International Journal of Mathematics and Mathematical Sciences
Volume 2004 (2004), Issue 43, Pages 2279-2298

The fluid profile during spin-coating over a small sinusoidal topography

M. A. Hayes1 and S. B. G. O'Brien2

1Department of Mathematics, National University of Ireland, Galway, Ireland
2Department of Mathematics and Statistics, University of Limerick, Limerick, Ireland

Received 15 August 2003

Copyright © 2004 M. A. Hayes and S. B. G. O'Brien. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


We consider spin-coating over a small sinusoidal topography modelling the physical problem of the coating of a television screen. This involves depositing a phosphor layer on a substrate with a precoating consisting of small parallel striations. Despite the fact that the basic flow is radial, we show that the final liquid coating does not have radial variation; rather, it varies according to the underlying topography. We use a thin film model resulting in an evolution equation for the fluid thickness and sketch several techniques for obtaining approximate solutions in appropriate limiting situations.