Shear-driven arrest of dip-coating film entrainment

Abstract

A plate withdrawn from a bath of partially wetting liquid entrains a film above a critical velocity. Here, we show that this critical threshold can be substantially increased by the presence of a laminar gas flow opposed to the plate velocity that exerts a tangential shear stress on the liquid-gas interface. Using two-phase immiscible Navier-Stokes simulations and confining the gas to a narrow channel, we derive a closed-form expression for the interfacial stress, which combined with lubrication theory relates the thickness of the film and the contact line velocity to the applied shear stress. As the gas velocity is increased, the film thins and the contact line velocity slows down, until the imposed shear overcomes the drag of the moving plate and entrainment is arrested. As in the quiescent case, the velocity mismatch between plate and contact line is independent of the plate velocity and is set by the applied shear alone. We find that one set of varying gas flow simulations, with constant critical plate velocity, therefore determines the critical gas flow for every smaller plate velocity.