Slot coating flows with a Boussinesq–Scriven viscous interface

Abstract

We present a computational study of free surface flows with rheologically complex interfaces in the film formation region of a slot coater. The equations of motion for incompressible Newtonian liquids in the bulk flow are coupled with the Boussinesq–Scriven constitutive equation for viscous interfaces in the dynamic boundary condition at the liquid-air free surface and solved with a mixed finite element method. We show that the interfacial viscosity plays a major role in the flow dynamics and operating limits of slot coating. We find that the interfacial viscosity makes viscous interfaces generally stiffer than their simple counterparts, affecting both the normal and the tangential stress jumps across the free surface. As a result, the interfacial viscosity counteracts the meniscus retraction and slows down the film flow, increasing the development length over the substrate and changing the topology of the recirculation region in the coating bead. Remarkably, we also find that the interfacial viscosity can substantially broaden the operating boundaries of the coating window associated with the low-flow limit, suggesting that surface-active components can be suitably designed to allow for the stable production of thinner films at higher speeds by tuning interfacial material properties in slot coating applications.