Stokes flow of an incompressible couple stress fluid confined between two eccentric spheres

The quasi-steady translational motion of an incompressible couple stress fluid confined between two eccentric spherical surfaces is investigated. It is assumed that the motion is generated by allowing the internal sphere to translate with a constant velocity. The Stokesian assumption of low Reynolds numbers is considered so that the nonlinear terms of the equation of motion are neglected. The superposition principle is employed to construct the general solution of the governing equations in the presence of spherical surfaces using two spherical systems of coordinates relative to the centers of the two spherical surfaces. The no-slip boundary conditions on the spherical boundaries are applied. In addition, the conditions of vanishing couple stresses on the bounding surfaces are imposed. The boundary collocation technique is utilized numerically to satisfy the boundary conditions on the spherical surfaces. The drag force experienced by the fluid flow on the spherical particle is obtained and represented numerically through table and graphs. The numerical results show that the values of the drag force increases monotonically with the increase in the radii ratio. It increases also with the increase of the couple stress viscosity parameter. The obtained results are consistence with the results available in the literature for viscous fluids.(c) 2021 Elsevier Masson SAS. All rights reserved.

Automated summary

This study investigates the quasi-steady translational motion of an incompressible couple stress fluid confined between two eccentric spherical surfaces. The drag force experienced by the fluid flow on the spherical particle is numerically obtained and represented through tables and graphs. The results show that the drag force increases monotonically with the increase in the radii ratio and the couple stress viscosity parameter.