechanisms to
transport a continuous phase in several
micro-fluidic settings. In particular, we study the
transport of a dielectric liquid in a heterogeneous
ratchet capacitor that is periodically switched on
and off. The second system consists of drops on a
solid substrate that are transported by different
types of harmonic substrate vibrations. We argue
that the latter can be seen as a self-ratcheting
process and discuss analogies between the employed
class of thin film equations and Fokker-Planck
equations for transport of discrete objects in a
particle ratchet.},
Author = {Thiele, U. and John, K.},
DOI = {10.1016/j.chemphys.2010.07.011},
File = {ThJo2010cp.pdf:ThJo2010cp.pdf:PDF},
Journal = {Chem. Phys.},
Pages = {578--586},
Title = {Transport of free surface liquid films and drops by external ratchets and self-ratcheting mechanisms},
Volume = {375},
Year = {2010}
}
@Article{BeHT2009el,
Abstract = {Substrate defects crucially influence the onset of
sliding drop motion under lateral driving. A finite
force is necessary to overcome the pinning influence
even of microscale heterogeneities. The depinning
dynamics of three-dimensional drops is studied for
hydrophilic and hydrophobic wettability defects
using a long-wave evolution equation for the film
thickness profile. The model is studied employing
effective algorithms for the parameter continuation
of pinned steady drops and for the time simulation
of the dynamics of sliding drops that perform a
stick-slip motion. The discussion focuses on common
features and significant differences of the depinning
process for three-dimensional and two-dimensional
drops.},
Author = {Beltrame, P. and H{\"a}nggi, P. and Thiele, U.},
DOI = {10.1209/0295-5075/86/24006},
File = {BHT09.pdf:BeHT2009el.pdf:PDF},
Journal = {Europhys. Lett.},
Pages = {24006},
Title = {Depinning of three-dimensional drops from wettability defects},
Volume = {86},
Year = {2009}
}
@Article{BSTR2009l,
Abstract = {Electric-field-induced instabilities in thin
bilayers composed of either purely viscous or purely
elastic films resting on a solid substrate are
studied. In contrast to the electric-field-induced
instability in a single elastic film, the
lengthscale of the instability for elastic bilayers
can be tuned by changing the ratios of the shear
moduli, thicknesses, and dielectric permittivities
of the films. Linear stability analysis is employed
to uncover the variations in the wavelength. The
instabilities of the viscous bilayers follow
different modes of interfacial evolution: either
in-phase bending or antiphase squeezing. Linear and
nonlinear analyses show that the mode type can be
switched by changing the dielectric permittivities
of the films. Nonlinear simulations find a number of
intriguing interfacial morphologies: (a) an embedded
upper layer in an array of lower layer columns, (b)
upper layer columns encapsulated by lower layer
beakers, (c) lower layer columns covered by the
upper layer liquid resulting in concentric
core-shell columns, (d) droplets of upper liquid on
a largely undisturbed lower layer, and (f) evolution
of two different wavelengths at the two interfaces
of the bilayer. The simulated morphology types (a),
(b) and (d) have been seen previously in
experiments. The effect of the film viscosities on
the evolution of the instability and final
morphologies is also discussed.},
Author = {Bandyopadhyay, D. and Sharma, A. and Thiele, U. and Reddy, P. D. S.},
DOI = {10.1021/la900635f},
File = {BSTR09.pdf:BSTR2009l.pdf:PDF},
Journal = {Langmuir},
Pages = {9108--9118},
Title = {Electric Field Induced Interfacial Instabilities and Morphologies of Thin Viscous and Elastic Bilayers},
Volume = {25},
Year = {2009}
}
@Article{MaTh2009pf,
Abstract = {We study the linear stability with respect to lateral
perturbations of free surface films of polymer
mixtures on solid substrates. The study focuses on
the stability properties of the stratified and
homogeneous steady - states studied in Part I
U. Thiele, S. Madruga, and L. Frastia, Phys. Fluids
19, 122106 (2007). To this aim, the linearized bulk
equations and boundary equations are solved using
continuation techniques for several different cases
of energetic bias at the surfaces corresponding to
linear and quadratic solutal Marangoni effects. For
purely diffusive transport, an increase in the film
thickness either exponentially decreases the lateral
instability or entirely stabilizes the
film. Including convective transport leads to a
further destabilization as compared to the purely
diffusive case. In some cases the inclusion of
convective transport and the related widening of the
range of available film configurations (it is then
able to change its surface profile) change the
stability behavior qualitatively. We furthermore
present results regarding the dependence of the
instability on several other parameters, namely, the
Reynolds number, the surface tension number, and the
ratio of the typical velocities of convective and
diffusive transport. },
Author = {Madruga, S. and Thiele, U.},
DOI = {10.1063/1.3132789},
File = {MaTh09.pdf:MaTh2009pf.pdf:PDF},
Journal = {Phys. Fluids},
Pages = {062104},
Title = {Decomposition driven interface evolution for layers of binary mixtures: {II. I}nfluence of convective transport on linear stability},
Volume = {21},
Year = {2009}
}
@Article{PTTK2009epjst,
Abstract = {We investigate the interaction of thin films with
chemical reactions by using as a model system a
horizontal film with a reactive mixture of insoluble
surfactants on its free surface. The reaction is
modeled by a bistable/excitable FitzHugh-Nagumo
(FHN) prototype. The chemical reaction can
destabilize the film leading to the propagation of
solitary pulses on its free surface. },
Author = {Pereira, A. and Trevelyan, P. M. J. and Thiele, U. and Kalliadasis, S.},
DOI = {10.1140/epjst/e2009-00891-1},
File = {PTTK09.pdf:PTTK2009epjst.pdf:PDF},
Journal = {Eur. Phys. J. Special Topics},
Pages = {121--125},
Title = {Interfacial instabilities driven by chemical reactions},
Volume = {166},
Year = {2009}
}
@Article{ThGV2009pf,
Abstract = {The time evolution of a thin liquid film flowing down
a heated solid porous substrate is
investigated. Using the Navier-Stokes and
Darcy-Brinkman equations in the film and the porous
layer, respectively, the problem is reduced to the
study of the evolution equation for the free surface
of the liquid film derived through a long-wave
approximation. A linear stability analysis of the
base flow is performed and the critical Reynolds and
Marangoni numbers are obtained. A nonlinear analysis
using continuation techniques shows that the base
flow yields to stationary surface structures ranging
from surface waves to large amplitude structures
resembling sliding drops or ridges. It is also shown
under what conditions the porous layer can be
replaced by an effective slip boundary condition at
the liquid-solid interface. Then, the corresponding
slip length is calculated from the porous layer
characteristics (thickness, porosity, and Darcy
number).},
Author = {U. Thiele and B. Goyeau and Velarde, M. G.},
DOI = {10.1063/1.3054157},
File = {TGV09.pdf:ThGV2009pf.pdf:PDF},
Journal = {Phys. Fluids},
Pages = {014103},
Title = {Stability analysis of thin film flow along a heated porous wall},
Volume = {21},
Year = {2009}
}
@Article{Thie2009pj,
Author = {U. Thiele},
File = {Thie09b.pdf:Thie2009pj.pdf:PDF},
Journal = {Physik Journal},
Number = {10},
Pages = {16--17},
Title = {Weine nicht, wenn der {R}egen zerf{\"a}llt},
Urrl = {http://www.pro-physik.de/details/articlePdf/1103005/issue.html},
Volume = {8},
Year = {2009}
}
@Article{TVAR2009jpm,
Abstract = {We review recent experiments on dewetting thin films
of evaporating colloidal nanoparticle suspensions
(nanofluids) and discuss several theoretical
approaches to describe the ongoing processes
including coupled transport and phase changes. These
approaches range from microscopic discrete
stochastic theories to mesoscopic continuous
deterministic descriptions. In particular, we
describe (i) a microscopic kinetic Monte Carlo
model, (ii) a dynamical density functional theory
and (iii) a hydrodynamic thin film model. Models
(i) and (ii) are employed to discuss the formation
of polygonal networks, spinodal and branched
structures resulting from the dewetting of an
ultrathin 'postcursor film' that remains behind a
mesoscopic dewetting front. We highlight, in
particular, the presence of a transverse instability
in the evaporative dewetting front, which results in
highly branched fingering structures. The subtle
interplay of decomposition in the film and contact
line motion is discussed. Finally, we discuss a
simple thin film model (iii) of the hydrodynamics on
the mesoscale. We employ coupled evolution equations
for the film thickness profile and mean particle
concentration. The model is used to discuss the
self-pinning and depinning of a contact line related
to the 'coffee-stain' effect. In the course of the
review we discuss the advantages and limitations of
the different theories, as well as possible future
developments and extensions. },
Author = {Thiele, U. and Vancea, I. and Archer, A. J. and Robbins, M. J. and Frastia, L. and Stannard, A. and Pauliac-Vaujour, E. and Martin, C. P. and Blunt, M. O. and Moriarty, P. J.},
DOI = {10.1088/0953-8984/21/26/264016},
File = {Thie09.pdf:TVAR2009jpm.pdf:PDF},
Journal = {J. Phys.-Cond. Mat.},
Nnote = {selected for inclusion in IOP Select, http://Select.iop.org},
Pages = {264016},
Title = {Modelling approaches to the dewetting of evaporating thin films of nanoparticle suspensions},
Volume = {21},
Year = {2009}
}
@Article{JoHT2008sm,
Abstract = {We present a two-layer thin film model allowing us to
study the behavior of a general class of
wettability ratchets that can be employed to
transport a continuous phase. Brownian ratchets, in
contrast, are normally used to transport particles
or molecules within a continuous carrier fluid
without transporting the fluid itself. The
wettability ratchet is based on a switchable,
spatially asymmetric, periodic interaction of the
free surface of the film and the walls. To
illustrate the general concept, we focus on an
electrical dewetting mechanism based on the
effective force exercised by a static electric field
on the liquid-liquid interface between two
dielectric liquids. In particular, we analyse (i) an
on-off ratchet with a constant lateral force
resulting in a dewetting-spreading cycle, (ii) a
ratchet switching between two shifted potentials
that shows a transition between oscillating and
sliding drops, and (iii) a flashing external force
ratchet. For the three cases, the macroscopic
transport is studied in its dependence on spatial
and temporal characteristics of the ratchet, and
physical properties and volume of the liquids.},
Author = {K. John and P. H{\"a}nggi and U. Thiele},
DOI = {10.1039/b718850a},
File = {JHT08.pdf:JoHT2008sm.pdf:PDF},
Journal = {Soft Matter},
Pages = {1183--1195},
Title = {Ratchet-driven fluid transport in bounded two-layer films of immiscible liquids},
Volume = {4},
Year = {2008}
}
@Article{PSMB2008prl,
Abstract = {The growth of fingering patterns in dewetting
nanofluids (colloidal solutions of thiol-passivated
gold nanoparticles) has been followed in real time
using contrast-enhanced video microscopy. The
fingering instability on which we focus here arises
from evaporatively driven nucleation and growth in a
nanoscopically thin precursor solvent film behind
the macroscopic contact line. We find that
well-developed isotropic fingering structures only
form for a narrow range of experimental
parameters. Numerical simulations, based on a
modification of the Monte Carlo approach introduced
by Rabani et al. [Nature (London) 426, 271 (2003)],
reproduce the patterns we observe experimentally.},
Author = {Pauliac-Vaujour, E. and Stannard, A. and Martin, C. P. and Blunt, M. O. and Notingher, I. and Moriarty, P.J. and Vancea, I. and Thiele, U.},
DOI = {10.1103/PhysRevLett.100.176102},
File = {Paul08.pdf:PSMB2008prl.pdf:PDF},
Journal = {Phys. Rev. Lett.},
Pages = {176102},
Title = {Fingering instabilities in dewetting nanofluids},
Volume = {100},
Year = {2008}
}
@Article{PTTK2008cpoxicotaami9aa22,
Author = {Pereira, A. and Trevelyan, P. M. J. and Thiele, U. and Kalliadasis, S.},
File = {PTTK08.pdf:PTTK2008cpoxicotaami9aa22.pdf:PDF},
Journal = {CD-ROM Proceedings of XXII International Congress of Theoretical and Applied Mechanics (ISBN 978-0-9805142-1-6), Adelaide, Aug 24-30, 2008},
Pages = {Paper no.~11312},
Title = {Hydrodynamics of reactive thin films},
Urrl = {http:// },
Year = {2008}
}
@Article{SMPM2008jpcc,
Abstract = {A pseudo-3D lattice gas-based Monte Carlo simulation
is used to reproduce dual-scale nonequilibrium
structures formed from drying colloidal nanoparticle
solutions. Morphologies possessing multiple length
scale features are recreated by coupling the
chemical potential to the solvent density, modeling
a film thickness-dependent disjoining pressure. By
assigning a sigmoidal form to the chemical
potential, a switch in the dewetting mechanism at a
threshold solvent density is capable of producing
nanoparticle patterning at two length
scales. Dual-scale cellular networks, and
nanoparticle ring and fingering structures
coexisting with small scale patterning, can all be
generated in this way with suitable simulation
parameters. Extensive exploration of the model
parameter space maps the temperature-dependent
spinodal line and demonstrates the influence of
nanoparticle concentration on morphology.},
Author = {Stannard, A. and Martin, C. P. and Pauliac-Vaujour, E. and Moriarty, P.J. and Thiele, U.},
DOI = {10.1021/jp803399d},
File = {Stan08.pdf:SMPM2008jpcc.pdf:PDF},
Journal = {J. Phys. Chem. C},
Pages = {15195--15203},
Title = {Dual-scale pattern formation in nanoparticle assemblies},
Volume = {112},
Year = {2008}
}
@Article{VTPS2008pre,
Note = {selected for the 8 October 2008 issue of Virtual Journal of Nanoscale Science {\&} Technology},
Abstract = { Various experimental settings that involve drying
solutions or suspensions of nanoparticles often
called nanofluids have recently been used to produce
structured nanoparticle layers. In addition to the
formation of polygonal networks and spinodal-like
patterns, the occurrence of branched structures has
been reported. After reviewing the experimental
results we use a modified version of the Monte Carlo
model first introduced by Rabani et al. [Nature 426,
271 (2003)] to study structure formation in
evaporating films of nanoparticle solutions for the
case that all structuring is driven by the interplay
of evaporating solvent and diffusing
nanoparticles. After introducing the model and its
general behavior we focus on receding dewetting
fronts which are initially straight but develop a
transverse fingering instability. We analyze the
dependence of the characteristics of the resulting
branching patterns on the driving effective chemical
potential, the mobility and concentration of the
nanoparticles, and the interaction strength between
liquid and nanoparticles. This allows us to
understand the underlying instability mechanism.},
Author = {Vancea, I. and Thiele, U. and Pauliac-Vaujour, E. and Stannard, A. and Martin, C. P. and Blunt, M. O. and Moriarty, P. J. },
DOI = {10.1103/PhysRevE.78.041601},
File = {Vanc08.pdf:VTPS2008pre.pdf:PDF},
Journal = {Phys. Rev. E},
Pages = {041601},
Title = {Front instabilities in evaporatively dewetting nanofluids},
Volume = {78},
Year = {2008}
}
@Article{JoTh2007apl,
Abstract = {
The authors develop a model for ratchet-driven macroscopic transport
of a continuous phase. The transport relies on a field-induced
dewetting-spreading cycle of a liquid film based on a switchable,
spatially asymmetric, periodic interaction of the free surface of the
film and the solid substrate. The concept is exemplified using an
evolution equation for a dielectric liquid film under an inhomogeneous
voltage. The authors analyze the influence of the various phases of
the ratchet cycle on the transport properties. Conditions for maximal
transport and the efficiency of transport under load are discussed.},
Author = {K. John and U. Thiele},
DOI = {10.1063/1.2751582},
File = {JoTh07.pdf:JoTh2007apl.pdf:PDF},
Journal = {Appl. Phys. Lett.},
Pages = {264102},
Title = {Liquid transport generated by a flashing field-induced wettability ratchet},
Volume = {90},
Year = {2007}
}
@Book{KalliadasisThiele2007,
Address = {Wien},
Amazon = {http://www.amazon.com/Matter-International-Centre-Mechanical-Sciences/dp/3211698078},
Editor = {S. Kalliadasis and U. Thiele},
ISBN = {978-3211698075},
Pdf = {no},
Publisher = {Springer},
Title = {Thin Films of Soft Matter},
Year = {2007}
}
@Article{MBPS2007prl,
Abstract = {
We have achieved highly localized control of pattern formation in
two-dimensional nanoparticle assemblies by direct modification of
solvent dewetting dynamics. A striking dependence of
nanoparticle organization on the size of atomic force
microscope-generated surface heterogeneities is observed
and reproduced in numerical simulations. Nanoscale features induce a
rupture of the solvent-nanoparticle film, causing the local flow of
solvent to carry nanoparticles into confinement. Microscale
heterogeneities instead slow the evaporation of the solvent, producing
a remarkably abrupt interface between different nanoparticle patterns.},
Author = {Martin, C. P. and Blunt, M. O. and Pauliac-Vaujour, E. and Stannard, A. and Moriarty, P. and Vancea, I. and Thiele, U.},
DOI = {10.1103/PhysRevLett.99.116103},
File = {Mart07.pdf:MBPS2007prl.pdf:PDF},
Journal = {Phys. Rev. Lett.},
Pages = {116103},
Title = {Controlling pattern formation in nanoparticle assemblies via directed solvent dewetting},
Volume = {99},
Year = {2007}
}
@Article{PTTK2007fdamp,
Abstract = {We investigate the interaction between thin films and
chemical reactions by using two prototype systems: a
thin liquid film falling down a planar inclined
substrate in the presence of an exothermic chemical
reaction and a horizontal thin liquid film with a
reactive mixture of insoluble surfactants on its
surface. In the first case the chemical reaction has
a stabilizing influence on the dynamics of the film
and dampens the free-surface solitary pulses. In the
second case the chemical reaction can destabilize
the filmand lead to the formation of free-surface
solitary pulses.},
Author = {Pereira, A. and Trevelyan, P. M. J. and Thiele, U. and Kalliadasis, S.},
File = {PTTK07c.pdf:PTTK2007fdamp.pdf:PDF},
Journal = {Fluid Dynamics and Materials Processing},
Pages = {303--316},
Title = {Thin films in the presence of chemical reactions},
Volume = {3},
Year = {2007}
}
@Article{PTTK2007jem,
Author = {Pereira, A. and Trevelyan, P. M. J. and Thiele, U. and Kalliadasis, S.},
DOI = {10.1007/s10665-007-9143-9},
File = {PTTK07.pdf:PTTK2007jem.pdf:PDF},
Journal = {J. Engg. Math.},
Pages = {207--220},
Title = {Interfacial hydrodynamic waves driven by chemical reactions},
Volume = {59},
Year = {2007}
}
@Article{PTTK2007pf,
Abstract = {
We investigate the interplay between a stable horizontal thin liquid
film on a solid substrate and an excitable or bistable reactive
mixture on its free surface. Their coupling is twofold. On the one
hand, flow in the film transports the reacting surfactants
convectively. On the other hand, gradients in the surfactant
concentration exert Marangoni stresses on the free surface of the
film. A reduced model is derived based on the long-wave
approximation. We analyze the linear stability of the coupled system
as well as the nonlinear behavior, including the propagation of
solitary waves, fronts, and pulses. We show, for instance, that the
coupling of thin film hydrodynamics and surfactant chemistry can
either stabilize instabilities occurring in the pure chemical system,
or in a regime where the pure hydrodynamic and chemical subsystems are
both stable, the coupling can induce instabilities.
},
Author = {Pereira, A. and Trevelyan, P. M. J. and Thiele, U. and Kalliadasis, S.},
DOI = {10.1063/1.2775938},
File = {PTTK07b.pdf:PTTK2007pf.pdf:PDF},
Journal = {Phys. Fluids},
Pages = {112102},
Title = {Dynamics of a horizontal thin liquid film in the presence of reactive surfactants},
Urrl = {http://link.aip.org/link/?PHFLE6/19/112102/1},
Volume = {19},
Year = {2007}
}
@InBook{Thie2007chapter,
URL = {https://doi.org/10.1007/978-3-211-69808-2_2},
Abstract = {We outline some recent developments in the theoretical description of structure formation in thin liquid films. The main focus is systems involving a single layer of liquid on a solid substrate that can be described using an evolution equation for the film thickness profile. We review the history of the subject and we sketch important experimental and theoretical results and practical applications. After discussing the classification of the different cases, we introduce the common mathematical framework for studies of thin films of soft matter, namely by deriving the generic evolution equation for such films from the Navier-Stokes equations. In the main part we first introduce the different possible geometries and the transitions between them, i.e. from homogeneous to inhomogeneous substrates, or from horizontal to inclined substrates. We then present the physical questions posed by the individual systems and discuss approaches and results for: {\textbullet} Dewetting on a horizontal homogeneous substrate. We investigate the solution structure and its consequences for the system behavior. For the initial film rupture we distinguish nucleation-dominated and instability-dominated behavior for linearly unstable thin films. {\textbullet} Dewetting on a horizontal inhomogeneous substrate. The solution structure of the governing equation is analysed as a function of the strength of a chemical heterogeneity. We describe a pinning-coarsening transition with a large range of multistability, implying a large hysteresis and strong dependence on initial conditions and noise. {\textbullet} Heated thin films on a horizontal homogeneous substrate. We discuss nucleation and drop solutions and show that it is possible to construct all drop solutions separated by dry regions. Incorporating a disjoining pressure allows to study the coarsening behaviour of the drop pattern. {\textbullet} Sliding drops on an inclined homogeneous substrate. Using a model that incorporates a disjoining pressure allows to calculate the frequently used adhoc parameters of models for moving contact lines from surface chemistry. The involved transition from a Cahn-Hilliard-like to a Kuramoto-Sivashinsky-like dynamics that occurs for increasing inclination angle is analyzed for heated films. {\textbullet} Transverse instabilities of a liquid ridge are discussed encompassing all the above geometries. Particular attention is given on the stabilization of such an instability due to stripe-like heterogeneities for a resting ridge on a horizontal substrate and on the drastic change in the mode type when inclining the substrate. It changes from a symmetric varicose mode (horizontal substrate) via an asymmetric varicose mode and via an asymmetric zigzag mode to decoupled front and back modes. },
Address = {Vienna},
Author = {U. Thiele},
Booktitle = {Thin Films of Soft Matter},
DOI = {10.1007/978-3-211-69808-2\_2},
Editor = {S. Kalliadasis and U. Thiele},
File = {Thie07.pdf:Thie2007.pdf:PDF},
ISBN = {978-3-211-69808-2},
Pages = {25--93},
Publisher = {Springer Vienna},
Title = {Structure formation in thin liquid films},
Year = {2007}
}
@Article{ThMF2007pf,
Abstract = {
A dynamical model is proposed to describe the coupled decomposition
and profile evolution of a free surface film of a binary mixture. An
example is a thin film of a polymer blend on a solid substrate
undergoing simultaneous phase separation and dewetting. The model is
based on model-H describing the coupled transport of the mass of one
component convective Cahn-Hilliard equation and momentum
Navier-Stokes-Korteweg equations supplemented by appropriate
boundary conditions at the solid substrate and the free
surface. General transport equations are derived using
phenomenological nonequilibrium thermodynamics for a general
nonisothermal setting taking into account Soret and Dufour effects and
interfacial viscosity for the internal diffuse interface between the
two components. Focusing on an isothermal setting the resulting model
is compared to literature results and its base states corresponding to
homogeneous or vertically stratified flat layers are analyzed.
},
Author = {Thiele, U. and Madruga, S. and Frastia, L.},
DOI = {10.1063/1.2824404},
Eeprint = {arXiv:0707.3374v1},
File = {TMF07.pdf:ThMF2007pf.pdf:PDF},
Journal = {Phys. Fluids},
Pages = {122106},
Title = {Decomposition driven interface evolution for layers of binary mixtures: {I. M}odel derivation and stratified base states},
Volume = {19},
Year = {2007}
}
@Article{MBPR2006el,
Abstract = {Multiscale polymeric patterns resulting from flow on an inclined
substrate of a binary polymer blend solution of polystyrene and
poly-n-butylacrylate in toluene are analyzed with sub-microbeam
GISAXS and real space techniques. The locally isotropic
phase-separation structure on the 1 micron scale, including a
molecular substructure, is embedded in a superstructure on the
100 micron scale of stripe-like variations of film thickness
and composition oriented perpendicular to the flow direction. It
is argued that the multiscale pattern results from the interplay
of evaporation, convective flow, differential diffusion and
spinodal decomposition.
},
Author = {M{\"u}ller-Buschbaum, P. and Bauer, E. and Pfister, S. and Roth, S. V. and Burghammer, M. and Riekel, C. and David, C. and Thiele, U.},
DOI = {10.1209/epl/i2005-10369-6},
File = {Muel06.pdf:MBPR2006el.pdf:PDF},
Journal = {Europhys. Lett.},
Pages = {35--41},
Title = {Creation of multi-scale stripe-like patterns in thin polymer blend films},
Volume = {73},
Year = {2006}
}
@Article{PBMT2006el,
Abstract = {The structuring process of two-layer liquid films driven by van der
Waals interxfactions is investigated numerically for three-dimensional
systems. Different types of dynamical transitions of the interface
morphologies are characterised using coupled evolution equations for
the thickness profiles. We introduce a global deflection measure that
faithfully captures the transitions occurringin the course of the
short- and long-time evolution. Using an Si/PMMA/PS/air system as
example, transitions via branch switchingand via coarsening are
analysed in detail.},
Author = {Pototsky, A. and Bestehorn, M. and Merkt, D. and Thiele, U.},
DOI = {10.1209/epl/i2006-10026-8},
File = {PBMT06.pdf:PBMT2006el.pdf:PDF},
Journal = {Europhys. Lett.},
Pages = {665--671},
Title = {Evolution of three-dimensional interface patterns in dewetting two-layer liquid films},
Volume = {74},
Year = {2006}
}
@Article{PiTh2006pf,
Abstract = {An asymptotic theory is developed for a moving drop driven by a
wettability gradient. We distinguish the mesoscale where an exact
solution is known for the properly simplified problem. This solution
is matched at both the advancing and the receding side to respective
solutions of the problem on the microscale. On the microscale the
velocity of movement is used as the small parameter of an asymptotic
expansion. Matching gives the droplet shape, velocity of movement as a
function of the imposed wettability gradient, and droplet volume.
},
Author = {L. M. Pismen and U. Thiele},
DOI = {10.1063/1.2191015},
Eeprint = {physics/0509260},
File = {PiTh06.pdf:PiTh2006pf.pdf:PDF},
Journal = {Phys. Fluids},
Pages = {042104},
Title = {Asymptotic theory for a moving droplet driven by a wettability gradient},
Volume = {18},
Year = {2006}
}
@Article{ThKn2006njp,
Abstract = {
We study the depinning of driven drops on a heterogeneous substrate
using a long-wave evolution equation for the film thickness
profile. The heterogeneity is incorporated into an additional pressure
term describing the interaction of the liquid with the substrate or
with an external field. A drop may be pinned by a hydrophilic defect
at the back or a hydrophobic defect at the front. Two types of
depinning occur depending on the strength of the driving. The first
occurs via a saddle-node (sniper) bifurcation, while the second
involves a Hopf bifurcation. The parameter dependence of the depinning
process is studied using linear stability theory, and direct numerical
simulations are used to explore the dynamical properties of the
stick-slip motion of the drop after depinning. },
Author = {U. Thiele and E. Knobloch},
DOI = {10.1088/1367-2630/8/12/313},
File = {ThKn06.pdf:ThKn2006njp.pdf:PDF},
Journal = {New J. Phys.},
Pages = {313},
Ppages = {1--37},
Title = {On the depinning of a driven drop on a heterogeneous substrate},
Volume = {8},
Year = {2006}
}
@Article{ThKn2006prl,
Abstract = {
Pinning and depinning of driven drops on heterogeneous substrates is
studied as a function of the driving and heterogeneity amplitude. Two
types of heterogeneity are considered: a 'hydrophobic' defect that
blocks the drop in front and a 'hydrophilic' one that holds it at the
back. Two different types of depinning leading to sliding motion are
identified, and the resulting stick-slip motion is studied
numerically. },
Author = {U. Thiele and E. Knobloch},
DOI = {10.1103/PhysRevLett.97.204501},
File = {ThKn06b.pdf:ThKn2006prl.pdf:PDF},
Journal = {Phys. Rev. Lett.},
Pages = {204501},
Title = {Driven drops on heterogeneous substrates: {O}nset of sliding motion},
Volume = {97},
Year = {2006}
}
@Article{ThVK2006jfm,
Abstract = {The effect of vertical vibration on the long wave
instability of a Marangoni system is studied. The
vibration augments the stabilizing effect of surface tension in
bounded systems. In laterally unbounded systems nonlinear terms
can stabilize non-flat states and prevent the appearance of dry
spots. The effect of a slight inclination of the system is also
considered.
},
Author = {Thiele, U. and Vega, J. M. and Knobloch, E.},
DOI = {10.1017/S0022112005007007},
File = {TVK06.pdf:ThVK2006jfm.pdf:PDF},
Journal = {J. Fluid Mech.},
Pages = {61--87},
Title = {Long-wave {M}arangoni instability with vibration},
Volume = {546},
Year = {2006}
}
@Article{JoBT2005epje,
Abstract = {
We study chemically driven running droplets on a partially wetting
solid substrate by means of coupled evolution equations for the
thickness profile of the droplets and the density profile of an
adsorbate layer. Two models are introduced corresponding to two
qualitatively different types of experiments described in the
literature. In both cases an adsorption or desorption reaction
underneath the droplets induces a wettability gradient on the
substrate and provides the driving force for droplet motion. The
difference lies in the behavior of the substrate behind the
droplet. In case I the substrate is irreversibly changed whereas in
case II it recovers allowing for a periodic droplet movement (as long
as the overall system stays far away from equilibrium). Both models
allow for a non-saturated and a saturated regime of droplet movement
depending on the ratio of the viscous and reactive time scales. In
contrast to model I, model II allows for sitting drops at high
reaction rate and zero diffusion along the substrate. The transition
from running to sitting drops in model II occurs via a super- or
subcritical drift-pitchfork bifurcation and may be strongly hysteretic
implying a coexistence region of running and sitting drops.},
Author = {John, K. and B{\"a}r, M. and Thiele, U.},
DOI = {10.1140/epje/i2005-10039-1},
Eeprint = {cond-mat/0506326},
File = {JBT05.pdf:JoBT2005epje.pdf:PDF},
Journal = {Eur. Phys. J. E},
Pages = {183--199},
Title = {Self-propelled running droplets on solid substrates driven by chemical reactions},
Volume = {18},
Year = {2005}
}
@Article{MPBT2005pf,
Abstract = {We consider two layers of immiscible liquids
confined between an upper and a lower rigid
plate. The dynamics of the free liquid-liquid
interface is described for arbitrary amplitudes by
an evolution equation derived from the basic
hydrodynamic equations using long-wave
approximation. After giving the evolution equation
in a general way, we focus on interface
instabilities driven by gravity, thermocapillary and
electrostatic fields. First, we study the linear
stability discussing especially the conditions for
destabilizing the system by heating from above or
below. Second, we use a variational formulation of
the evolution equation based on an energy functional
to predict metastable states and the long-time
pattern morphology (holes, drops or maze
structures). Finally, fully nonlinear
three-dimensional numerical integrations are
performed to study the short- and long-time
evolution of the evolving patterns. Different
coarsening modes are discussed and long-time scaling
exponents are extracted.},
Author = {D. Merkt and A. Pototsky and M. Bestehorn and U. Thiele},
DOI = {10.1063/1.1935487},
Eeprint = {nlin/0412040},
File = {MPBT05.pdf:MPBT2005pf.pdf:PDF},
Journal = {Phys. Fluids},
Numpages = {20},
Pages = {064104},
Title = {Long-wave theory of bounded two-layer films with a free liquid-liquid interface: {S}hort- and long-time evolution},
Volume = {17},
Year = {2005}
}
@Article{PBMT2005jcp,
Abstract = {We consider a thin film consisting of two layers of
immiscible liquids on a solid horizontal (heated)
substrate. Both, the free liquid-liquid and the
liquid-gas interface of such a bilayer liquid film
may be unstable due to effective molecular
interactions relevant for ultrathin layers below 100
nm thickness, or due to temperature-gradient caused
Marangoni flows in the heated case. Using a long
wave approximation we derive coupled evolution
equations for the interface profiles for the general
non-isothermal situation allowing for slip at the
substrate. Linear and nonlinear analyses of the
short- and long-time film evolution are performed
for isothermal ultrathin layers taking into account
destabilizing long-range and stabilizing short-range
molecular interactions. It is shown that the initial
instability can be of a varicose, zigzag or mixed
type. However, in the nonlinear stage of the
evolution the mode type and therefore the pattern
morphology can change via switching between two
different branches of stationary solutions or via
coarsening along a single branch.},
Author = {A. Pototsky and M. Bestehorn and D. Merkt and U. Thiele},
DOI = {10.1063/1.1927512},
Eeprint = {nlin/0412039},
File = {PBMT05.pdf:PBMT2005jcp.pdf:PDF},
Journal = {J. Chem. Phys.},
Numpages = {12},
Pages = {224711},
Title = {Morphology changes in the evolution of liquid two-layer films},
Volume = {122},
Year = {2005}
}
@Article{SRTK2005jfm,
Abstract = {The Benney equation including thermocapillary
effects is considered to study a liquid film flowing
down a homogeneously heated inclined wall. The link
between finite-time blow-up of the Benney equation
and absence of one-hump travelling-wave solution of
the associated dynamical system is accurately
demonstrated in the whole range of linearly unstable
wavenumbers. Then the blow-up boundary is tracked in
the whole space of parameters accounting for flow
rate, surface tension, inclination and
thermocapillarity. Especially, the latter two
effects can strongly reduce the validity range of
the Benney equation. It is also shown that the
subcritical bifurcation found for falling films with
the Benney equation is related to the blow-up of
solutions and is unphysical in any case, even with
the thermocapillary effect, in contrast with
horizontally heated films. The accuracy of bounded
solutions of the Benney equation is also analysed by
comparison with a reference weighted integral
boundary layer model. A distinction is made between
closed and open flow conditions, when calculating
travelling-wave solutions; the former corresponding
to the conservation of mass and the latter to the
conservation of flow rate. The open flow condition
matches experimental conditions more closely and is
explored for the first time through the associated
dynamical system. It yields bounded solutions for
larger Reynolds numbers than the closed flow
condition. Finally, solutions that are conditionally
bounded are found to be unstable to disturbances of
larger periodicity. In this case, coalescence is the
pathway yielding finite-time blow-up. },
Author = {Scheid, B. and Ruyer-Quil, C. and Thiele, U. and Kabov, O. A. and Legros, J. C. and Colinet, P.},
DOI = {10.1017/S0022112004003179},
File = {Sche05.pdf:SRTK2005jfm.pdf:PDF},
Journal = {J. Fluid Mech.},
Pages = {303--335},
Title = {Validity domain of the {B}enney equation including {M}arangoni effect for closed and open flows},
Volume = {527},
Year = {2005}
}
@Article{PBMT2004pre,
Abstract = {We consider two stacked ultrathin layers of
different liquids on a solid substrate. Using
long-wave theory, we derive coupled evolution
equations for the free liquid-liquid and liquid-gas
interfaces. Depending on the long-range van der
Waals forces and the ratio of the layer thicknesses,
the system follows different pathways of
dewetting. The instability may be driven by varicose
or zigzag modes and leads to film rupture either at
the liquid-gas interface or at the substrate. We
predict that the faster layer drives the evolution
and may accelerate the rupture of the slower layer
by orders of magnitude, thereby promoting the
rupture of rather thick films. },
Author = {A. Pototsky and M. Bestehorn and D. Merkt and U. Thiele},
DOI = {10.1103/PhysRevE.70.025201},
Eeprint = {nlin/0401042},
File = {PBMT04.pdf:PBMT2004pre.pdf:PDF},
Journal = {Phys. Rev. E},
Pages = {025201(R)},
Title = {Alternative pathways of dewetting for a thin liquid two-layer film},
Urrl = {http://link.aps.org/abstract/PRE/v70/e025201},
Volume = {70},
Year = {2004}
}
@Article{PoBT2004pd,
Abstract = {We propose two methods to control the structuring of
unstable thin films of soft matter. The first one is
a non-contact method, where an external disturbance
can be used to move a single drop, front or hole in
a certain direction. The principle is illustrated by
incorporating a sonic disturbance in a thin film
equation to study the evolution of ultrathin films
unstable due to their wetting properties. The second
one is based on inhomogeneous templating of the
substrate. Here, we study the influence of periodic
modulation on coarsening in the long-time
limit. Finally, the fully nonlinear evolution of a
3D system is presented by numerical integration. },
Author = {Pototsky, A. and Bestehorn, M. and Thiele, U.},
DOI = {10.1016/j.physd.2004.08.019},
File = {PBT04.pdf:PoBT2004pd.pdf:PDF},
Journal = {Physica D},
Nnumber = {1-2},
Pages = {138--148},
Title = {Control of the structuring of thin soft matter films by means of different types of external disturbance},
Volume = {199},
Year = {2004}
}
@Article{ScTh2004epje,
Abstract = {A simple model investigates the amplification of
fluctuations for membranes composed of two lipids
having different characteristic length. Van der
Waals and electrostatic interactions across the
lipid bilayer then result in a destabilization
favoring thickness variations of the membrane. Close
to spontaneous demixing of the two components, the
additional gain in free energy due to thickness
undulations shifts the stability boundary promoting
phase separation into domains. Interestingly, this
effect can be induced by an applied electric field
or membrane potential. In biological systems, the
dynamic model presented here indicates that electric
fields might be important for controlling phase
separation and the formation of domains called
``rafts''. },
Author = {E. Sch{\"a}ffer and U. Thiele},
DOI = {10.1140/epje/i2003-10147-x},
File = {ScTh04.pdf:ScTh2004epje.pdf:PDF},
Journal = {Eur. Phys. J. E},
Nnumber = {2},
Pages = {169--175},
Title = {Dynamic domain formation in membranes: {T}hickness fluctuation induced phase separation},
Volume = {14},
Year = {2004}
}
@PhdThesis{Thiele2004-phd,
Note = {habilitation-thesis},
Author = {U. Thiele},
Title = {Structure formation in thin liquid films},
Year = {2004}
}
@Article{ThJB2004prl,
Abstract = {We propose coupled evolution equations for the
thickness of a liquid film and the density of an
adsorbate layer on a partially wetting solid
substrate. Therein, running droplets are studied
assuming a chemical reaction underneath the droplets
that induces a wettability gradient on the substrate
and provides the driving force for droplet
motion. Two different regimes for moving droplets --
reaction-limited resp.\ saturated regime -- are
described corresponding to increasing resp.\
decreasing velocities with increasing reaction rates
and droplet sizes. The existence of the two regimes
offers a natural explanation of prior experimental
observations. },
Author = {Thiele, U. and John, K. and B{\"a}r, M.},
DOI = {10.1103/PhysRevLett.93.027802},
Eeprint = {cond-mat/0403043},
File = {TJB04.pdf:ThJB2004prl.pdf:PDF},
Journal = {Phys. Rev. Lett.},
Pages = {027802},
Title = {Dynamical Model for Chemically Driven Running Droplets},
Urrl = {http://link.aps.org/abstract/PRL/v93/e027802},
Volume = {93},
Year = {2004}
}
@Article{ThKn2004pd,
Abstract = {The behavior of a thin liquid on a uniformly heated
substrate is considered. When the substrate is
horizontal and the Marangoni number sufficiently
large the film breaks up into a periodic array of
drops. When the substrate is slightly inclined this
drop-like state slides down the substrate. The
relation between these states is discussed and their
stability properties examined. The results shed
light on the multiplicity of states accessible to
systems of this type. },
Author = {U. Thiele and E. Knobloch},
DOI = {10.1016/j.physd.2003.09.048},
File = {ThKn04.pdf:ThKn2004pd.pdf:PDF},
Journal = {Physica D},
Nnumber = {3-4},
Pages = {213--248},
Title = {Thin liquid films on a slightly inclined heated plate},
Volume = {190},
Year = {2004}
}
@Article{BePT2003epjb,
Abstract = {We study large scale surface deformations of a
liquid film unstable due to the Marangoni effect
caused by external heating on a smooth and solid
substrate. The work is based on the thin film
equation which can be derived from the basic
hydrodynamic equations. To prevent rupture, a
repelling disjoining pressure is included which
accounts for the stabilization of a thin precursor
film and so prevents the occurrence of completely
dry regions. Linear stability analysis, nonlinear
stationary solutions, as well as three-dimensional
time dependent numerical solutions for horizontal
and inclined substrates reveal a rich scenario of
possible structures for several realistic fluid
parameters. },
Author = {M. Bestehorn and A. Pototsky and U. Thiele},
DOI = {10.1140/epjb/e2003-00186-3},
File = {BPT03.pdf:BePT2003epjb.pdf:PDF},
Journal = {Eur. Phys. J. B},
Pages = {457--467},
Title = {{3D} large scale {M}arangoni convection in liquid films},
Volume = {33},
Year = {2003}
}
@Article{SkTS2003jfm,
Abstract = {We analyse the stability of a thin film falling
under the influence of gravity down a locally heated
plate. Marangoni flow, due to local temperature
changes influencing the surface tension, opposes the
gravitationally driven Poiseuille flow and forms a
horizontal band at the upper edge of the heater. The
thickness of the band increases with the surface
tension gradient, until an instability forms a
rivulet structure periodic in the transverse
direction. We study the dependence of the critical
Marangoni number, a non-dimensional measure of the
surface tension gradient at the onset of
instability, on the associated Bond and Biot
numbers, non-dimensional measures of the curvature
pressure and heat-conductive properties of the film
respectively. We develop a model based on long-wave
theory to calculate base-state solutions and their
linear stability. We obtain dispersion relations,
which give us the wavelength and growth rate of the
fastest growing mode. The calculated film profile
and wavelength of the most unstable mode at the
instability threshold are in quantitative agreement
with the experimental results. We show via an energy
analysis of the most unstable linear eigenmode that
the instability is driven by gravity and an
interaction between base-state curvature and the
perturbation thickness. In the case of non-zero Biot
number transverse variations of the temperature
profile also contribute to destabilization. },
Author = {Skotheim, J. M. and Thiele, U. and Scheid, B.},
DOI = {10.1017/S0022112002001957},
File = {STS03.pdf:SkTS2003jfm.pdf:PDF},
Journal = {J. Fluid Mech.},
Pages = {1--19},
Title = {On the instability of a falling film due to localized heating},
Volume = {475},
Year = {2003}
}
@Article{TBBB2003epje,
Abstract = {We study the dewetting process of a thin liquid film
on a chemically patterned solid substrate (template)
by means of a thin-film evolution equation
incorporating a space-dependent disjoining
pressure. Dewetting of a thin film on a homogeneous
substrate leads to fluid patterns with a typical
length scale, that increases monotonously in time
(coarsening). Conditions are identified for the
amplitude and periodicity of the heterogeneity that
allow to transfer the template pattern onto the
liquid structure ("pinning") emerging from the
dewetting process. A bifurcation and stability
analysis of the possible liquid ridge solutions on a
periodically striped substrate reveal parameter
ranges where pinning or coarsening ultimately
prevail. We obtain an extended parameter range of
multistability of the pinning and coarsening
morphologies. In this regime, the selected pattern
depends sensitively on the initial conditions and
potential finite perturbations (noise) in the system
as we illustrate with numerical integrations in
time. Finally, we discuss the instability to
transversal modes leading to a decay of the ridges
into rows of drops and show that it may diminish the
size of the parameter range where the pinning of the
thin film to the template is successful. },
Author = {U. Thiele and L. Brusch and M. Bestehorn and M. B{\"a}r},
DOI = {10.1140/epje/i2003-10019-5},
File = {TBBB03.pdf:TBBB2003epje.pdf:PDF},
Journal = {Eur. Phys. J. E},
Pages = {255--271},
Title = {Modelling thin-film dewetting on structured substrates and templates: {B}ifurcation analysis and numerical simulations},
Volume = {11},
Year = {2003}
}
@Article{Thie2003epje,
Abstract = {This contribution summarizes the present
understanding of dewetting focusing on three points
that are either controversial or open. The first
issue concerns the initial formation of holes,
i.e. the film rupture. The second point concerns the
unstable growth of holes, i.e. the transversal
instability of the receding contact line. Finally,
recent extensions towards dewetting on heterogeneous
substrates are examined. In passing the long time
evolution in dewetting and the coupling of dewetting
with other effects are discussed. },
Author = {U. Thiele},
DOI = {10.1140/epje/e2004-00009-4},
File = {Thie03.pdf:Thie2003epje.pdf:PDF},
Journal = {Eur. Phys. J. E},
Pages = {409--416},
Title = {Open questions and promising new fields in dewetting},
Volume = {12},
Year = {2003}
}
@Article{Thie2003epjeb,
Author = {U. Thiele},
DOI = {10.1140/epje/e2004-00011-x},
File = {Thie03b.pdf:Thie2003epjeb.pdf:PDF},
Journal = {Eur. Phys. J. E},
Pages = {427--430},
Title = {Tentative interpretation of the dewetting morphologies presented by {T}sui et al.},
Volume = {12},
Year = {2003}
}
@Article{ThKn2003pf,
Abstract = {We study the transverse instability of a liquid
ridge on horizontal and inclined substrates using a
film evolution equation based on a long wave
approximation. The equation incorporates an
additional pressure term-the disjoining
pressure-accounting for the effective interaction of
the film with the substrate. On a horizontal
substrate the dominant instability mode is varicose,
but may turn into a zigzag mode on a slightly
inclined substrate depending on the inclination
angle and the ridge volume. For larger angles or
volumes the instabilities at the front and back
decouple. The linear stability properties of a
one-dimensional transverse ridgelike state are
studied in detail, and an energy analysis is used to
demonstrate that the disjoining pressure provides
the dominant instability mechanism at both the front
and the back, while the body force is responsible
for the main differences between these two
instabilities. An amplitude equation for the time
evolution of perturbations with small transverse
wave numbers is derived that predicts correctly the
linear crossing of the most dangerous eigenvalues at
zero wave number in the inclined case, in contrast
to the situation on a horizontal substrate. },
Author = {Thiele, U. and Knobloch, E.},
DOI = {10.1063/1.1545443},
File = {ThKn03.pdf:ThKn2003pf.pdf:PDF},
Journal = {Phys. Fluids},
Pages = {892--907},
Title = {Front and back instability of a liquid film on a slightly inclined plate},
Volume = {15},
Year = {2003}
}
@Article{BiTQ2002csa-pea,
Abstract = {We discuss quantitatively the wetting of a solid
textured by a designed roughness. Both the
hydrophilic and the hydrophobic case are described,
together with possible implications for the wetting
of porous materials. },
Author = {Bico, J. and Thiele, U. and Quere, D.},
DOI = {10.1016/S0927-7757(02)00061-4},
File = {BTQ02.pdf:BiTQ2002csa-pea.pdf:PDF},
Journal = {Colloids Surf. A - Physicochem. Eng. Asp.},
Pages = {41--46},
Title = {Wetting of textured surfaces},
Volume = {206},
Year = {2002}
}
@Article{BKTB2002pre,
Abstract = {We study a model for a thin liquid film dewetting
from a periodic heterogeneous substrate
(template). The amplitude and periodicity of a
striped template heterogeneity necessary to obtain a
stable periodic stripe pattern, i.e., pinning, are
computed. This requires a stabilization of the
longitudinal and transversal modes driving the
typical coarsening dynamics during dewetting of a
thin film on a homogeneous substrate. If the
heterogeneity has a larger spatial period than that
of the critical dewetting mode, weak heterogeneities
are sufficient for pinning. Our results imply a
large region of coexistence between coarsening
dynamics and pinning. },
Author = {Brusch, L. and K{\"u}hne, H. and Thiele, U. and B{\"a}r, M.},
DOI = {10.1103/PhysRevE.66.011602},
File = {BKTB02.pdf:BKTB2002pre.pdf:PDF},
Journal = {Phys. Rev. E},
Numpages = {5},
Pages = {011602},
Title = {Dewetting of thin films on heterogeneous substrates: Pinning versus coarsening},
Urrl = {http://link.aps.org/abstract/PRE/v66/e011602},
Volume = {66},
Year = {2002}
}
@Article{SOCT2002pf,
Abstract = {The present theoretical study focuses on the
dynamics of a thin liquid film falling down a
vertical plate with a nonuniform, sinusoidal
temperature distribution. The results are compared
to those obtained in the case of the uniform
temperature distribution. The governing evolution
equation for the film thickness profile based on
long-wave theory accounts for two instability
mechanisms related to thermocapillarity. The first
mechanism is due to an inhomogeneity of the
temperature at the liquid-gas interface induced by
perturbations of the film thickness, when heat
transfer to the gas phase is present, while the
second one is due to the nonuniform heating imposed
at the plate and leads to steady-state deformations
of the liquid-gas interface. For a moderate
nonuniform heating the traveling waves obtained in
the case of a uniform heating are modulated by an
envelope. When the temperature modulation along the
plate increases the shape of the liquid-gas
interface becomes ''frozen'' and the oscillatory
traveling wave regime is suppressed. The enhancement
of the heat transfer due to permanent deformations
and traveling waves is also assessed. The latter is
found to have no significant effect on the heat
transfer coefficient, while the former can increase
it significantly. A good agreement between the
theoretical model and the experimental data obtained
for a step-wise temperature distribution at the
plate is found and the reason for discrepancies is
explained. },
Author = {Scheid, B. and Oron, A. and Colinet, P. and Thiele, U. and Legros, J. C.},
DOI = {10.1063/1.1515270},
File = {Sche02.pdf:SOCT2002pf.pdf:PDF},
Journal = {Phys. Fluids},
Pages = {4130--4151},
Title = {Nonlinear evolution of nonuniformly heated falling liquid films},
Volume = {14},
Year = {2002}
}
@Article{TNBP2002csa-pea,
Abstract = {An evolution equation for the film thickness was
derived recently combining diffuse interface theory
and long-wave approximation (Phys. Rev. E 62 (2000)
2480). Based on results for the structure formation
in a thin liquid film on a horizontal plane, we
study one-dimensional periodic drop profiles sliding
down an inclined plane. The analysis of the
dependence of their amplitude, velocity, advancing
and receding dynamic contact angles on period and
the interaction parameters reveals an universal
regime of flat drops. The main properties of the
flat drops do not depend on their volume. Both types
of drops-the universal flat drops and the
non-universal drops-are analyzed in detail,
especially the dependence of their properties on
inclination angle. Finally, an outlook is given on
two-dimensional drops and front instabilities. },
Author = {Thiele, U. and Neuffer, K. and Bestehorn, M. and Pomeau, Y. and Velarde, M. G.},
DOI = {10.1016/S0927-7757(02)00082-1},
File = {Thie02.pdf:TNBP2002csa-pea.pdf:PDF},
Journal = {Colloids Surf. A - Physicochem. Eng. Asp.},
Pages = {87--104},
Title = {Sliding drops on an inclined plane},
Volume = {206},
Year = {2002}
}
@Article{TNPV2002csa-pea,
Abstract = {The process of dewetting of a thin liquid film is
usually described using a long wave approximation
yielding a single evolution equation for the film
thickness. This equation incorporates an additional
pressure term-the disjoining pressure-accounting for
the effective interaction of the thin film with the
substrate. We use the equation to study the
evolution of unstable thin films examining the
thickness ranges for linear instability and
metastability for flat films, the families of
stationary periodic and localized solutions and
their linear stability. From this we conclude that
within the linearly unstable thickness range exists
a well defined subrange where finite perturbations
are crucial for the time evolution and the resulting
structures. In the remainder of the linearly
unstable thickness range the resulting structures
are controlled by the fastest flat film mode as was
assumed up to now for all the linearly unstable
thickness range. The results are shown for a
disjoining pressure derived by coupling
hydrodynamics to the diffuse interface model and for
disjoining pressures combining destabilizing
[stabilizing] polar shortrange interaction with
stabilizing [destabilizing] apolar long- range
interaction. Finally, the implications for spinodal
decomposition of a binary mixture are discussed. },
Author = {Thiele, U. and Neuffer, K. and Pomeau, Y. and Velarde, M. G.},
DOI = {10.1016/S0927-7757(02)00069-9},
File = {TNPV02.pdf:TNPV2002csa-pea.pdf:PDF},
Journal = {Colloids Surf. A - Physicochem. Eng. Asp.},
Pages = {135--155},
Title = {On the importance of nucleation solutions for the rupture of thin liquid films},
Volume = {206},
Year = {2002}
}
@Article{MBHT2001ct,
Abstract = {A variety of pattern formation phenomena in
catalytic surface reactions can be attributed to the
dynamics of interfaces, or fronts, separating
distinct uniform states. The states may represent
surface coverages by different adsorbates or in the
case of forced oscillations, different phases of
oscillation. The dynamics of fronts are strongly
affected by front instabilities and by diffusion
anisotropy. We identify two new pattern formation
mechanisms associated with different front behaviors
in orthogonal directions: an ordering process by
which stationary labyrinths in an isotropic system
evolve into ordered stationary stripes, and
confinement of isotropic spatiotemporal chaos to one
space dimension, a state we term stratified chaos. },
Author = {Meron, E. and B{\"a}r, M. and Hagberg, A. and Thiele, U.},
DOI = {10.1016/S0920-5861(01)00341-8},
File = {MBHT01.pdf:MBHT2001ct.pdf:PDF},
Journal = {Catal. Today},
Pages = {331--340},
Title = {Front dynamics in catalytic surface reactions},
Volume = {70},
Year = {2001}
}
@Article{ThVN2001prl,
Abstract = {Unstable thin liquid films on solid substrates dewet
by hole nucleation on defects or by a linear surface
instability (spinodal dewetting). A system with
destabilizing short-range and stabilizing long-range
molecular interactions is investigated. We show
that, for a subrange within the linearly unstable
film thickness range, nucleation determines the
final structure, whereas spinodal dewetting is of
negligible influence. The results are also
applicable to the spinodal decomposition of binary
mixtures. },
Author = {Thiele, U. and Velarde, M. G. and Neuffer, K.},
DOI = {10.1103/PhysRevLett.87.016104},
File = {TVN01.pdf:ThVN2001prl.pdf:PDF},
Journal = {Phys. Rev. Lett.},
Pages = {016104},
Title = {Dewetting: {F}ilm rupture by nucleation in the spinodal regime},
Urrl = {http://link.aps.org/abstract/PRL/v87/p016104},
Volume = {87},
Year = {2001}
}
@Article{TVNB2001pre,
Abstract = {Using a film thickness evolution equation derived
recently combining long-wave approximation and
diffuse inter-face theory [L. M. Pismen and
Y. Pomeau, Phys. Rev. E 62, 2480 (2000)] we study
one-dimensional surface profiles for a thin film on
an inclined plane. We discuss stationary flat film
and periodic solutions including their linear
stability. Flat sliding drops are identified as
universal profiles, whose main properties do not
depend on mean film thickness. The flat drops are
analyzed in detail, especially how their velocity,
advancing and receeding dynamic contact angles and
plateau thicknesses depend on the inclination of the
plane. A study of nonuniversal drops shows the
existence of a dynamical wetting transition with
hysteresis between droplike solutions and a flat
film with small amplitude nonlinear waves. },
Author = {Thiele, U. and Velarde, M. G. and Neuffer, K. and Bestehorn, M. and Pomeau, Y.},
DOI = {10.1103/PhysRevE.64.061601},
File = {Thie01.pdf:TVNB2001pre.pdf:PDF},
Journal = {Phys. Rev. E},
Pages = {061601},
Title = {Sliding drops in the diffuse interface model coupled to hydrodynamics},
Urrl = {http://link.aps.org/abstract/PRE/v64/e061601},
Volume = {64},
Year = {2001}
}
@Article{TVNP2001pre,
Abstract = {The process of dewetting of a thin liquid film is
usually described using a long-wave approximation
yielding a single evolution equation for the film
thickness. This equation incorporates an additional
pressure term-the disjoining pressure-accounting for
the molecular forces. Recently a disjoining pressure
was derived coupling hydrodynamics to the diffuse
interface model [L. M. Pismen and
Y. Pomeau. Phys. Rev. E 62, 2480 (2000)]. Using the
resulting evolution equation as a generic example
for the evolution of unstable thin films, we examine
the thickness ranges for linear instability and
metastability for flat films, the families of
stationary periodic and localized solutions. and
their linear stability. The results are compared to
simulations of the nonlinear time evolution. From
this we conclude that. within the linearly unstable
thickness range, there exists a well defined
subrange where finite perturbations are crucial for
the time evolution and the resulting structures. In
the remainder of the linearly unstable thickness
range the resulting structures are controlled by the
fastest flat film mode assumed up to now for the
entire linearly unstable thickness range. Finally,
the implications for other forms of disjoining
pressure in dewetting and for spinodal decomposition
are discussed.},
Author = {Thiele, U. and Velarde, M. G. and Neuffer, K. and Pomeau, Y.},
DOI = {10.1103/PhysRevE.64.031602},
File = {TVNP01.pdf:TVNP2001pre.pdf:PDF},
Journal = {Phys. Rev. E},
Numpages = {14},
Pages = {031602},
Title = {Film rupture in the diffuse interface model coupled to hydrodynamics},
Urrl = {http://link.aps.org/abstract/PRE/v64/e031602},
Volume = {64},
Year = {2001}
}
@Article{BHMT2000pre,
Abstract = {The effects of diffusion anisotropy on pattern
formation in bistable media are studied using a
FitzHugh-Nagumo reactiondiffusion model. A relation
between the normal velocity of a front and its
curvature is derived and used to identify distinct
spatiotemporal patterns induced by the diffusion
anisotropy. In a wide parameter range anisotropy is
found to have an ordering effect: initial patterns
evolve into stationary or breathing periodic stripes
parallel to one of the principal axes. In a
different parameter range, anisotropy is found to
induce spatiotemporal chaos confined to one space
dimension, a state we term "stratified chaos."},
Author = {B{\"a}r, M. and Hagberg, A. and Meron, E. and Thiele, U.},
DOI = {10.1103/PhysRevE.62.366},
File = {BHMT00.pdf:BHMT2000pre.pdf:PDF},
Journal = {Phys. Rev. E},
Pages = {366--374},
Title = {Front propagation and pattern formation in anisotropic bistable media},
Urrl = {http://link.aps.org/abstract/PRE/v62/p366},
Volume = {62},
Year = {2000}
}
@Article{BHMT1999prl,
Abstract = {Numerical simulations of two-dimensional pattern
formation in an anisotropic bistable
reaction-diffusion medium reveal a new dynamical
state, stratified spatiotemporal chaos,
characterized by strong correlations along one of
the principal axes. Equations that describe the
dependence of front motion on the angle illustrate
the mechanism leading to stratified chaos.},
Author = {B{\"a}r, M. and Hagberg, A. and Meron, E. and Thiele, U.},
DOI = {10.1103/PhysRevLett.83.2664},
File = {BHMT99.pdf:BHMT1999prl.pdf:PDF},
Journal = {Phys. Rev. Lett.},
Pages = {2664--2667},
Title = {Stratified spatiotemporal chaos in anisotropic reaction-diffusion systems},
Urrl = {http://link.aps.org/abstract/PRL/v83/p2664},
Volume = {83},
Year = {1999}
}
@InProceedings{TMPW1999,
Note = {Proceedings of the NATO advanced study institute on foams, emulsions and cellular materials, Carg{\`e}se Corsica 5/97},
Adress = {Dordrecht},
Author = {Thiele, U. and Mertig, M. and Pompe, W. and Wendrock, H.},
Booktitle = {Foams and Emulsions},
Editors = {Sadoc, J. F. and N. Rivier},
File = {TMPW99.pdf:TMPW1999.pdf:PDF},
Pages = {127--136},
Publisher = {Kluver Academic Publishers},
Title = {Polygonal networks resulting from dewetting},
Year = {1999}
}
@InProceedings{MKBT1998,
Adress = {Tokyo},
Author = {Mertig, M. and D. Klemm and J. Bradt and U. Thiele and Pompe, W.},
Booktitle = {Proc. 4\textsuperscript{th} Int. Conf. Intelligent Materials},
Editors = {T. Tagaki and M. Aizaiwa and T. Okano and N. Shinya},
Pages = {228--9},
Title = {Controlled pattern formation in thin biomolecular coatings},
Year = {1998}
}
@Article{MTBK1998apa-msp,
Abstract = {We have studied structure formation of thin
monomeric collagen films prepared by spin coating on
hydrophobic highly oriented pyrolytic graphite
substrates. The biomolecular coatings have been
investigated by scanning force microscopy. Pattern
formation takes place as the result of dewetting of
the liquid precursor initiated by pore nucleation in
the drying film. The growth of pores leads to an
accumulation of collagen monomers along the
perimeter of the dry patches formed. Depending on
the evaporation velocity of the solvent, different
well-defined film morphologies have been
observed. The pore radius distribution function
exhibits two well-separated peaks, indicating the
occurrence of two distinct dewetting mechanisms:
heterogeneous pore nucleation and spinodal
dewetting. The distribution function of the pores
initiated by heterogeneous nucleation is analysed in
detail. A model is introduced that captures the main
distribution features depending on humidity.},
Author = {Mertig, M. and Thiele, U. and Bradt, J. and Klemm, D. and Pompe, W.},
DOI = {10.1007/s003390051202},
File = {Mert98.pdf:MTBK1998apa-msp.pdf:PDF},
Journal = {Appl. Phys. A - Mater. Sci. Process.},
Pages = {S565--S568},
Title = {Dewetting of thin collagenous precursor films},
Volume = {66},
Year = {1998}
}
@Article{ThEc1998pre,
Abstract = {We apply stochastic geometry to the transition from
hexagonal to square cells recently observed in
surface-tension-driven B{\'e}nard convection. In
particular we study the metric and topological
evolution of B{\'e}nard patterns as a function of
the temperature difference, Delta T, across the
layer. The preference of square B{\'e}nard cells at
higher Delta T is a consequence of both a higher
efficiency in heat transfer and more favorable
metric properties. Most notably, the perimeterarea
ratio of a square cell exceeds that of a hexagonal
cell by an unexpectedly high value. From a
topological point of view, the B{\'e}nard pattern
obeys the Aboav-Weaire law at all rimes, even in the
presence of threefold and fourfold vertices. The
regimes above and below the transition are
characterized by different topological correlations
between neighboring cells. With the appearance of
fourfold vertices, the topological correlation
changes from negative to positive. },
Author = {Thiele, U. and Eckert, K.},
DOI = {10.1103/PhysRevE.58.3458},
File = {ThEc98.pdf:ThEc1998pre.pdf:PDF},
Journal = {Phys. Rev. E},
Pages = {3458--3468},
Title = {Stochastic geometry of polygonal networks: An alternative approach to the hexagon-square transition in {B\'e}nard convection},
Urrl = {http://link.aps.org/abstract/PRE/v58/p3458},
Volume = {58},
Year = {1998}
}
@PhdThesis{Thiele1998Dresden-phd,
Note = {{PhD}-thesis, Dresden},
Address = {Dresden},
Author = {U. Thiele},
File = {Thiele1998Dresden-phd.pdf:Thiele1998Dresden-phd.pdf:PDF},
Title = {Entnetzung von {K}ollagenfilmen},
Year = {1998}
}
@Article{ThMP1998prl,
Abstract = {Film rupture as the initial stage of dewetting is
investigated for a volatile, spin-coated nonwetting
film. During structure formation in the liquid film
the film thickness is continuously reduced via
evaporation. The dynamical character of the
experiment allows the study of hole formation caused
by distinct rupture mechanisms occurring at
different film thicknesses. Both heterogeneous
nucleation for thick films as well as spinodal
dewetting for him thickness below 10 nm have been
observed. The balance between both processes can be
shifted by controlling the ambient humidity. The
structures resulting from film rupture are
quantified with respect to their different
geometrical properties. For the first time we find
that spinodal dewetting is caused by destabilizing
polar interactions. },
Author = {Thiele, U. and Mertig, M. and Pompe, W.},
DOI = {10.1103/PhysRevLett.80.2869},
File = {TMP98.pdf:ThMP1998prl.pdf:PDF},
Journal = {Phys. Rev. Lett.},
Pages = {2869--2872},
Title = {Dewetting of an evaporating thin liquid film: Heterogeneous nucleation and surface instability},
Urrl = {http://link.aps.org/abstract/PRL/v80/p2869},
Volume = {80},
Year = {1998}
}
@Article{MTBL1997sia,
Abstract = {Monomeric collagen films were prepared by
spin-coating of acidic collagen solutions on
different atomically flat surfaces. The thin
biomolecular coatings have been investigated by
scanning force microscopy. Depending on both the
wetting behaviour and the microtopology of the
substrates used, different film morphologies have
been observed. Collagen monomers cover the surface
of hydrophilic substrates homogeneously, whereas
pore formation due to dewetting processes takes
place at non-structured hydrophobic surfaces. The
size of pores depends on the evaporation velocity of
the solvent during spin-coating. Topological and
metric properties of the resulting networks have
been analysed and compared to soap foam network
structures. },
Author = {Mertig, M. and Thiele, U. and Bradt, J. and Leibiger, G. and Pompe, W. and Wendrock, H.},
DOI = {10.1002/(SICI)1096-9918(199706)25:7/8<514::AID-SIA261>3.0.CO;2-D},
File = {Mert97.pdf:MTBL1997sia.pdf:PDF},
Journal = {Surf. Interface Anal.},
Pages = {514--521},
Title = {Scanning force microscopy and geometric analysis of twodimensional collagen network formation},
Volume = {25},
Year = {1997}
}
@InProceedings{BMWT1996,
Note = {Proc. SPIE 2779},
Abstract = {Two different kinds of collagen assembly have been
studied: The reconstitution of type I collagen to
fibrils and the formation of two dimensional
networks on surfaces. The kinetics of fibril
assembly are influenced by polyaspartate, as
measured turbidimetrically. Addition of
polyaspartate increases the fibril diameter. The
reconstituted fibrils are imaged by atomic force
microscopy and scanning electron microscopy. The
preparation of thin collagen films on highly
oriented pyrolytic graphite leads to networks or
tree like structures depending on the collagen
concentration in the precursor. The results
presented are of interest for the development of new
bone--like implant materials and the covering of
bone grafts with a biocompatible layer. },
Author = {Bradt, J.--H. and Mertig, M. and Winzer, B. and Thiele, U. and Pompe, W.},
Booktitle = {Proceedings of the Third International Conference on Intelligent Materials and Third European Conference on Smart Structures and Materials Lyon June 1996},
Editors = {Gobin, Pierre F. and Tatibou{\"e}t, Jacques},
Pages = {78--82},
Publisher = {SPIE--The International Society for Optical Engineering},
Title = {Collagen assembly from acid solution to networks on solid surfaces and to fibrils},
Year = {1996}
}
@Article{ThDi1995pla,
Abstract = {We introduce a two-level procedure for the
description of the DLA-cluster. It starts from the
overall structure of the DLAaggregates and moves
down to a description in terms of a finger
structure. For both levers we assume the same law
for the density of aggregation. Comparison of the
two descriptions leads to an estimation of the
fractal dimension D. },
Author = {Thiele, U. and Diener, G.},
DOI = {10.1016/0375-9601(95)00657-O},
File = {ThDi95.pdf:ThDi1995pla.pdf:PDF},
Journal = {Phys. Lett. A},
Pages = {365--369},
Title = {A simple phenomenological estimation of the fractal dimension of {DLA}-clusters},
Volume = {206},
Year = {1995}
}
@PhdThesis{Thiele1994-diploma,
Note = {diploma-thesis},
Author = {U. Thiele},
File = {Thiele1994-diploma.pdf:Thiele1994-diploma.pdf:PDF},
Title = {Zur Theorie von DLA-Clustern},
Year = {1994}
}
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