Interaction of two rigid spheres translating collinearly in a couple stress fluid

Abstract

Abstract This paper considers the steady translational motion of two collinear rigid spheres in an incompressible couple stress fluid. The two spheres are assumed to be of different sizes and are moving with two different speeds along a line axis connecting their centers. First, the general solution for the steady motion of an incompressible couple stress fluid past an axially symmetric particle is obtained analytically in the form of an infinite series. Second, the obtained solution is employed to construct the general solution for the steady motion of a couple stress fluid flow past two translating spheres using the principle of superposition. The boundary collocation technique is then used to satisfy the imposed boundary conditions on the surfaces of the two spheres. The normalized drag force acting on each of the two spherical particles is evaluated and presented numerically through tables and graphs. The tabulated results show that the convergence of the numerical results is achieved rapidly. In addition, it is observed that the increase in the couple stress viscosity parameter increases the values of the normalized drag force on each of the spherical particles.