Inertial effects in thin film drainage

Abstract

Intertial effects during the drainage of thin uniform Newtonian fluid under the influence of a normal force are considered. An analytical solution from the Hermite transformed Navier-Stokes equation neglecting the vertical component of the fluid velocity is obtained under quasi-steady state conditions when one or both surface of the film are immobile. This may be reduced to simpler solutions involving only pressure and either inertial or viscous effects. The analytical solution agrees well with the numerical solution of the Navier—Stokes equation including the vertical component of the fluid velocity when the initial approach velocity corresponds to the quasi-steady state conditions. The three solutions are identical at small and large times for all values of the parameter P (which allows for the physical properties, film radius, initial thickness, normal force and mobility of the surface). At intermediate values of time, the analytical solution predicts slower drainage rates that the numerical solution at small values of P and faster rates at large values of P.