A model for Marangoni drying

Abstract

We propose a simple theoretical model for the movement of a thin liquid film on a flat plate that is vertically withdrawn from a large liquid reservoir in the presence of a surface tension gradient. This problem is relevant to Marangoni drying - a technique that is used in the semiconductor industry for the purpose of water removal from wafers. Due to the smallness of the capillary number the fluid flow can be described by the classical Landau-Levich equation with an additional term accounting for the Marangoni effect. A numerical solution of this equation shows that the thickness of the residual film is a monotonically decreasing function of the surface tension gradient, thereby providing an explanation of the Marangoni drying process. © 1999 American Institute of Physics.