Osmotic flow in charged membranes

Abstract

The osmotic flow through a porous charged membrane separating electrolyte solutions of different concentrations but at a constant temperature is studied theoretically, using a capillary model for the membrane. The assumptions used are that theDebye-Huckel 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 the differential equations derived are obtained subject to the external conditions that the concentrations of the outer solutions are maintained constant and no pressure head is applied across the membrane. It is shown that the volume rate of osmotic flow is the sum of two terms, one arising from the fact that the membrane is electrically charged and the other being independent of the membrane charge and thus observable commonly both in charged and uncharged membranes. The former corresponds to whatGrim andSollner have referred to as the true anomalous osmosis. The plot of this electric part of osmosis against the logarithm of the concentration of one outer solution gives a bell-shaped curve, when the concentration ratio of the outer solutions is fixed. This theoretical curve follows well theGrim-Sollner data of the true anomalous osmosis for various aqueous electrolyte solutions. The true anomalous osmosis is an electro-osmotic flow caused by the electric field which is set up inside the membrane so that no net transport of electric charge occurs from one solution compartment to the other. The dependence of the electroosmotic coefficient on salt concentration is responsible for the characteristic behavior of the osmotic flow rates through charged membranes.