A treatment for contaminated interfaces and its application to study the hydrodynamics of a spherical bubble contaminated by surfactants

Abstract

A numerical model for the contaminated interface is discussed, and then it is applied to investigate detailedly the interfacial surfactant concentration, the interfacial properties and the wake flow of a contaminated spherical bubble. For the present model, the surfactant molecules adsorbed on the bubble surface are assumed to be distributed over the concentration boundary layer adjacent to the bubble. The thickness of concentration boundary layer is obtained through the revised value from a theoretical formula. Then, the interfacial surfactant concentration is evaluated by coupling the transport equations of interfacial and bulk surfactant concentrations with the Navier-Stokes equations. The connection between the tangential stress and the interfacial surfactant concentration is set through the Marangoni stress and the state equation. The current results show that the present numerical model is reliable. The convention from the main flow, the Marangoni effect and the wake vortex determine the distribution of interfacial surfactant concentration on the bubble surface. The gradient of interfacial surfactant concentration along the bubble surface further affects the interfacial properties which react on the surrounding flow as feedbacks. The gradient of interfacial surfactant concentration at the front edge of the “contaminated” interface (FECI) is closely related to the location of FECI to the strongest convection position in the bulk around the bubble. The peak point on the curves of tangential stress and interfacial vorticity corresponds to the inflection point on the curve of interfacial surfactant concentration. The vortex size is affected by the positive pressure gradient at the bubble rear in bulk and the abrupt change of interfacial vorticity at FECI.