The steady propagation of a surfactant-laden liquid plug in a two-dimensional channel

Abstract

In this study, we investigate the steady propagation of a liquid plug in a two-dimensional channel lined by a uniform, thin liquid film. The liquid contains soluble surfactant that can exist both in the bulk fluid and on the air-liquid interface. The Navier-Stokes equations with free-surface boundary conditions and the surfactant transport equations are solved using a finite volume numerical scheme. The adsorption/desorption process of the surfactant is modeled based on pulmonary surfactant properties. As the plug propagates, the front meniscus sweeps preexisting interfacial surfactant from the precursor film, and the surfactant accumulates on the front meniscus interface. As the front meniscus converges on the precursor film from the region where the interfacial surfactant concentration is maximized, the Marangoni stress opposes the flow. In this region, the Marangoni stress results in nearly zero surface velocity, which causes the precursor film thickness near the meniscus to be thicker than the leading film thickness. Since the peaks of wall pressure and wall shear stress occur due to narrowing of the film thickness, the observed increase of the minimum film thickness weakens these stresses. In the thicker film region, however, the drag forces increase due to an increase in the surfactant concentration. This causes the overall pressure drop across the plug to increase as a result of the increasing surfactant concentration. A recirculation flow forms inside the plug core and is skewed toward the rear meniscus as the Reynolds number increases. When no surfactant exists, the recirculation flow is in contact with both the front and the rear interfaces. As the surfactant concentration increases, the Marangoni stress begins to rigidify the front interface and forces the recirculation flow away from the front interface. Subsequently, the recirculation flow is directed away from the rear interface in a manner similar to that for the front interface. When the plug length is shorter, this change in recirculation pattern occurs at a smaller surfactant concentration.