Enhanced Dip Coating on a Soft Substrate

TL;DR

This paper develops a dip-coating model for soft substrates, revealing a new softness-dependent regime for liquid film thickness influenced by elastocapillary effects, with potential implications for soft material applications.

Contribution

It introduces a novel dip-coating model incorporating elastocapillary coupling on soft substrates, identifying a new power-law regime for film thickness at small capillary numbers.

Findings

Discovered a new softness-dependent power-law regime for film thickness.

Identified the crossover point where substrate deformation affects film formation.

Provided numerical and asymptotic analysis of the elastocapillary dip-coating process.

Abstract

A solid, withdrawn from a liquid bath, entrains a thin liquid film. This simple process, first described by Landau, Levich and Derjaguin (LLD), is commonly observed in everyday life. It also plays a central role in liquid capture by animals, and is widely used for surface-coating purposes in industry. Motivated by the emerging interest in the mechanics of very soft materials, and in particular the resulting elastocapillary coupling, we develop a dip-coating model that accounts for the additional presence of a soft solid layer atop the rigid plate. The elastic response of this soft layer is described by a Winkler's foundation. Using a combination of numerical, scaling and asymptotic-matching methods, we find a new softness-dependent power-law regime for the thickness of entrained liquid at small capillary number, which corresponds to a modified physics at play in the dynamic meniscus. The crossover between this regime and the classical dip-coating one occurs when the substrate's deformation is comparable to the thickness of the entrained liquid film.