Zeta Potential General Theory for Spherical Particles

5 ZETA POTENTIAL GENERAL THEORY FOR SPHERICAL PARTICLES 

It is apparent from the above sections that the understanding of electrophoretic mobility involves both the phenomena of fluid flow as discussed in Chapter 4 and the double-layer potential as discussed in Chapter 11. In both places we see that theoretical results are dependent on the geometry chosen to describe the boundary conditions of the system under consideration. This continues to be true in discussing electrophoresis, for which these two topics are combined. As was the case in Chapters 4 and 11, solutions to the various differential equations that arise are possible only for rather simple geometries, of which the sphere is preeminent. 

4 The domain within which most investigations of aqueous colloidal systems lie in terms of particle radii and 1 1 electrolyte concentration. The diagonal lines indicate the limits of the Hiickel and the Helmholtz-Smoluchowski equations. (Redrawn with permission from J. Th. G., Overbeek, Quantitative Interpretation of the Electrophoretic Velocity of Colloids. In Advances in Colloid Science, Vol. 3 (H. Mark and E. J. W. Verwey, Eds.), Wiley, New York, 1950.) 

By assuming that the external field - deformed by the presence of the colloidal particle-and the field of the double layer are additive, D. C. Henry derived the following expression for mobility  

We return to the solution of the Poisson-Boltzmann equation for a spherical particle, Equation (19), with B = 0  

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