Modelling Pattern Formation in Dip-Coating Experiments

TL;DR

This paper reviews mathematical models of pattern formation in dip-coating and Langmuir-Blodgett transfer experiments, emphasizing gradient dynamics formulations and comparing hydrodynamic and phenomenological approaches.

Contribution

It provides a comprehensive comparison of models based on free energy functionals, highlighting their structure and relation, and discusses implications and open issues in the field.

Findings

Models successfully describe pattern formation across nanometre to micrometre scales.

Gradient dynamics formulation clarifies the governing principles of pattern evolution.

Comparison reveals the strengths and limitations of hydrodynamic versus phenomenological models.

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.