Theoretical and numerical results for spin coating of viscous liquids

• Published in: Physics of fluids (1994) 2004-03, Vol.16 (3), p.569-584
• Main Authors: Schwartz, Leonard W., Roy, R. Valery
• Format: Article
• Language: English
• ISSN: 1070-6631; 1089-7666
• DOI: 10.1063/1.1637353

A mathematical model is developed for fluid flow in the spin coating process. Spin coating employs centrifugal force to produce coatings of uniform thickness. The long-wave or lubrication approximation is used for the flow of thin liquid layers that are exposed to the air and lie on a spinning horizontal solid substrate. For low rotation rates, steady axisymmetric drop shapes can be found analytically. The stability of these drops is investigated, using an energy method, both with and without the long-wave approximation. For industrially relevant high-speed motions, we formulate and solve a theoretical and numerical model for the three-dimensional time-dependent motion of the deforming drop. We pay particular attention to the formation of “fingers” at the expanding front. The model includes viscous, capillary, gravitational, centrifugal, Coriolis, and finite-contact-angle effects. Both homogeneous and chemically heterogeneous substrates are considered. In agreement with published experiments, the model demonstrates that imperfect wetting behavior is the principal cause of fingering during spin coating. Features of the finger profiles are in close agreement with experimental observations.