Transient Electro‐osmosis in Capillary Tubes

TLDR: In this paper, the authors considered the transient response of a glass capillary tube to a step change in either pressure or voltage under various external loading conditions, and the resulting time histories of the induced force (voltage or pressure) and the fluid flow and electrical current were solved for.

Abstract: Transient electro‐osmosis of water in glass capillary tubes is treated analytically. The usual selective ion adsorption mechanism is assumed. The analysis is restricted to tube radii greater than about 3 × 10−5 m for which the effects of fluid compressibility and electrical capacitance and inductance are negligible. The problem considered is the transient response of the system to a step change in either pressure or voltage under various external loading conditions. The resulting time histories of the induced force (voltage or pressure) and the fluid flow and electrical current are solved for. A Laplace transform technique is employed. Coupling coefficients are established in the Laplace domain relating the electrical current and fluid flow rate to the electric field and pressure gradient. The cross‐coupling coefficients are shown to obey the reciprocal relations for nonsteady‐state irreversible processes.