Slow viscous stream over a non-Newtonian fluid sphere in an axisymmetric deformed spherical vessel

Abstract

The creeping motion of a non-Newtonian (Reiner-Rivlin) liquid sphere at the instant it passes the center of an approximate spherical container is discussed. The flow in the spheroidal container is governed by the Stokes equation, while for the flow inside the Reiner-Rivlin liquid sphere, the expression for the stream function is obtained by expressing it in the power series of a parameter S , characterizing the cross-viscosity. Both the flow fields are then determined explicitly by matching the boundary conditions at the interface of Newtonian fluid and non-Newtonian fluid, and also the condition of imperviousness and no-slip on the outer surface. As an application, we have considered an oblate spheroidal container. The drag and wall effects on the liquid spherical body are evaluated. Their variations with regard to the separation parameter l , viscosity ratio \( \lambda\), cross-viscosity S, and deformation parameter \( \varepsilon\) are studied and demonstrated graphically. Several renowned cases are derived from the present analysis. It is observed that the drag not only varies with \( \varepsilon\), but as l increases, the rate of change in behavior of drag force also increases. The influences of these parameters on the wall effects has also been studied and presented in a table.