Approximate analytic expressions for the electrophoretic mobility of spherical colloidal particles and the conductivity of their dilute suspensions

An approximate analytic expression is obtained for the electrophoretic mobility of a spherical colloidal particle in a symmetric electrolyte solution. This expression includes, consistently to order 1/κa(where κ is the Debye–Hückel parameter and a is the particle radius), all correction terms to Smoluchowski's formula and is found to be in good agreement with the exact computer calculation by the method of O'Brien and White (J. Chem. Soc., Faraday Trans. 2, 1978, 74, 1607). On the basis of this expression a semi-empirical formula with relative errors < 1% for κa 10 is derived. The same approximation method is employed to obtain a large κa approximate expression for the conductivity of a dilute suspension of spherical colloidal particles.