Stratified biphasic dip coating flows on permeable substrates

Abstract

The present work models dip coating flows on saturated porous substrates in a biphasic configuration wherein two immiscible Newtonian liquids are simultaneously entrained. The model accounts for the effect of substrate permeability through a modified Navier slip boundary condition. New scaling laws have been derived for the two interface heights in the no-slip and strong-slip limits. Numerical solutions to the mathematical model predict that the presence of outer liquid reduces the effect of slip experienced by the inner liquid in the biphasic configuration when compared with slip effects in the monophasic configuration. This reduction of wall-slip effect is found to be amplified by increasing the interfacial tension between the two fluids. Moreover, the inner film thickness becomes independent of substrate surface permeability at high values of capillary number. Interestingly, the substrate permeability induces thickening effect on the outer liquid film at high values of permeability factor and a more viscous outer liquid. Process regime maps for inner and outer liquid film thickness as a function of permeability factor, withdrawal speed, and viscosity ratio have also been constructed.