Transient inertial hydrodynamic interaction between two identical spheres settling at small Reynolds number

Abstract

The flow pattern generated by a sphere accelerated from rest by a small constant applied forceshows scaling behaviour at long times, as can be shown from the solution of the linearized Navier–Stokes equations. In the scaling regime the kinetic energy of the flow grows with thesquare root of time. For two distant settling spheres starting from rest the kinetic energy ofthe flow depends on the distance vector between centres; owing to interference of the flowpatterns. It is argued that this leads to relative motion of the two spheres. Thecorresponding interaction energy is calculated explicitly in the scaling regime.