﻿306 Profs. J. N. Mukherjee and B. C. Papaconstantinou on 



concentrations. This was assumed to prove that the radius 

 of attraction reached a maximum value. 



Smoluchowslu utilized this idea of a sphere of action 

 to avoid a consideration of the forces that influence the 

 coalescence. He considers the probability of particles 

 coming within their mutual sphere of action when the 

 radius of the sphere has a constant value determined by 

 the conditions. It is assumed that as soon as a particle 

 comes within the sphere of attraction by virtue of its 

 Brownian movement the two particles coalesce. This dis- 

 continuous view of the obviously continuous process of 

 coalescence was assumed to avoid a consideration of the 

 nature and distribution of the forces that are present. 



Considering the effect of the motion of each particle 

 and also that each of the aggregates acts as a condensation 

 centre, he derives the following equations : 



2» = ^p , (l) 



^=~°TV 2 , (2) 



K) 



(a.n .t) k l ". 



^.(S^" • .... (3) 



where ' ; w " denotes the total number of particles originally 

 present per unit volume before coalescence begins. They 

 are all assumed to be spherical and equal in size. u t '•' is 

 the time in seconds that has elapsed since the electrolyte 

 and the sol have been mixed. " T " is a constant charac- 

 teristic of the rate of coagulation and is given by 



T = ^Tr.D.Ka.V ^ 



where "D"* is the diffusion constant as given by Einstein's 

 equation; a = 4.7r.D.Ra, and Ra is the radius of the 

 sphere of action. 



TT 9 1 



* 1) = ^ =77— — ■■- , where 11= the gas constant, 



1 ° )7r • V •> S = the absolute temperature, 



N =Avogadro's number, 

 »7 = the viscosity, 

 and r= radius of the pavticle. 



