Dip coating in the presence of an opposing Marangoni stress.

Theoretical analysis of the dip coating process of uniformly wetting and selectively wetting substrates with a shear-thinning power-law fluid is presented. The viscosity is modeled by a three-constant Ellis model that allows for Newtonian and power-law fluids at low and high shear, respectively. The effect of an opposing Marangoni stress is studied on the entrained film thickness. Ellis number and Marangoni number are the important parameters in the analysis that control the film thickness. Numerical results show that the film thickness is a monotonically decreasing function of these two parameters. A correlation between the parameters is found for both the surfaces to obtain an apparent "dry" substrate with a microscopically thin film attached to the surfaces.