On the maximum of the magnitude of the electrophoretic mobility of a spherical colloidal particle in an electrolyte solution

The magnitude of the electrophoretic mobility mu of a spherical colloidal particle in an electrolyte solution with kappa a > 3 (kappa = the Debye-Huckel parameter of the electrolyte solution and a = particle radius), when plotted as a function of the particle zeta potential zeta, exhibits a maximum mu (max) at zeta = zeta (max). Analytic expressions applicable for large kappa a (kappa a a parts per thousand yenaEuro parts per thousand 30) are derived for mu (max) and zeta (max) for a spherical particle in a symmetrical electrolyte solution. Analytic expressions for mu (max) and zeta (max) are also derived for a spherical particle in a 2:1 or 1:2 electrolyte solution. Finally, it is to be noted that mu (max) and zeta (max) for a cylindrical particle of radius a when the particle is oriented perpendicular to the applied electric field are the same as those for a spherical particle of radius a for large kappa a (kappa a >= 30).