Main scientific interest
My present main interest is the
interface-dominated dynamics of complex liquids and soft matter, i.e.,
the influence of capillarity, wettability and/or internal structural
forces on dynamical processes like, dewetting, deposition,
crystallisation, phase separation, etc.. This includes active
(biologically inspired) media.
Examples are (driven) droplets on homogeneous and
heterogeneous substrates; surface-active substances, e.g., in
Langmuir-Blodgett transfer; (active) liquid crystals; colloidal (nano)particle
suspensions and polymer solutions; self-propelled droplets; and
multilayer fluid systems. Related side interests include epitaxial
growth, crystallisation dynamics and gelation processes; the dynamics of phase
transitions; ratchet-driven transport in nano- and micro-fluidic
systems; dynamics of wetting transitions of binary and ternary systems;
An important objective is to understand the structure forming interaction of the
various interdependent advective and diffusive transport processes, phase
transitions and possibly chemical reactions. On
this basis one may successfully control the pertinent experimental
systems and technological applications from coating and printing
processes to bottom-up nanostructuring and micro- (and nano-)fluidics.
The various systems are investigated employing and developing
analytical and numerical tools of
nonlinear science. To facilitate students to enter the field early on
(even with their Bachelor theses) we are building up the
Münsteranian Torturials - set of hands-on tutorials on nonlinear science (numerical
path-following and time-stepping methods, analytical methods - slowly
but continuously progressing)
website under "Lehre", then "Münsteranian Torturials" (direct link)
Scientific disciplines and model types
Many of the individual systems are situated in the twilight zone
between physics, biology, chemistry and the engineering sciences and
are described with methods of Theoretical Physics, Chemical and
Biological Physics, Applied Mathematics, including non-equilibrium and
equilibrium thermodynamics and statistical physics, physico-chemical
hydrodynamics, surface science and nonlinear science.
The aim to understand soft matter systems on mesoscopic scales is
pursued through the application, further development and analysis of a
variety of microscopic stochastic discrete and microscopic and mesoscopic
deterministic continuum descriptions. Examples include kinetic Monte Carlo
models, Molecular Dynamics approaches, phase field and phase field
crystal models, Dynamical Density Functional Theory and mesoscopic
Analytical and Computational Approach
As the investigated effects are rather complex and the models
are nonlinear, the reach of analytical approaches is limited. Analytically,
one may study the linear and marginal stability of
trivial steady and stationary states and of selected non-trivial ones; asymptotic
methods often allow to determine the solution structure far away
from the interesting transitions; and bifurcation theory allows
for studies very close to some of the transitions.
The analytical work is accompanied by large-scale computations
performed on systems ranging from standard laptops, to graphic cards
(CUDA framework), and High Performance Parallel Computing
systems. Numerical algorithms we develop and employ include standard
finite difference methods or exponential propagation methods for
the time stepping of ODE and PDE; pseudo arclength path
continuation methods to determine steady and stationary states,
and time-periodic space-dependent states. We also work on micro-meso hybrid
methods, e.g., by matching Molecular Dynamics / (D)DFT and mesoscopic
hydrodynamics for nano-droplets on solid substrates.
There exist collaborations with a number of experimentally and theoretically
working groups at Departments of Mathematics, Physics, Chemical and
Mechanical Engineering of various institutions as, for example, at the
University of California at Berkeley,
Technische Universität Berlin,
Université Libre de Bruxelles,
Université Joseph Fourier Grenoble,
Hong Kong University of Science and Technology,
University of Manchester,
École Polytechnique Paris,
Finally, I list some particular systems/effects I am interested in. The
related studies can by found on the publication page under the numbers given at the
end of the particular point.
I distinguish emerging subjects where we are in the
stage of literature study, preliminary calculations, or proposal
writing; fully active subjects about which we published
recently or plan to publish soon; and past subjects that we
were very interested in in the past, but do at the moment (nearly) not work on
- Dynamics of drops and films of nematic liquid crystals [79,80], liquid crystals close to
- Films of active liquids, dynamics of adhesion/locomotion, tissue spreading
- Large-scale continuation techniques for multi-field long-wave
- Phase-field crystal models for crystalisation in evaporating suspensions
- Dynamics of wetting transitions of binary and ternary systems
- Phase Field Crystal models for one- and
two-component colloidal systems and their relation to standard model
equations for pattern formation (Swift-Hohenberg Equation) [69,71,76]
- Dynamical models for bacterial carpets [88,p17,97], biofilms  and active
- Hybrid micro-meso models for contact lines of simple and complex
liquids, e.g., via parameter passing from Molecular Dynamics  or
Density Functional Theory [94,105] to mesoscopic hydrodynamics
. Also comparison of Kinetic Monte Carlo and mesoscopic
- Patterned deposition in Langmuir-Blodgett transfer (substrate mediated
condensation) [66,89], dip coating [93,103] and for drying suspensions and solutions [53,62,70]. Partial
reviews in [84,93].
- Morphological Transitions of Sliding Drops - Dynamics and Bifurcations .
- Thermodynamic consistent description of the dynamics of
free-interface films with solutes or surfactants (cases of high concentration,
phase separating surfactants, nearby solid surface) [64,72,81,92,102],
applied to experiment e.g., in [78,96].
- (Dynamical) Density Functional Theory for drops at walls
[82,94,105], driven interacting colloidal particles in nano-pores
, cluster coarsening , solidification fronts [91,p16],
- Depinning of driven drops:
Various depinning mechanisms (Hopf vs. sniper vs. homoclinic bifurcation) [35,36,49,51,55,61,73]. Relation to drops on rotating cylinder [58,98].
- Structure formation in films of fluids or diffusing molecules:
Competition of different ruture mechanisms in the dewetting of simple
liquids -- spinodal dewetting vs. nucleation [8,9,13,21,55]; the
long-wave Marangoni instability [19,22];
effects of evaporation [52,65,90]; relation to epitaxial growth
; dragged films and dynamic wetting transitions [85,86]; ridge
instabilities [20,95,106]; terrassed spreading .
- Application of path-continuation methods to (active) fluid and soft matter
systems , singularity solutions , tutorials on CeNoS website
- Transport in nano-pores:
Depinning transitions for and ratcheting of driven interacting colloidal particles in heterogeneous nano-pores 
- Dewetting of polymer mixtures:
Coupling of decomposition of mixture and evolution of film surface profile [41,48,59,68]
- Dewetting of nanoparticle suspensions:
Deposition patterns resulting from the process of evaporative dewetting of a nanoparticle suspension [40,44-46,53,57] or a macromolecular solution [2-4]. Theory: kinetic Monte Carlo [40,45,46], Dynamical Density Functional theory [50,53], Thin film hydrodynamics [53,62,64,70].
- Climbing vibrated droplets:
Analysis of a self-ratcheting mechanism [54,56,74] and other vibration
effects on thin film flow . Relation to Fokker-Planck description
for particle ratchets . See also the Overview (in german) in the
Physik Journal of February 2013 [p12].
- Electric field induced interfacial instabilities [29,38,43,51,67];
Ratchet-induced micro-fluidic transport [38,43,56]
- Dynamic domain formation in membranes: Thickness modulation
induced phase separation .
- Film instability and flow on heated substrates:
Long-wave Marangoni instability on horizontal [19,22] and inclined
 substrates. Instability modes, non-linear structures,
coarsening. As well some interest in heterogeneously heated substrates [16,17].
- Reactive surfactants:
Interaction of thin film hydrodynamics and reaction-diffusion system [37,39,42].
- Chemically driven running droplets:
Several models for different experimental settings [23,30].
- Sliding droplets, falling films and front instabilities:
Dynamic wetting transition in a precursor film model [10,14], front instabilities , drops and films on a heated plate  and the validity domain of the Benney equation .
- Wetting of textured surfaces .
- Dewetting of two-layer films:
Different rupture and coarsening pathways [26,28,34,54].
- Two-layer films in a closed geometry:
Various linear instabilities, non-linear behaviour and coarsening .
- Film flow on a porous substrate:
Various linear instability and non-linear behaviour in their dependence on porosity and layer thickness .
- Dewetting of ultrathin films of simple liquids on heterogeneous horizontal
substrates, including influence of noise, and stabilisation of Plateau
Rayleigh instability by the heterogeneity [15,20]
- Reaction-Diffusion systems: Surface reactions on anisotropic
- Dewetting of thin film of aqueous collagen solution [2-4].
- Stochastic geometry of polygonal networks applied to
the hexagon-square-transition in Rayleigh-Bénard convection 
For more information move mouse over picture. Click on picture to obtain corresponding paper.
Binary Phase Field Crystal model
Depinning of driven colloidal particles
Evaporative dewetting of nanoparticle suspension
Gradient dynamics formulations for layers of solutions/suspensions
Depinning ridges and drops
Front snaking in Langmuir-Blodgett transfer close to a phase transition