A New Analytical Formulation for the Electrophoretic Mobility of a Colloidal Sphere

Abstract

A new analytical equation for the electrophoretic mobility of a colloidal sphere, homogeneously charged, is derived. This equation reduces to the well-known Henry’s formulation for low surface potentials. For high surface potentials, the equation is compared to the full numerical result. It is found that the equation performs well up to surface potentials of 50 mV. For larger surface potentials, the equation performs well for 𝜅𝑎>10, where 𝜅 is the inverse of Debye’ s length and a the radius of the particle. Differences between analytical and numerical solutions for 𝜅𝑎<10 are studied. The case of a particle with a constant surface charge is discussed. In that case, a very simple equation relates the surface charge of the particle to the electrophoretic mobility for 𝜅𝑎>10.