Creeping flow of couple stress fluid past a fluid sphere with a solid core

Abstract

AbstractThe steady axisymmetric uniform flow of an incompressible couple stress fluid past a fluid sphere with a solid core has been studied analytically. No‐slip boundary condition and vanishing couple stress condition are applied on the surface of the sphere. The problem is formulated using the V. K. Stokes equation describing the flow outside the fluid sphere as well as the flow inside the fluid sphere. The stream function solution for the axisymmetric motion and pressure distribution for both regions are solved explicitly. The stresses acting on the fluid sphere are estimated and the drag force experienced by a fluid sphere is determined. Numerical study is undertaken to study the effect of couple stress parameter and viscosity coefficients on the drag and the results are presented in graphical forms. The results reveal that drag force, pressure and velocity of the fluid decreases in the presence of couple stresses. Some special cases of flow past a fluid sphere have been validated with earlier well‐known cases.