HYDRODYNAMIC INTERACTIONS BETWEEN TWO SPHERICAL PARTICLES.

A study is made of hydrodynamic interactions between two spherical particles immersed in an incompressible fluid. An extended mobility matrix relates the translational and rotational velocities of the two particles, in addition to their symmetric force dipole moments, to the forces, torques and the strain fields due to an incident flow. We derive an efficient scheme from which the elements of the extended mobility matrix may be evaluated as series expansions in powers of the inverse centre-to-centre distance. A few hundred coefficients may easily be evaluated numerically and lead to accurate results, even at very small distances. The two particles may have different radii and different structure. The theory applies to hard spheres with mixed slip-stick boundary conditions, as well as to permeable spheres and spherical fluid droplets.