Electrical and convective polarization of the cylindrical macroions

The calculation of the dipole moment induced in the ion atmosphere of a cylindrical macroion is divided into two parts: first, the polarization in the absence of relative motion between the macroion and the solvent, and second, the convective polarization due to the relative, electrophoretic motion. The first calculation is carried through, for longitudinal and transverse polarizations of counterions and co-ions, according to the variational procedure described in the preceding paper [M. Fixman, J. Chem. Phys. 75, 4040 (1981)]. The convective polarization is further divided into two contributions: first, the polarization that would result from a constant relative motion (equal to the macroscopic electrophoretic velocity), and second, the correction due to the decrease in relative velocity in the vicinity of the macroion surface. The second convective contribution is estimated to be relatively small unless the cylinders are long compared to the Debye length. Longitudinal polarization of the counterions is not large compared to co-ion polarization, or to transverse polarization of co-ions and counterions, unless the cylinder is long compared to the Debye length. Otherwise, the outer parts of the ion atmosphere make the dominant contributions and are quite susceptible to convective effects.