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 μ of a spherical colloidal particle in an electrolyte solution with κa > 3 (κ = the Debye-Hückel parameter of the electrolyte solution and a = particle radius), when plotted as a function of the particle zeta potential ζ, exhibits a maximum μmax at ζ = ζmax. Analytic expressions applicable for large κa (κa ≥ 30) are derived for μmax and ζmax for a spherical particle in a symmetrical electrolyte solution. Analytic expressions for μmax and ζmax are also derived for a spherical particle in a 2:1 or 1:2 electrolyte solution. Finally, it is to be noted that μmax and ζmax 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 κa (κa ≥ 30).