Orthokinetic collisions of hard spheres in simple shear flow

From the rigorous hydrodynamic interaction theory of a pair of neutral hard spheres of radius b in a viscous fluid undergoing simple shear flow, the two-body collision theory has been developed which corrects the classical Smoluchowski theory based on rectilinear approach by applying the modern rigorous (and experimentally verified) curvilinear theory of approach. The difficulties in defining a collision are eliminated by defining a curvilinear collision sphere of radius ρm around a reference sphere. In this way correction factors for the area of the collision cross-section, the collision frequency, the average doublet life time, and the steady-state doublet concentrations of separating (or transient) doublets have been calculated as a function of ρm. The results show that the two theories are compatible for a ρm/b close to 2.38.