Modelling Pattern Formation in Dip-Coating Experiments

¹ Institute for Theoretical Physics, University of Münster, 48149 Münster, Germany
² Département de Physique, École Normale Supérieure, 75005 Paris, France
³ Physical Institute, University of Münster, 48149 Münster, Germany
⁴ Center for Nonlinear Science (CeNoS), University of Münster, 48149 Münster, Germany
⁵ Center for Multiscale Theory and Computation (CMTC), University of Münster 48149 Münster, Germany

^⋆ Corresponding author. E-mail: markuswilczek@uni-muenster.de

Abstract

We briefly review selected mathematical models that describe the dynamics of pattern 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.