Electrophoretic motion of two solid particles embedded in an unbounded and viscous electrolyte

This work determines the electrophoretic motion of two colloidal particles embedded in a viscous and unbounded electrolyte. Contrary to other works in the field, the advocated method does not calculate the perturbation electric potential and the electrolyte Stokes flow in the whole fluid domain and its range of applications is not restricted to the case of uniformly charged particles embedded in a uniform electric field E_∞. The idea consists in establishing and solving thirteen Fredholm boundary integral equations (one of the second kind plus twelve of the first kind). The numerical implementation is briefly reported. Numerical benchmarks and new results are both presented and discussed with a special attention to the interactions between the particles.