Clarification of a Common Misunderstanding of Collision Frequencies in the Smoluchowski Equation

Abstract

Flocculation is universally modeled on the basis of the seminal work of M. von Smoluchowski. The key equation is a particle number balance that expresses the net rate of formation of particles of a given type as the difference between the rate at which such particles are formed by collisions of smaller particles and the rate at which they are destroyed by collisions with other particles to form larger ones. The equation is commonly presented in a concise form in which the rates of formation and destruction of particles of a given size are each represented by a single summation containing the term