786 THE MECHANISM OF AGGLUTINATION 



trostatic. Substituting the viscosity of water and the dielectric constant at 20° C. 

 and changing to millivolts, the formula becomes 



.... , Ai per second 



p.D. in miliivolts= 13 



Volts per centimeter 



This formula was derived on the assumption that each particle acts like a small 

 condenser and is surrounded by a Helmholtz double layer. The charge on the particle 

 as a whole, including the film of liquid, is, therefore, zero. A potential difference exists, 

 however, between the two oppositely charged layers, and it is between these layers 

 that the motion occurs. It follows that the value for the dielectric constant of the 

 liquid between the two layers should be inserted in the formula. There is no way of 

 determining this value, however, so that the dielectric constant of the pure liquid is 

 generally used. It has been found by numerous investigators that this formula is ex- 

 perimentally correct so far as it concerns the relation between the rate of migration 

 and the impressed e.m.f., or the viscosity.' There is, however, no evidence concerning 

 the correctness of the actual value of the potential calculated from the velocity. It 

 was shown by Hardy that the size of the particles was without effect on the observed 

 motion, which also agrees with the theory. 



The theory of Helmholtz and Lamb gives us no information as regards the origin 

 of this potential difference, and no satisfactory theory has been suggested up to the 

 present. It has been shown by Haber and Klemensiewicz- that the cataphoretic 

 potential is not the same as the Nernst electrode potential. This has been ascribed 

 by von Smoluchowski to the fact that the p.d. between the interior of the particle and 

 the liquid is the Nernst potential, whereas the cataphoretic p.d. is between the mova- 

 ble and fixed films. 



Freundlich^ has shown that the discrepancy may be accounted for by assuming 

 that the double layer is of appreciable thickness and that the electrode potential is 

 the total potential across the entire double layer while the electrokinetic potential is 

 that across a part of the layer. Burton"" has suggested that the thickness of this double 

 layer may be affected by the electrolytes present in accordance with the Gouy-Debye 

 theory. This point of view accounts for the effect of the valence and concentration of 

 the electrolyte on the potential and hence on the stability of the suspension. 



McTaggart's experiments with air bubbles and Lenard's measurements of water- 

 fall electricity indicate that the source of the potential may be entirely in the film of 

 liquid surrounding the particle. ^ 



Wilson,'' on the other hand, suggested that the p.d. was due to a Donnan equilib- 

 rium, and Loeb' has found that there is some analogy between the two but that 

 quantitatively they are different. This point of view has been followed by Winslow, 

 Falk, and Caulfeild, who were able to show that the migration of bacteria was similar 



' Burton, E. F.: op. cit., p. 137. 1921. 



^ Freundlich, H. : op. cil., p. 341. Leipzig, 1922. 



i Freundlich, H.: Colloid. Symp., 3, 7. 1925. t Burton, F. F.: ibid., 4, 132. 1926. 



5 Cf. Loeb, J.: J. General Physiol., 5, 515. 1922-23. 



''Wilson, J. A.: /. Am. CItcm. Sac, 8, 19S2. 1916. 'Loeb. J.: he. cit. 



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