ELECTROPHORESIS OF SLENDER PARTICLES

The hydrodynamic theory of slender bodies is used to model electrophor etic motion of a slender particle having a charge (zeta potential) tha t Varies with position along its length. The theory is limited to syst ems where the Debye screening length of the solution is much less than the typical cross-sectional dimension of the particle. A stokeslet re presentation of the hydrodynamic force is combined with the Lorentz re ciprocal theorem for Stokes flow to develop a set of linear equations which must be solved for the components of the translational and angul ar velocities of the particle. Sample calculations are presented for t he electrophoretic motion of straight spheroids and cylinders and a to rus in a uniform electric field. The theory is also applied to a strai ght uniformly charged particle in a spatially varying electric field. The uniformly charged particle rotates into alignment with the princip al axes of del E(infinity); we suggest that such alignment can lead to electrophoretic transport of particles through a small aperture in an otherwise impermeable wall. The theory developed here is more general than just for electrophoresis, since the final result is expressed in terms of a general 'slip velocity' at the surface of the particle. Th us, the results are applicable to diffusiophoresis of slender particle s if the proper slip-velocity coefficient is used.