Rapid Force-Flux Transitions in Highly Porous Membranes

When a steady electric current is passed through a porous membrane which separates two electrolyte solutions at different concentrations the system can, in a suitable experimental configuration, enter a state of stable oscillations of the trans-membrane pressure and potential. This system, sometimes called the Teorell membrane oscillator, also displays unusual stationary state behaviour when the pressure difference across the membrane is held constant. These phenomena arise because the pressure-driven flow of volume through the membrane is virtually independent of the concentration of the solution in its pores, whereas the electro-osmotic flow decreases as the concentration increases. If the pressure-driven and electro-osmotic flows are opposed and pressure is applied to the concentrated solution then at low currents pressure drives the concentrated solution into the pores and at high currents electro-osmosis drags the dilute solution into the pores. At some intermediate current the transition from concentrated to dilute solution in the pores occurs and is accompanied by a sudden increase in the membrane resistance and potential difference. These observations have been made on various membranes of ill-defined structure, it is shown here that they can be reproduced with Nuclepore filters which have readily characterized uniform circular and parallel pores. This observation has facilitated the development and testing of a quantitative theory of the phenomenon. The theory developed here follows the lines laid down by Kobatake & Fujita (1964) and by Mikulecky & Caplan (1966). The membrane pores are treated as independent capillaries lined by an electrical double layer with a diffuse counter charge in the pore solution. A system of flux equations consistent with non-equilibrium thermodynamics is developed and the minimum assumptions and idealizations needed to obtain well-defined results are identified. Flow in the pores is treated via the Navier—Stokes equation and equations for the membrane fluxes and forces are obtained in terms of the membrane properties and external parameters under the control of an experimenter. Two cases are considered. In the first the surface charge density on the pore walls is independent of the solution concentration and in the second the surface charge density is proportional to the cube root of the concentration. The second case applies to Nuclepore membranes because the surface charge on polycarbonate is probably due mainly to ad