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

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.

Automated summary

Thin-film flows of viscoelastic fluids play an important role in both industrial and biological applications. While there is a well-developed understanding of thin viscous film flows in Newtonian fluids, the study of thin-film flows of viscoelastic fluids is still relatively limited. In this paper, we derive the thin-film equation for a second-order fluid and apply it to investigate the Landau-Levich dip-coating problem, shedding light on the influence of viscoelasticity on the thickness of deposited films and addressing discrepancies in existing literature.