LAUSR

A theory of free coating of a Newtonian liquid on a plate is developed based on scaling analysis of the flow. The analysis addresses the flow in the apical portion of the meniscus, where the film is entrained, and also of the bulk liquid conveyed from pool depths up to the surface. Film thickness as well as the characteristic curvature of the meniscus is predicted as a function of the capillary number Ca and the non-dimensional parameter Po=μ(g∕ρσ3)1∕4. No term in the Navier-Stokes equations is arbitrarily neglected; thus, the theory is valid virtually for any Ca and Po. The theory entails two adjustable constants, determined by least-squares fitting with the experimental data of Kizito et al. [“Experimental free coating flows at high capillary and Reynolds number,” Exp. Fluids 27, 235 (1999)]. However, once determined, these constants are to be considered as “universal” for free-coating on a plate. Rich thickness-vs-Ca behavior as a function of Po is predicted with a steep ascent of thickness at a certai...