Filtration potential across membranes containing selective layers

The filtration potential in the membranes containing selective layers is studied both theoretically and experimentally. A general thermodynamic expression is obtained for the pressure-induced potential difference across a membrane with an arbitrary number of macroscopically homogeneous layers. That expression is specified for the model of straight cylindrical capillaries in each of the layers. The limiting cases of very wide and very fine pores are considered for the supports and active layers, respectively. In membranes containing selective layers, the dependencies of filtration potential on the transmembrane volume flow are usually nonlinear. That occurs because the concentration differences arising in the membrane depend nonlinearly on the transmembrane volume flow. The concentration gradients cause nonlinearities due to the occurrence of membrane potential and because the streaming potential coefficient in coarse-porous layers (e.g., membrane supports) depends on electrolyte concentration. The membrane potential gives rise to a sublinear behavior while the concentration dependence of support electrokinetic properties causes a superlinearity. Therefore, the pattern of nonlinearity essentially depends on the relative contribution of constituent layers into the filtration potential. That contribution is shown to be roughly proportional to the layer's hydraulic resistance and to the effective zeta-potential in its pores and inversely proportional to the layer electric conductivity. The filtration potential measured with plane ceramic nanofiltration membranes shows a slightly superlinear dependence on the transmembrane volume flow. After the subtraction of support contribution (carried out with the due account of the dependence of support electrokinetic properties on the concentration) the sub-linear pattern characteristic of the active layer contribution is restored. That pattern allows for an extrapolation from which information can be obtained on the ion transport numbers in active layers.