Hydrodynamic interaction between two rotating spheres in an incompressible couple stress fluid

Abstract

This paper focuses on the study of the hydrodynamic interaction between two rotating spheres in an incompressible couple stress fluid. The two spheres are assumed to rotate steadily about the line of their centers with different angular velocities. The general solution for the steady motion of an incompressible couple stress fluid past an axisymmetric particle is obtained analytically in the form of an infinite series. The principle of superposition is utilized to construct the general solution for the steady motion of a couple stress fluid past two rotating spheres using two moving spherical coordinate systems with origins located at the centers of the two spheres. The boundary collocation method is employed to satisfy the imposed boundary conditions on the spherical boundaries. The torque experienced by the fluid on each of the spherical objects is evaluated and represented numerically through tables and graphs. The tabulated results show that the convergence is rapid. In addition, the numerical results show that the increase in the couple stress viscosity parameter increases the values of the normalized torque on each of the two spheres.