Coating thickness prediction for a viscous film on a rough plate

TL;DR

This paper introduces a homogenization-based predictive model for liquid film thickness on rough plates during dip coating, accounting for surface roughness effects without fitting parameters, and validated against experiments.

Contribution

The novel model accurately predicts coating thickness on rough surfaces using homogenization, incorporating slip and permeability effects, applicable to arbitrary periodic textures.

Findings

Model agrees well with experimental data

No fitting parameters needed for predictions

Applicable to various roughness patterns

Abstract

Surface roughness significantly modifies the liquid film thickness entrained when dip coating a solid surface, particularly at low coating velocity. Using a homogenization approach, we present a predictive model for determining the liquid film thickness coated on a rough plate. A homogenized boundary condition at an equivalent flat surface is used to model the rough boundary, accounting for both flow through the rough texture layer, through an interface permeability term, and slip at the equivalent surface. While the slip term accounts for tangential velocity induced by viscous shear stress, accurately predicting the film thickness requires the interface permeability term to account for additional tangential flow driven by pressure gradients along the interface. We find that a greater degree of slip and interface permeability signifies less viscous stress that would promote deposition, thus reducing the amount of free film coated above the textures. The model is found to be in good agreement with experimental measurements and requires no fitting parameters. Furthermore, our model may be applied to arbitrary periodic roughness patterns, opening the door to flexible characterization of surfaces found in natural and industrial coating processes.