Electrophoresis of rods

Abstract

The electrophoresis of a long, rod-shaped particle of length 2l is studied. The surrounding equilibrium charge cloud is given by the linearized Poisson-Boltzmann equation, and relaxation of the cloud is ignored: the analysis is therefore similar to that of Henry. The charge cloud is assumed thick compared with the radius of the rod, but is otherwise unrestricted. When the cloud is large compared with the length of the rod, its presence may be ignored and the direct electric force on the particle balances the hydrodynamic drag. A correction due to the cloud is obtained. End effects are negligible when the double layer is thin compared with the rod length, and Henry's results are valid. Numerical computations give results for intermediate values of the Debye length κ^–1. The asymptotic results are good when κ^–1 > 10l or κ^–1 < 0.1l.