J.A.M. Smit

Slow evaporation and condensation

In a previous paper an explicit condition for the jump coefficients in a one-component fluid was found within the context of non-equilibrium thermodynamics for the occurence of, on the one hand, an inverted temperature profile in the vapor phase between an evaporating and a condensing liquid surface and of, on the other hand, the supersaturation of the vapor close to the evaporating surface. By making comparisons with the kinetic theory description in the vapor phase we obtained explicit expressions for these jump coefficients. Using these expressions, the conditions found using non-equilibrium thermodynamics reduced to those given in the context of kinetic theory for these phenomena. For a fluid that obeys Troutons rule, as most fluids do, the conditions were found to be satisfied. In the present paper we analyse how a low concentration of dissolved material modifies this situation. For this purpose, the jump conditions for the temperature, the chemical potentials and the pressure are formulated for a multicomponent system in the context of non-equilibrium thermodynamics. Explicit conditions for the occurence of supersaturation and an inverted temperature profile are then given in terms of the jump coefficients. It is found that the inverted temperature profile and supersaturation no longer occur under the same conditions. A comparison is made with the results from kinetic theory, which makes it possible to give explicit expressions for these jump coefficients. We then find that the inverted temperature profile will already disappear for concentrations of dissolved material of the order of the mean-free path divided by the typical size of the system while supersaturation occurs under essentially the same conditions as in the one-component system. The disappearance of the inverted temperature profile is related to the build-up of the concentration of dissolved material near the condensing surface and the corresponding temperature increase.

Positive and negative ion retention curves of mixed electrolytes in reverse osmosis with a cellulose acetate membrane. An analysis on the basis of the generalized Nernst—Planck equation

Abstract It is experimentally shown that in mixtures of two electrolytes in water the ion with the highest permeation activity may be rejected in an anomalous way during reverse osmosis with a CA membrane, e.g., the hydrogen ion shows a negative retention in mixtures of HClCa(NO 3 ) 2 , HClCaCl 2 , and HClNaCl. The sodium ion behaves similarly in a mixture of NaCl and CaCl 2 . Starting from the extended Nernst—Planck equation analytical expressions are derived for the retention in the limiting regimes of high and low volume fluxes. The treatment refers to a neutral membrane. A heuristic explanation of the anomalies is given by considering the electric field generated by the individual ions permeating with different mobilities and partition properties ( P i ) and with different ion reflections (σ i ).

The application of the space-charge model to the permeability properties of charged microporous membranes

Abstract In the recent past the space-charge model (Morrison, F. A., and Osterle, J. F., J. Chem. Phys.43, 2111 (1965)) has been extensively used for predicting electrokinetic transport coefficients of charged microcapillary pores. With respect to the other transport coefficients, e.g., the reflection coefficient σ, the solute permeability ω, and the electric transport number ti, this model has played a minor part up to now. In this paper these quantities are evaluated as functions of electrolyte concentrations, pore radius, and density of the pore wall charge. Instead of the method usually followed of solving the Poisson-Boltzmann equation numerically, an approximative analytical approach (Levine, S., Marriott, J. R., Neale, G., and Epstein, N., J. Colloid Interface Sci.52, 136 (1975)) has been chosen. As a result analytical expressions for σ and ω are formulated. For the regime of low electrolyte concentrations explicit equations are presented in which these quantities are expressed in terms of the pore radius and the charge density of the pore wall for a z1–z2 electrolyte. The theoretically predicted behavior of the coefficients is compared with experimental data obtained from osmotic measurements with an aqueous solution of sodium chloride and weakly charged Nuclepore membranes.

Reverse osmosis in charged membranes: Analytical predictions from the space-charge model

Abstract The Poisson-Boltzmann equation has been solved for a single charged cylindrical pore with a high surface potential. The analytical solution satisfies a general boundary condition allowing for the electrical properties of the pore wall and is easily reducible to the specific boundary conditions of constant surface charge or constant surface potential. With this solution the space-charge model yields analytical expressions for the rejection of electrolyte in charged microporous membranes. Final rejection coefficients and rejection curves obtained in this way are compared with numerical and experimental results reported in the literature. The validity of the analytical predictions is excellent for surface potentials >77 mV.

Slow evaporation and condensation. II: A dilute mixture

Abstract In a previous paper an explicit condition for the jump coefficients in a one-component fluid was found within the context of non-equilibrium thermodynamics for the occurence of, on the one hand, an inverted temperature profile in the vapor phase between an evaporating and a condensing liquid surface and of, on the other hand, the supersaturation of the vapor close to the evaporating surface. By making comparisons with the kinetic theory description in the vapor phase we obtained explicit expressions for these jump coefficients. Using these expressions, the conditions found using non-equilibrium thermodynamics reduced to those given in the context of kinetic theory for these phenomena. For a fluid that obeys Troutons rule, as most fluids do, the conditions were found to be satisfied. In the present paper we analyse how a low concentration of dissolved material modifies this situation. For this purpose, the jump conditions for the temperature, the chemical potentials and the pressure are formulated for a multicomponent system in the context of non-equilibrium thermodynamics. Explicit conditions for the occurence of supersaturation and an inverted temperature profile are then given in terms of the jump coefficients. It is found that the inverted temperature profile and supersaturation no longer occur under the same conditions. A comparison is made with the results from kinetic theory, which makes it possible to give explicit expressions for these jump coefficients. We then find that the inverted temperature profile will already disappear for concentrations of dissolved material of the order of the mean-free path divided by the typical size of the system while supersaturation occurs under essentially the same conditions as in the one-component system. The disappearance of the inverted temperature profile is related to the build-up of the concentration of dissolved material near the condensing surface and the corresponding temperature increase.

Analytical approximations for potential profiles in charged micropores originating from the Poisson-Boltzmann equation

Abstract The Poisson-Boltzmann equation has been solved numerically within a microcapillary immersed in an aqueous electrolyte. Using this solution as reference, various analytical approximations to the solution of the Poisson-Boltzmann equation have been tested on their applicability.

Highly Swollen Gels of Semi-flexible Polyelectrolyte Chains Near the Rod Limit

Abstract In this paper, analytical expressions are derived that describe the swelling behaviour and elastic properties of highly swollen permanent networks, consisting of rodlike, charged macromolecules with hexafunctional chemical crosslinks, ordered in a regular, cubic arrangement. The polyelectrolyte chains are semi-flexible; only semi-circular bending modes of the chains are taken into account. The equilibrium swelling volume and the elastic properties of these simple hydrogel models are calculated as a function of the ionic strength of the electrolyte solution surrounding the gel, and of the external pressure exerted on the gel. Counterion condensation and Donnan exclusion of salt are taken into account, following the description of Manning. The results show the correct trends, without the strong initial shrinking and complete collapse upon immersion in salt solutions, as predicted by gel models employing chains with Gaussian behaviour. Semi-quantitative agreement with experimental data for swelling phenomena is found.

Transient diffusion through a membrane with a selective skin

Abstract A model is introduced for a membrane with a skin. The isothermal nonstationary diffusion through the membrane is described for a system with, on one side of the membrane, a binary solution with a constant concentration, and, on the other side, a binary solution with an initially uniform concentration, contained in a closed cell with a finite volume. The orientation of the asymmetric membrane toward the external phases is taken into account. Diffusion of solute through the membrane results in a decay of the experimental osmotic pressure across the membrane. This pressure depends not only on the concentrations on both sides of the membrane but also on the concentration profile in the membrane. Practical equations are given allowing the determination of the average reflection coefficient and of the solute permeabilities of the selective skin and the supporting layer from observed pressure-time curves. The influence of the volume flow history on the initial concentration profile is taken into account. Special attention is paid to the occurrence of asymmetry pressures (osmotic pressures at zero concentration difference over the membrane, which are induced by the initial volume flow).

The influence of membrane heterogeneity on the solute retention

A Spiegler—Kedem type expression for the retention R as a function of the volume flow Jν is derived for heterogeneous membranes. Linearization of the expression yields a well practicable equation by which reverse osmosis experiments can be simply analysed and the reflection coefficient and the solute permeability or their ratio can be determined. A discussion is presented on the meaning of the slope and the intercept of the linear plot of 1/R against 1/Jν. The results are specified for membranes of known simple membrane structures. Special attention is paid to the Loeb—Sourirajan type membrane. Finally the proposed linear equation is compared with other known linear equations and some reverse osmosis experiments are reanalysed.v

Translocations (X;10)(p22;q24) and (1;10)(q21;q11) in a Follicular Adenoma of the Thyroid without Apparent Involvement of the RET Protooncogene

We report here the cytogenetic analysis of a follicular adenoma of the thyroid which revealed an abnormal clone with a t(X;10)(p22;q24) and a t(1;10)(q21;q11) together with normal cells. Fluorescence in situ hybridization (FISH) with YACs 273E3 and 344H4, which are located on 10q11.2 and are specific for the RET protooncogene, showed no abnormalities. It would therefore appear that this gene is not involved in the particular tumor, as has been reported in a number of papillary thyroid carcinomas. Several chromosomal aberrations have been suggested as been specific for follicular thyroid adenoma. However, until now, only a few such cases have been reported which involve structural abnormalities of chromosomes 10q11.2 and 10q24. We believe this to be the first report of a follicular thyroid adenoma with a t(X;10)and a t(1;10).