The Effect of surfactant on the drag and wall correction factor of a drop in a bounded medium

Abstract

Abstract In the present article, the analytical solution for creeping motion of a drop/bubble characterized by insoluble surfactant is examined at the instant it passes the center of a spherical container filled with Newtonian fluid at low Reynolds number. The presence of surfactant characterizes the interfacial region by an axisymmetric interfacial tension gradient and coefficient of surface dilatational viscosity. Under the assumption of the small capillary number, the deformation of spherical phase interface is not taken into account. The computations not only yield information on drag force and wall correction factor, but also on interfacial velocity and flow field for different values of surface tension gradient and surface dilatational viscosity. In the limiting cases, the analytical solutions describing the drag force and wall correction factor for a drop in a bounded medium reduces to expressions previously stated by other authors in literature. The results reveal the strong influence of the surface dilatational viscosity and surface tension gradient on the motion of drop/bubble. Increasing the surface tension gradient and surface dilatational viscosity, results in linear variation of drag force. When the surface tension gradient increases, the drag force for unbounded medium increases more as compared to the bounded medium hence wall correction factor decreases with increase in surface tension gradient whereas it increases with increase in surface dilatational viscosity.