Reduction of edge beading defects on rectangular substrates using a rotation about an axis perpendicular to the spin axis

Here, we consider the coating dynamics of a binary liquid on a rectangular substrate that both spins and rotates about an axis perpendicular to the spin axis. This rotation causes not only a force parallel to the substrate but a large normal force on the horizontal region of the substrate, known as elevated gravity. This force not only smooths out any irregularities in the film, it also causes an increase in the evaporation rate, resulting in a higher viscosity, which in turn decreases the thinning of the coating due to centrifugal forces. We derive the lubrication form of the governing equations for such a geometry that includes surface tension and body forces acting on the liquid due to the spinning and rotation of the substrate, as well as viscosity changes and surface tension gradients due to evaporation of the volatile component. The resultant coupled nonlinear differential equations are solved numerically using an efficient alternating direction implicit method. The numerical results indicate that the rotation can reduce edge beading defects for parameters typically employed by the spin coating industry. It is particularly effective for small average coating thicknesses, where it can almost eliminate edge beading. Surface tension gradients, which act in the post rotation dry phase, can also further affect edge beading, particularly in the corner regions.