Osmotic Flows in Charged Membranes. II. Thermo-Osmosis

Abstract

Thermo-osmotic flow rates of an electrolyte solution through a porous charged membrane separating two solutions which are at different temperatures but have the same concentration is studied theoretically, using a capillary model for the membrane. The assumptions used are that the Debye-Hückel approximation is applicable for the ion distribution in the double layer formed near the fixed charges on the capillary wall, and that the thickness of the double layer is much smaller than the capillary radius. The steady-state solutions of a set of differential equations derived are obtained subject to appropriate external conditions. It is shown that plots for the flow rate of fluid against the logarithm of the concentration of the outer solution give a bell-shaped curve. This theoretical curve follows well the Carr—Sollner data of the thermo-osmosis for various electrolyte solutions. The thermo-osmosis is an electro-osmotic flow caused by the electric field which is set up in the membrane so that no net electric charge is allowed to be transported across the membrane. The dependence of the electro-osmotic coefficient on salt concentration is the primary cause for the characteristic behavior of the thermo-osmosis in charged membranes. It has been shown in Part I of this series that this effect is also responsible for the anomalous osmosis.