Spin-coating of vertically stratified thin liquid films

Abstract

Spin-coating is a process used to fabricate thin films for device applications. In this paper, lubrication theory is used to derive an axisymmetric model for the spin-coating of two immiscible vertically stratified Newtonian thin films. The model includes gravitational, van der Waals, capillary and viscous forces, differences in liquid layer properties and evaporation/condensation effects. Thinning calculations focus on the effects of viscosity and condensation/evaporation. In this case, for layers of uniform thickness, the lower layer thins monotonically yet never reaches zero thickness. With evaporation mass loss the upper layer disappears in finite time, whereas with condensation effects the upper layer approaches a steady-state thickness. Fully nonlinear calculations are carried out for films with non-uniform thickness and the deviation of the interfaces from the flat state is monitored. In general, disturbances to the lower layer have a greater effect on the upper layer than those of disturbances of the upper layer on the lower layer. Disturbances along the upper gas–liquid free surface propagate outward more rapidly than those along the lower liquid–liquid interface and disturbances that decrease the film thickness tend to dissipate more slowly.