Thus diffusion coefficient is independent of particle size. Solving this differential equation (10.18) we can get concentration as a function of time. Initial concentration can be taken as N_o. Applying this as initial condition and solving it we get

(10.22)

From this equation we can get half life for coagulation as

(10.23)

Experiments are done in volume fraction so it would be better to write t_1/2 in terms of volume fraction.

Volume fraction of particle                                                           (10.24)

Substituting No from equation (10.24) in equation (10.23) we get t_1/2 in volume fraction.