The effects of inertia and interfacial shear on film flow on a rotating disk

Abstract

In this paper the issue is addressed of how a liquid film of uniform thickness thins on a rotating disk because of the action of centrifugal force. The Navier–Stokes equations in self-similar form are solved numerically by a finite-difference method. The effects of film inertia, disk acceleration protocols, and interfacial shear are studied. The numerical results show that inertia has a marked influence on the rate of thinning when the Reynolds number is large and that existing asymptotic theories are inadequate for predicting the transient film thickness. When the disk has a finite acceleration at start-up, the effects of local inertia are important even at low Reynolds numbers and the thinning rate is reduced. When the overlying phase is a gas, interfacial shear enhances the rate of thinning at sufficiently long spinning times.