OSMOSIS AND REVERSE-OSMOSIS IN FINE-POROUS CHARGED DIAPHRAGMS AND MEMBRANES

The theory of osmosis and reverse osmosis in fine-porous charged membr anes and diaphragms is presented in a deductive way with several well- structured levels of consideration. The analysis starts from the disco ntinuous version of irreversible thermodynamics where the membrane is considered as an absolutely black box without any information needed a bout its internal structure. As a trade-off for generality, however, t he thermodynamic forces must be small. A number of qualitative conclus ions is drawn proceeding from rather evident assumptions about the ord er of magnitude of various phenomenological coefficients. In the case of electrolyte mixtures those conclusions turn out surprisingly numero us and non-trivial including predictions of reflection coefficients la rger than unity and strong negative osmosis. Both those anomalous phen omena are confirmed by experimental findings. The next step is the int roduction of a 'uniformly black' box, namely a macroscopically homogen eous membrane with otherwise unspecified internal structure. That perm its to employ the continuous version of irreversible thermodynamics th us allowing to drop the restriction of small thermodynamic forces. In the case of binary electrolytes general solutions in quadratures are o btained for the problems of apparent osmotic pressure and of reverse o smosis, and a very accurate approximate solution in quadratures is obt ained for the problem of osmosis. Some of the theoretical predictions are compared with experimental data on the reverse osmosis of binary e lectrolytes in track-etched membranes with the pore size of 8 nm. In t he case of electrolyte mixtures a semi-quantitative asymptotic analysi s is performed in the limiting case of reverse osmosis at sufficiently large Peclet numbers, and in the particular case of one dominant elec trolyte in the mixture an exact solution in quadratures is obtained. T hose analyses make possible to predict a number of non-trivial regular ities that are confronted with experimental data on the pressure-drive n transport of ternary electrolyte mixtures across various charged por ous membranes. A good qualitative agreement between the theory and exp eriments is recorded. The next step is the specification of phenomenol ogical coefficients within the scope of a general capillary model. Tha t makes the box grey but not transparent, yet, as the shape of capilla ry cross-section as well as the nature of surface forces are not speci fied. General expressions for phenomenological coefficients derived in terms of ion distribution and diffusion coefficients make possible a qualitative analysis of the effect of inhomogeneity of ion distributio n inside pores. Finally, the capillary space charge model is introduce d making the analysis completely mechanistic. Several approaches are c onsidered to the approximate description of the structure of overlappe d diffuse parts of double electric layers in fine pores. Since qualita tive effects of microscopic heterogeneity appear to be not dependent o n the details of the pore geometry sample numerical calculations are p erformed for slit-like capillaries where there is a general solution o f Poisson-Boltzmann equation in quadratures. A more general model of p ores in an electrically conducting gel is introduced in an attempt to quantitatively describe the results of complete characterization of ca tion-exchange membranes in terms of irreversible thermodynamics.