Modelling Pattern Formation in Dip-Coating Experiments

Wilczek Markus, Tewes Walter B.H., Gurevich Svetlana V., Köpf Michael H., Chi Lifeng, Thiele Uwe

Abstract

We briefly review selected mathematical models that describe the dynamics of pat-tern formation phenomena in dip-coating and Langmuir-Blodgett transfer experiments, wheresolutions or suspensions are transferred onto a substrate producing patterned deposit layers withstructure length from hundreds of nanometres to tens of micrometres. The models are presentedwith a focus on their gradient dynamics formulations that clearly shows how the dynamics isgoverned by particular free energy functionals and facilitates the comparison of the models. Inparticular, we include a discussion of models based on long-wave hydrodynamics as well as ofmore 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 discussedbefore we conclude with a discussion of implications of the gradient dynamics formulation andof some related open issues.