Approximate analytic expressions are derived for the electrophoretic mobility of spheroidal particles (prolate and oblate) carrying low zeta potential in an electrolyte solution under an applied tangential or transverse electric field. The present approximation method, which is based on the observation that the electrophoretic mobility of a particle is determined mainly by the distortion of the applied electric field by the presence of the particle. The exact expression for the equilibrium electric potential distribution around the particle, which can be expressed as an infinite sum of spheroidal wave functions, is not needed in the present approximation. The electrophoretic mobility values calculated with these approximate expressions for spheroidal particles with constant surface potential or constant surface charge density are in excellent agreement with the exact numerical results of previous reports with the relative errors less than about 4%.

中文翻译：

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球状粒子电泳迁移率的近似解析表达式

在施加的切向或横向电场下，在电解质溶液中携带低 zeta 电位的球形颗粒（扁长和扁圆形）的电泳迁移率得到了近似解析表达式。本近似方法是基于观察到粒子的电泳迁移率主要由粒子的存在引起的施加电场的畸变决定的。在目前的近似中不需要粒子周围的平衡电势分布的精确表达式，它可以表示为球面波函数的无限和。