Two-layer spin coating flow of Newtonian liquids: A computational study

Spin coating is the most commonly used method in industries to form coating films of desired thickness and functionality. In case of two-layer spin coating process, stratified layers of two immiscible liquids are deposited onto the substrate simultaneously, which spread and thin to form two-layer coating film of finite thickness. Questions concerning the effect of surface/interfacial tension on uniformity of these films and contact line evolution are relevant and need thorough investigation. Therefore, an axisymmetric model governing the flow of two-layer spin coating process is developed here. Liquids used for the study are assumed to be Newtonian and fully wetting. The contact line singularity is resolved using a precursor layer model and the governing equations are simplified using lubrication approximation. A Galerkin finite-element method (G/FEM) based scheme is developed to solve the resulting fourth order non-linear PDEs. Simulation results reveal that the fluid properties like ratio of the viscosity of upper layer fluid to lower layer and ratio of the upper gas-liquid surface tension to inner liquid-liquid interfacial tension have profound impact on the time evolution of the film profile, contact radius and shape of the capillary ridges. It is observed that a uniform two-layer film surrounded by thin single layer film is formed when the viscosity ratio is small. On the contrary, when viscosity ratio is large, a thin two-layer film surrounded by bulky capillary ridges is formed. Similarly, the results also show that sharpness of capillary ridge increases with decrease in the surface tension ratio. Further, it is found that increase in the precursor layer thickness increases the spreading rate, thereby making the film more uniform. Finally, the uniformity of the final two-layer film does not get affected by the initial volume of fluid present in the upper layer.