Effect of insoluble surfactants on the motion of Reiner–Rivlin fluid sphere in a spherical container with Newtonian fluid

Abstract

The problem of flow past fluid spheres was first solved by Rybczynski and Hadmard where they had assumed both the flow field to be Newtonian. However, there are many practical cases where one or both of these immiscible fluids are non-Newtonian. One such case of importance is emulsions, where the non-Newtonian droplets are in the Newtonian liquid. To facilitate studies in this area, we present a systematic investigation on the motion of a Reiner–Rivlin fluid sphere(drop) contaminated with a monomolecular layer of surfactant film and dispersed in a spherical container having Newtonian fluid. The effect of surfactants is taken into account by the thermodynamic approach, which assumes a linear difference in the surface tension from the equilibrium value. The interfacial tension gradient caused by the surfactant adsorption at the drop surface generates surface forces exerted within the boundary region of the drop. The effect of the variable interfacial tension induces the Marangoni flow which causes the motion of the neighboring liquids by viscous traction and generates the Marangoni force which acts on the drop surface. The result shows that the drag force increases with the non-Newtonian cross-viscous parameter of the drop. The normalized force also increases with non-Newtonian cross-viscous parameter and when the Reiner–Rivlin viscous forces dominate the Newtonian viscous forces, which is offset in the presence of surface tension gradient forces. Further, as the surface tension gradient and non-Newtonian cross-viscous parameter of non-Newtonian fluid increases, the motion inside the drop slows down. The center of the internal circulation vortex migrates in Reiner–Rivlin fluid drop toward its center, when the Reiner–Rivlin viscous forces dominates the Newtonian viscous forces.