Electrokinetic effects in charged capillary tubes

Abstract

The electrokinetic phenomenological coefficients in a narrow tube filled with electrolyte solution and with a surface charge due to ionizable groups are calculated. The calculation holds for stationary, laminar flow of Newtonian fluids and (at least) within the domain of validity of the linearized Poisson–Boltzmann equation. Our formulae become identical to those given by Helmholtz in the limit of pores which are large compared with the Debye–Hückel length κ^–1. The reciprocity relation of Onsager is shown by hydrodynamic and electrostatic arguments to be strictly fulfilled even for an arbitrary cross-section with an arbitrary charge distribution.