Solutions to the equations for the kinetics of coagulation

The theory for the kinetics of coagulation of particles in Brownian motion is reviewed briefly. The relationship between the classical solution of Smoluchowski and the similarity solution to the kinetic equation is discussed. When the classical result is placed in the form of the similarity solution, a simple exponential expression results. In spite of the theoretical limitations, this expression for Smoluchowski's relation can be used to predict satisfactorily a substantial range of the size distribution which has a similar or a self-preserving form.