The graph shows how the half-life decreases with size and concentration. (For a given volume fraction the number increases as the size decreases.)

Fig.10.10: Half life of coagulation vs volume fraction for different particles sizes (a).

Radius of colloidal particle is of the order of 1μm. Thus and . This is an idea for the time required for rapid coagulation.

The simple Smoluchowski approach has its short-comings and limitations. The process of coagulation is described as the annihilation of particles by diffusion-controlled collision with other particles, without consideration for different particle sizes. The practical reason for this approach was that at that time data (Zsigmondy’s study) only contained numbers of particles without discrimination with respect to size. Another problem is that only doublet formation is counted and further formation of doublets and triplets etc is not considered. Smoluchowski recognized this and formulated a more general treatment of evolving multiplet formation later.