I70 ATOMS, IONS, SALTS, AND SURFACES 



millivolts for the droplet in question. The potential </> obtained by the use of the 

 equation of Stokes is always 3/2 the fictitious zeta (f) potential usually given in 

 books on colloid chemistry. 



According to the relations given above: (i) the effective ionization (A^) of a col- 

 loidal particle varies directly as its radius. (2) The effective ionization per unit area 



A^\ 



— ) varies inversely as the radius of the particle, and therefore directly as the curva- 

 ture of the surface. (3) The potential for the particle is independent of the radius. 

 Therefore the potential is the same for all spherical particles of the same material in 

 any certain solution. (4) The effective ionization (N) and the potential (</>) depend 

 upon the nature of the particle and upon the nature of the medium in which it is 

 suspended. 



The Helmholtz-Lamb equation for the velocity in cataphoresis is 



<f)rXD I 



v= -.. 



4 TTT? a 



Here D, -q, and d refer respectively to the dielective constant, viscosity, and thickness 

 of the electrical double layer, / is the coefficient of slip, and X is the impressed 

 potential gradient. Smoluchowski simplified this equation to 



4x7? ■ 

 If 77 is taken to be the viscosity of the solution and not of the double layer, 



v=- -, 



or 



^~ Wx 



gives the value of the fictitious zeta potential, so 



The equations give the potentials in electrostatic units. The value of in volts is 

 given by 



= 67r -^ y,X (300)2 volts . 



According to Debye and Hiickel, the constant of the Helmholtz-Lamb-Smolu- 

 chowski equation should be bir for spherical particles. On this basis the value of 

 f should be equal to that of 0. 



POTENTIAL AND STABILITY' 



According to the theory of Hardy, the stability of a colloidal suspension is de- 

 pendent upon the electrical repulsion of the charges of like sign upon the particles. 



' Cf. also chaps, xlii and Iviii in this volume. 



