Electrophoretic mobility of a spherical colloidal particle
The equations which govern the ion distributions and velocities, the electrostatic potential and the hydrodynamic flow field around a solid colloidal particle in an applied electric field are reexamined. By using the linearity of the equations which determine the electrophoretic mobility, we show that for a colloidal particle of any shape the mobility is independent of the dielectric properties of the particle and the electrostatic boundary conditions on the particle surface. The mobility depends only on the particle size and shape, the properties of the electrolyte solution in which it is suspended, and the charge inside, or electrostatic potential on, the hydrodynamic shear plane in the absence of an applied field or any macroscopic motion.
New expressions for the forces acting in the particle are derived and a novel substitution is developed which leads to a significant decoupling of the governing equations. These analytic developments allow for the construction of a rapid, robust numerical scheme for the solution of the governing equations which we have applied to the case of a spherical colloidal particle in a general electrolyte solution. We describe a computer program for the conversion of mobility measurements to zeta potential for a spherical colloidal particle which is far more flexible than the Wiersema graphs which have traditionally been used for the interpretation of mobility data. Furthermore it is free of the high zeta potential convergence difficulties which limited Wiersema's calculations to moderate values of ζ. Some sample computations in typical 1:1 and 2:1 electrolytes are exhibited which illustrate the existence of a maximum in the mobility at high zeta potentials. The physical explanation of this effect is given. The importance of the mobility maximum in testing the validity of the governing equations of electrophoresis and its implications for the colloid chemist's picture of the Stern layer are briefly discussed.