8oo THE MECHANISM OF AGGLUTINATION 



noted that in Powis' experiments with oil drops there was no coalescense of the drops. 

 There is no change in the oil-water surface, therefore, and hence it cannot be the oil- 

 water surface tension which draws the drops together. Whatever force is active must 

 reside in the surface film surrounding the drop, since it is these films that coalesce. 

 There is no evidence of molecular contact of the particles. 



THE VELOCITY OF COAGULATION 



The changes in a coagulating suspension or sol take place relatively slowly, and 

 complete coagulation may require several hours. The change in the potential on the 

 addition of the electrolyte, however, is almost instantaneous, at least in the suspen- 

 sions of bacteria studied by the writer and also in Powis' experiments. The time ele- 

 ment, therefore, consists in the time required for two or more particles to meet and 

 stick together. Von Smoluchowski' has been able to derive a formula for the rate of 

 this reaction based on the probability of collision of the particles. He assumes, as did 

 Zsigmondy, that the particles are uncharged and that the collisions are inelastic, i.e., 

 every collision between two particles results in the formation of an aggregate of two 

 particles. This leads to the equation 



* = l(i-fj=47rZ> 



in which Vo is the number of particles present at the beginning, ^v the number present 

 at time /, D the diffusion coefficient, and r the distance between the particles at which 

 they are attracted. It is assumed, further, that this is not much greater than twice 

 the radius of the particles. It may be noted that the formula is the same as that for 

 a bimolecular reaction, with the exception that all collisions are considered as leading 

 to combination, whereas, as is known, such an assumption will not hold with respect 

 to chemical reactions. The theory predicts the experimental results accurately, as was 

 found by Westgren and Reitstotter and by Kruyt and van Arkel.^ 



In the foregoing derivation it was assumed that the particles possessed no repul- 

 sive force. This is the condition at the isoelectric point. Experimentally, however, 

 it is known that agglutination occurs when the particles are slightly charged. Under 

 these conditions it might be supposed that only those particles having sufficient kinet- 

 ic energy would be able to approach one another within the "attraction sphere." The 

 coagulation would be, therefore, slower but eventually would become complete, as is 

 the case. Freundlich-' has taken this effect into account and derived a complete for- 

 mula which correctly predicts the course of the coagulation. 



In certain cases — "slow coagulation" — the rate curve resembles that of an auto- 

 catalytic reaction.4 According to von Smoluchowski, this is a secondary phenomenon. 

 It seems possible that this effect is due to a slow change in the potential. It was found 

 by Powis, for instance, that there was a very rapid change in the potential immediate- 

 ly on the addition of the electrolyte. This was followed, however, by a second slow 



' von Smoluchowski, M . : loc. cit. 



2 Freundlich, H.: Kapillarchemic (2d ed.), p. 596. Leipzig, 1922. 



3 Freundlich, H.: KoUoid-Ztschr., 23, 163. 1918. 

 '•Lottermoser, A.: ibid., is, 145. 1914. 



