Kinematic and volumetric analysis of coupled transmembrane fluxes of binary electrolyte solution components.

The paper deals with relationships between the individual transmembrane fluxes of binary electrolyte solution components and the experimentally measurable quantities describing rates of transfer processes, namely, the electric current, the transmembrane volume flow and the rates of concentration changes in the solutions adjacent to the membrane. Also, we collected and rigorously defined the kinetic coefficients describing the membrane selective and electrokinetic properties. A set of useful relationships between these coefficients is derived. An important specificity of the proposed analysis is that it does not use the Irreversible Thermodynamic approach by analyzing no thermodynamic forces that generate the fluxes under consideration. Instead, all the regularities are derived on the basis of conservation and linearity reasons. The terminology "Kinematics of Fluxes" is proposed for such an analysis on the basis of the analogy with Mechanics where Kinematics deals with regularities of motion by considering no mechanic forces. The only thermodynamic steps of the analysis relate to the discussion on the partial molar volumes of electrolyte and ions that are the equilibrium thermodynamic parameters of the adjacent solutions. These parameters are important for interrelating the transmembrane fluxes of the solution components and the transmembrane volume flow. The paper contains short literature reviews concerned with the partial molar volumes of electrolyte and ions: the methods of measurement, the obtained results and their theoretical interpretations. It is concluded from the reviews that the classical theories should be corrected to make them applicable for sufficiently concentrated solutions, 1 M or higher. The proposed correction is taken into account in the kinematic analysis.

Mechano-chemical effects in weakly charged porous media.

The paper is concerned with mechano-chemical effects, namely, osmosis and pressure-driven separation of ions that can be observed when a charged porous medium is placed between two electrolyte solutions. The study is focused on porous systems with low equilibrium interfacial potentials (about 30 mV or lower). At such low potentials, osmosis and pressure-driven separation of ions noticeably manifest themselves provided that the ions in the electrolyte solutions have different diffusion coefficients. The analysis is conducted by combining the irreversible thermodynamic approach and the linearized (in terms of the normalized equilibrium interfacial potential) version of the Standard Electrokinetic Model. Osmosis and the pressure-driven separation of ions are considered for an arbitrary mixed electrolyte solution and various porous space geometries. It is shown that the effects under consideration are proportional to a geometrical factor which, for all the considered geometries of porous space, can be expressed as a function of porosity and the Λ- parameter of porous medium normalized by the Debye length. For all the studied geometries, this function turns out to be weakly dependent on both the porosity and the geometry type. The latter allows for a rough evaluation of the geometrical factor from experimental data on electric conductivity and hydraulic permeability without previous knowledge of the porous space geometry. The obtained results are used to illustrate how the composition of electrolyte solution affects the mechano-chemical effects. For various examples of electrolyte solution compositions, the obtained results are capable of describing positive, negative and anomalous osmosis, positive and negative rejection of binary electrolytes, and pressure-driven separation of binary electrolyte mixtures.

Transport properties of long straight nano-channels in electrolyte solutions: a systematic approach.

The principle of local thermodynamic equilibrium is systematically employed for obtaining various transport properties of long straight nano-channels. The concept of virtual solution is used to describe situations of non-negligible overlap of diffuse parts of electric double layers (EDLs) in nano-channels. Generic expressions for a variety of transport properties of long straight nano-channels are obtained in terms of quasi-equilibrium distribution coefficients of ions and functionals of quasi-equilibrium distribution of electrostatic potential. Further, the Poisson-Boltzmann approach is used to specify these expressions for long straight slit-like nano-channels. In the approximation of non-overlapped diffuse parts of double electric layers in nano-channels, simple analytical expressions are obtained for the apparent electrophoretic mobilities of (trace) analytes of arbitrary charge as well as for the salt reflection coefficient (osmotic pressure), salt diffusion permeability and electro-viscosity (electrokinetic energy conversion). The approximate solutions are compared with the results of rigorous solution of non-linearized Poisson-Boltzmann equation, and the accuracy of approximation is shown to be typically excellent when the nano-channel half-height exceeds ca.3 Debye screening lengths. Due to non-negligible electrostatic adsorption of ions by nano-channels, the apparent electrophoretic mobilities of counter-ionic analytes in nano-channels are smaller than in micro-channels whereas those of co-ionic analytes are larger. This dependence on the charge is useful for the separation of analytes of close electrophoretic mobilities. The osmotic pressure is shown to be positive, negative or pass through maxima as a function of applied salt-concentration difference within a fairly narrow range of ratios of nano-channel height to the Debye screening length. The diffusion permeability of charged nano-channels to single salts is demonstrated (for the first time) to be typically larger than that of neutral nano-channels of the same dimensions due to electrical facilitation of salt diffusion.

Determination of diffusion and sorption parameters of thin confined clay layers by direct fitting of through-diffusion flux.

Diffusion in compacted clays is often studied in sandwich-like arrangements where the clay is confined by porous filter plates in order to control its swelling. In some clays (for example, Na-montmorillonite) equilibrated with dilute electrolyte solutions, the fluxes of cationic radiotracers can be quite high due to cation-exchange reactions. Accordingly, the diffusion resistance of clay layers can become comparable with or even smaller than the diffusion resistance of porous filters (such layers are called "thin" in this study). In view of the typical uncertainties (ca. 20%) of diffusion permeability of porous filters reported in the literature, the diffusion resistance of clay layers cannot be reliably determined from the steady-state diffusion permeability of the filter-clay-filter "sandwich" in this case. In this study, it is shown that, rather unexpectedly, information on the diffusion permeability of "thin" clay layers can be obtained from the time dependence of diffusant flux into the outlet compartment because at very short times, there is a characteristic flux delay that does not occur in the limiting case of infinitely large diffusion permeability of clay. The flux behavior at longer times is controlled by the diffusion permeability of the filters, which makes possible its determination directly from through-diffusion data and makes superfluous independent diffusion experiments with filters. This approach has been validated via theoretical interpretation of literature data on the diffusion of (22)Na radiotracers through confined compacted montmorillonite equilibrated with 0.01 M NaClO(4) solution. The filter and clay properties estimated in this way are in good agreement with the literature data.

Negative rejection of ions in pressure-driven membrane processes.

Negative rejections of ions in pressure-driven membrane processes can be caused by several distinct mechanisms. In a number of cases, in a final count, the phenomenon is brought about by increased concentration of an ion in the membrane phase. In the case of charged membranes, the increased concentration has to be accompanied by a weakening of electric field of filtration potential, which normally retards counter-ions and prevents the increased concentrations from manifesting themselves in negative rejections. This occurs in charge-mosaic membranes due to the so-called current circulation phenomenon or in electrolyte mixtures due to the presence of more mobile counter-ions. Negative rejections can also occur for ions whose concentration is decreased in the membrane phase. This occurs in electrolyte mixtures due to the acceleration of such ions by the electric field of diffusion potential arising because of strong rejections of other mixture components. This phenomenon is most pronounced for single-charge ions in the presence of predominant amounts of ions of higher charge of the same sign. All those mechanisms are considered within the scope of a common theoretical framework. An attempt is made of a tentative classification of mechanisms of negative rejections. An overview of available literature data is provided and it is shown that in a number of cases the published information is not sufficiently detailed for a reliable identification of the mechanisms. It is concluded that the studies of negative rejections could be a valuable membrane characterization tool but they need to be more systematic and targeted to fulfil this role.

Improved interpretation of in-diffusion measurements with confined swelling clays.

Diffusion is considered the principal transport mechanism of radio-nuclides and other low-molecular-weight pollutants in compacted clays used as barriers at various disposal and storage sites, for example, at projected deep repositories for radioactive waste. Porous filters are routinely used to confine swelling clays in diffusion studies of radio-tracers. The presence of the filter gives rise to considerable mass-transfer limitations at the clay boundary that result in erroneous diffusion parameters. We have solved the problem of in-diffusion with due account for this phenomenon by means of Fourier transforms. By using literature data on the in-diffusion of traces of radioactive cesium in an argillaceous rock (Opalinus clay) and a compacted bentonite (FEBEX bentonite), we have demonstrated that taking into account the mass-transfer limitations considerably improves the quality of the theoretical fit of the time evolution of radio-tracer concentration in the reservoir. Besides that, we have shown that ignoring the mass-transfer limitations leads to a noticeable underestimation of both the effective diffusion coefficient and the specific sorption capacity of the clay.

Some properties of electrolyte solutions in nanoconfinement revealed by the measurement of transient filtration potential after pressure switch off.

We have demonstrated that with a composite nanoporous ceramic membrane in a batch membrane cell it is technically feasible to switch off the trans-membrane hydrostatic pressure difference within tens of milliseconds. That enabled us to resolve practically the whole time evolution of transient filtration potential. Measurements of the latter have been complemented by measurements of steady-state salt rejection by the composite membrane and by measurements of the streaming potential and hydraulic permeability of membrane supports available separately. A theory has been developed in terms of network thermodynamics for the electrical response of a bilayer membrane to a pressure perturbation. In combination with the results of salt rejection measurements, from the time transients of filtration potential we could determine the ion transport numbers within the nanoporous layer. Besides that, from the dependence of steady-state salt rejection on the trans-membrane volume flow, we have determined the diffusion permeability of and the salt reflection coefficient in the nanoporous layer. This has enabled us to estimate the contributions of Donnan and non-Donnan mechanisms to the rejection of ions by the nanoporous membrane used in this study. It has been unexpectedly found that the Donnan exclusion played only a secondary role. Our hypothesis is that the non-Donnan exclusion of ions from the nanopores might be caused by changes in water properties in nanoconfinement. Proceeding from the results of steady-state filtration experiments with the membrane and the support, we also concluded that the nanoporous layer was imperfection-free and had a quite narrow pore size distribution, which made it a suitable object for fundamental studies of ion transfer mechanisms in nanopores.

A Model for the Shift of Isoelectric Points of Oxides in Concentrated and Mixed-Solvent Electrolyte Solutions.

It is shown theoretically that the experimentally observed shifts of isoelectric points of various oxide surfaces toward more basic pH's in concentrated and mixed-solvent electrolyte solutions can be explained by a model previously used to predict the phenomenon of "coagulation zones" in the stability of colloids with adsorption layers of nonionic polymers. The model assumes the standard solvation energies of ions near a solid-liquid interface to be different from those in the bulk due to changes in the solvent structure. To reproduce the trends of experimental data in aqueous solutions, the solubilities of both cations and anions must be decreased, but for cations that must occur to a smaller extent. In mixed solvents a qualitative agreement with the experimental data is achieved by assuming that there is a water-enriched layer near the oxide surface. Copyright 2001 Academic Press.