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

## TL;DR

This paper presents a new analytical equation for calculating the electrophoretic mobility of a charged colloidal sphere, which works well under various surface potential and particle size conditions.

## Contribution

The paper introduces a novel analytical formulation that extends Henry’s equation for higher surface potentials and specific particle conditions.

## Key findings

- The new equation aligns with Henry’s formulation for low surface potentials.
- It performs well for surface potentials up to 50 mV and for κa > 10.
- A simple equation links surface charge to electrophoretic mobility for κa > 10 in constant surface charge cases.

## 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.