A quantitative treatment of oscillatory phenomena in coarse-grained ion-exchanger membranes

The treatment developed in this text concerns the ion flux, volume flux and electric current through the highly porous ion-exchanger membrane of the Teorell membrane oscillator. It is based on the concept that inside the membrane exists a concentration profile of defined shape depending mainly on the volume flux caused by the hydrostatic pressure and the electro-osmotic effect of the membrane potential within the reach of the electric charge of the ion-exchanger grains forming the membrane texture.In particular it is shown that under conditions of zero volume flux the effective fixed charge responsible for the electro-osmotic driving force can be determined directly by measuring the hydrostatic pressure and its compensating electric potential. Like the electro-osmotic effect, also the derived flux equations proved to be independent of the special feature of the grain texture.The simultaneous differential equations describing the temporal (oscillatory) behaviour of the Teorell membrane system are derived on the basis of these flux equations leading to analog computer solutions which agree well with the experimental data.