Slip boundary conditions and the hydrodynamic effect on diffusion controlled reactions

Abstract

Approximate calculations of the hydrodynamic effect on diffusion controlled reaction rates yield finite corrections to the Smoluchowski law. However, exact calculations using hydrodynamics with stick boundary conditions have the unsatisfactory feature of predicting a vanishing coagulation rate. In this paper it is demonstrated that this failure of the theory is due to the stick boundary conditions. It is shown that hydrodynamic calculations with slip boundary conditions yield a finite coagulation rate. The exact slip hydrodynamics result indicates a reduction of 29% in the coagulation rate of neutral particles relative to the classical Smoluchowski theory. This is a smaller result than the 46% reduction predicted by the approximate Deutch–Felderhof theory for particles with stick boundary conditions.