Abstract
The present work examines the effect of substrate surface porosity on the coating thickness and meniscus profile during dip coating under saturated porous media conditions. The classical Landau-Levich formulation is modified by encoding the influence of porosity in an effective Navier slip boundary condition at the porous substrate surface. It is shown that simplified Navier slip-based model works well for creeping flow through the porous medium. The film height profile equation is derived as a function of a rescaled capillary number (Ca‾) and a substrate permeability factor, with inertial effects neglected. Numerical solutions show that the classical 2/3rd power dependence of film thickness on capillary number is recovered only at sufficiently high Ca‾ values. As Ca‾ is decreased, a marked deviation is seen. The shrinking of the entrainment meniscus and the change in meniscus curvature are analyzed in detail. The theoretical results are also validated with a suitable experimental system.
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