Modelling thin–film flow over a spinning disk #

Laura Milne, Alexander W Wray, Omar K Matar, Marc Pradas, Stephen K Wilson

10:30 Tuesday in 4Q08.

Part of the Thin films and contact lines session.

Abstract #

Film flows on spinning disks have a wide range of applications in industry, including, heat and mass transfer, where the waves generated create an increase in the surface area of the film which tend to augment transfer processes. Furthermore, the dynamics of the flow tend to lead to increased mixing, which can be beneficial in chemical production. Therefore, it is important to understand the dynamics of such flows so that we can optimise conditions for production. In this presentation, we study the dynamics of a thin, axisymmetric film of Newtonian fluid on a uniformly rotating disk with topography. The system is modelled via a thin–film (i.e. a lubrication) approximation together with the Method of Weighted Residuals [1]. The resulting model includes the effects of inertia, viscosity, centrifugation and capillarity. We obtain a closed initial value problem for the film thickness, and the radial and azimuthal fluxes which we solve numerically; this system shows convective instability. We use an integral measure of the free surface to allow us to compare the effects of different topographies. In particular, we find that the addition of topography can cause additional interfacial waves which can increase the surface area of the film.

[1] Ruyer-Quil C, Manneville P. Improved modeling of flows down inclined planes. The European Physical Journal B – Condensed Matter and Complex Systems. 2000;15(2):357–69.