Spin coating and air-jet blowing of thin viscous drops

Abstract

Using the lubrication approximation we investigate the spreading of a finite-sized thin drop of incompressible Newtonian fluid on a planar substrate subjected to a jet of air blowing normally to the substrate. Three specific problems are studied in detail: a jet of air acting normally to the substrate when gravity effects are negligible, a jet of air directed vertically downward onto a sessile drop on a horizontal substrate, and a jet of air directed vertically upward onto a pendent drop on a horizontal substrate. The dynamics of the moving contact line are modeled by means of a generalized “Tanner Law” relating the contact angle to the speed of the contact line. Both symmetric two-dimensional and axisymmetric three-dimensional geometries are considered; the latter case is equivalent to that of an axisymmetric drop spreading on a substrate rotating with constant angular velocity (the simplest model for spin coating). Quasistatic solutions for the drop profile are obtained in the limit of small capillary number and the stability of equilibrium solutions to small perturbations is determined. The analysis is then extended to include drops with a dry patch at their center which are found to be unconditionally unstable in all the cases investigated.