Coupling Between a Viscoelastic Gas/Liquid Interface and a Swirling Vortex Flow

Abstract

While the structure and dynamics of boundary layers on rigid no-slip walls in rotation dominated enclosed flows are still an area of active research, the interactions between rotating or swirling flows with a free surface have received comparatively less attention. For the most part, investigations in this area have been focused on clean free surfaces, which may be treated as stress-free. However, in most practical situations the surface is rarely clean, and even under laboratory conditions, it is quite difficult to achieve a clean free surface. Most impurities in liquids are surface active, and hence the name surface active agent or surfactant. These surfactants tend to establish an equilibrium surface concentration which alters the interfacial tension and interfacial viscoelastic properties of the gas/liquid interface. The coupling between the bulk swirling flow and the interface is provided via the tangential stress balances, and these stresses on the interface are dependent upon the surface concentration of surfactant, which in turn is altered by the interfacial flow. Forces acting on the interface include surface tension gradients (elastic) and the viscous resistance to shear and dilatation. These viscoelastic properties vary with the surfactant concentration on the surface. Here, we present numerical studies of flow in a cylinder driven by the constant rotation of the bottom endwall with the top free surface being contaminated by a Newtonian surfactant. Comparisons with a clean free surface and a no-slip stationary top endwall provide added insight into the altered dynamics that result from the presence of a small amount of surfactant.