General methodology to evaluate two-particle hydrodynamic friction inside cylinder-bound viscous fluid

This article presents a new method to describe creeping motion of two-particle system in quiescent fluid confined in a conduit. The analysis is specifically focused on two spheres in cylinder-bound viscous fluid where both interparticle and particle–wall flow interactions are significant. We quantify these interactions by the spatial variation of friction tensors relating motion-defining quantities like translation or rotation of each sphere with motion-inducing quantities like force or torque on them.The key component of the methodology is solving Stokes equation with no-slip condition at disconnected dissimilar surfaces—the cylinder and the spheres. Accordingly, the Stokesian fields are expanded in separable basis solutions for both cylindrical and spherical coordinates so that conditions at both conduit and particle can be enforced properly. This enables us to evaluate friction coefficients associated with different pairs of motion-defining and motion-inducing quantities representing different flow-conditions in a general class of problems. Thus, the results can be used to calculate force and torque on the particles with specified motion for their arbitrary radial positions, axial separation and azimuthal orientation.