A thin-film equation for a viscoelastic fluid, and its application to the Landau-Levich problem

TL;DR

This paper derives a new thin-film equation for viscoelastic fluids and applies it to the Landau-Levich problem, revealing how viscoelasticity influences film thickness and resolving existing literature discrepancies.

Contribution

The paper introduces the first thin-film equation for second-order viscoelastic fluids and demonstrates its application to classical coating problems.

Findings

Viscoelasticity affects the film thickness in dip-coating.

The derived equation explains discrepancies in previous studies.

Viscoelastic effects are significant in industrial coating processes.

Abstract

Thin-film flows of viscoelastic fluids are encountered in various industrial and biological settings. The understanding of thin viscous film flows in Newtonian fluids is very well developed, which for a large part is due to the so-called thin-film equation. This equation, a single partial differential equation describing the height of the film, is a significant simplification of the Stokes equation effected by the lubrication approximation which exploits the thinness of the film. There is no such established equation for viscoelastic fluid flows. Here we derive the thin-film equation for a second-order fluid, and use it to study the classical Landau-Levich dip-coating problem. We show how viscoelasticity of the fluid affects the thickness of the deposited film, and address the discrepancy on the topic in literature.