A Lubrication Model of Coating Flows over a Curved Substrate in Space

# A Lubrication Model of Coating Flows over a Curved Substrate in Space

## Abstract

Consider the 3D flow of a viscous Newtonian fluid upon a curved substrate when the fluid film is thin as occurs in many draining, coating and biological flows. We derive a model of the dynamics of the film, the model being expressed in terms of the film thickness $\eta$ and the curvature tensor of the substrate. The model accurately includes the effects of the arbitrary curvature of the substrate, via a physical multiple-scale approach, and gravity and inertia, via more rigorous centre manifold techniques. Numerical simulations exhibit generic features of the dynamics of such thin fluid films.

## Authors

R. Valery Roy
Dept of Mechanical Engineering, University of Delaware, USA
A J Roberts
Dept. Mathematics & Computing, University of Southern Queensland, Toowoomba, Queensland 4350, Australia
M E Simpson
Dept. Mathematics & Computing, University of Southern Queensland, Toowoomba, Queensland 4350, Australia