The effect of the Coriolis force on axisymmetric rotating thin film flows

Abstract

The axisymmetric flow of a thin Newtonian fluid layer subject to centrifugal and Coriolis forces, surface tension and gravity is considered. Employing lubrication theory the mathematical problem is reduced to the solution of a fourth-order nonlinear partial differential equation for the film height, which requires solving numerically. At the moving contact line a precursor film model is adopted. Once the film height is known other quantities, such as fluid velocities and pressure may be easily determined. Of particular interest, is the fact that, within the restrictions of lubrication theory the Coriolis term in the radial velocity equation is of the same order as the inertia terms and is therefore negligible. This means the velocity equations are not fully coupled and, when the flow is axisymmetric, the Coriolis force has no effect on the height of the fluid film.