Approximate analytic expression for the electrophoretic mobility of a cylindrical colloidal particle. Relaxation effect

An approximate expression is derived for the electrophoretic mobility μ _⊥ of an infinitely long cylindrical particle of radius a and zeta potential ζ oriented perpendicular to an applied electric field in an electrolyte solution. The obtained expression is applicable for cylinders with large radii such that κa≥ca. 30, where κ is the Debye–Hückel parameter. It is shown that the obtained mobility expression μ _⊥, which consists of Smoluchowski’s equation and the correction term of the order of exp(ze∣ζ∣/2kT)/κa (where z is the valence of counterions in the electrolyte solution, e is the elementary electric charge, k is Boltzmann’s constant, and T is the absolute temperature), coincides with the mobility expression for a sphere of radius a and zeta potential ζ correct to the order of exp(ze∣ζ∣/2kT)/κa.