Membrane pdf

The performance parameter would be a constant no matter how the element was used if the ideal assumptions, such as no concentration polarization, applied. Degradation of the parameter therefore indicates that unaccounted factors the major one being concentration polarization, but also flow channeling and others are reducing performance The ideal model considers a brine flow path having dimension x, increasing from the top to the bottom of the element At each position x there is a brine flow rate, F x , a concentration, C x , and an osmotic pressure, 7r x , that are functions of the position The assumptions are.

An iterative process was used, which was more straightforward than making the relation explicit for yC This procedure gives an averaged salt concentration at the unblocked areas of membrane all along the membrane length for a given set of flow conditions. Now consider the circumferential variation of salt concentration. The origin is placed at the point of the sector that is farthest from the center of rotation.

It is assumed that the salt concentration varies around the cylindrical section, but not with the radius of the arbitrarily chosen cylinder.

Variation in salt concentration along the length of the cylinder is averaged automatically by the use of the membrane performance parameter, Q, through wich average salt concentrations are inferred Typical data from one test series at 5 5 X 10 6 Pa total pressure and X g acceleration on the element are given in Fig 4.

The unshaded areas denote the blocked areas of the membrane, where no salt or permeate can pass. The effective osmotic pressure, 7C, is calculated from Eq 4 and the averaged surface salt concentrations are found by dividing by 7 Knowing the average concentration around a membrane for each of the three positions of the sealed sectors, it is possible to calculate more localized concentration levels.

First, the membrane is divided into sections of equal span Second, a salt concentration profile is assumed. Third, the areas under the assumed profile are matched with corresponding areas under the aver- age profiles. The three unknowns Cl , C2, and C3 may be found by matching the areas under the function in Fig 5 with the corresponding areas in Fig.

The solid lines m Fig. When the acceleration field is applied nearly parallel to the membrane surface, very little reduction in concentration polarization seems to result.

Fig 6 shows that for a lower total pressure, the amount of concentration polarization is reduced so that the effect of acceleration is reduced.

The test series with the modified FilmTec elements confirms that flow geometry and orientation of the spiral-wound membrane in the centrifuge are of primary concern. Energy consumption and recovery in reverse osmosis By Veera Gnaneswar Gude. Experimental versus theoretical study of reverse osmosis pilot scaling: The case of Algerian brackish water desalination By hakim lounici.

A mathematical modeling of two industrial seawater desalination plants in the Persian Gulf region By Ali Kargari. Download PDF. Click here to sign up. Download Free PDF. Electric fields in and around ion-exchange membranes1 Journal of Membrane Science, Boris Zaltzman. A short summary of this paper. Electric fields in and around ion-exchange membranes1. Rubinstein , B. Zaltzman a , O. It is an of ultrafiltration membranes: if one succeeds to tame attempt to present in logical order conclusions from the interactions in a suitable solvent so that an work done over a number of years, published largely unbalanced mixture of polybase and polyacid re- in a form and in Journals not readily accessible to mains in solution, one can cast membranes in which the readers of this Journal.

Ion-exchange membranes macromolecules are held together by the essentially are relatively easily prepared, robust, entities, but electrostatic forces. The same direct interaction be- their performance can be quite intricate. It is hoped tween polyelectrolytes or between ready-made that the results given here may contribute to a clearer crosslinked ion-exchange membranes prevented the picture.

It is neither between membrane and solution phases, double lay- feasible nor necessary to consider all these explicitly ers on the phase boundaries, and externally applied for every system.

Different simplifying assumptions fields. This phe- distribution and potentials — the TMS model w1,2x. They assumed homogeneous distribution of both the fixed charges and the mobile ions, ideal solutions, Corresponding author. For the overall Donnan potentials, the best wishes, Ora. All rights reserved. Rubinstein et al. Even in the classic analysis of faces, substantial deviations from equilibrium distri- polarisation, dealing with ion concentrations in the butions and instabilities at high current densities solutions near membranes, the membrane surface is were studied theoretically and experimentally in a regarded as a geometric plane, with discontinuities of series of investigations w9—25x.

In the following, the potentials and concentrations. Some of these assumptions and simplifications Start from reconsideration of the well-known cur- were later removed. Thus, e. Further, in the presence current I lim at a given concentration, c 0 , should be of the large volume flows created in pressure driven completely determined by the thickness of the un- processes, the major role of ionrwater interactions is stirred layer, d , the diffusion coefficient of the salt, expressed in the so-called extended Nernst—Planck D, and the transport number of the counterion, t.

A logical and notable identical hydrodynamic conditions. In fact, the mem- exception to this customary assumption is the analy- brane limiting current is smaller w26x. Moreover, targeted experiments carried out under The second, sometimes implicit, assumption is well defined conditions have shown that the limiting that all forces and flows are perpendicular to the current depends on the nature of the membrane membrane surface.

Model calculations, including w17,18x. Lower charge density on the membrane fluxes in the solutions near the membrane, are then surface leads to lower limiting current. From a gen- unidimensional. Slow transfer across the surface would unusual transport phenomena to be expected in these lead to a total concentration gradient in the solution structures was obtained by assuming lateral equili- smaller than c 0. Analysis of region III strengthens bration between membrane elements, leaving the the hypothesis that there are in the surface of ion-ex- driving forces perpendicular to the membrane sur- change membranes regions of different conductance.

The This means that the local current in the conducting conclusions, exceptionally high salt permeability, and regions is larger than the measured average value, negative salt rejection, were found to be in qualita- leading to a lower overall limiting value.

The main character- What happens in the plateau itself, when the istic element in such mosaic membranes is the paral- potential is increased and there is practically no lel flow of cations and anions which constitutes a increase in the current?

It is readily shown that the circular electric current w6,7x. A better approximation basic assumption of electroneutrality which underlies described explicitly the ion transport in the solution, the description of polarisation in the linear region along the membrane surface, which closes this cir- cannot hold near saturation. In this region it is cuit, still considering each membrane region as a essential to consider applied field and double layer, separate homogeneous membrane w8x.

More precisely: while the general hydrodynamic conditions. Whatever the na- thickness of the equilibrium diffuse double layer is ture of the bulk flow, laminar or turbulent, natural or about equal to the Debye length, rd , an extended forced, gravitational instability will destroy an al- space charge tail, a non-equilibrium diffuse double ready existing diffusion layer only if the dimension- layer, is added in applied fields.

Its length is of the less Rayleigh number, Ra, is above a certain thresh- order old value. III, was long attributed to so-called water splitting, Consider an unstirred layer of mm or less. In fact, that polarisation creates a heavier layer on top of a there was consistent evidence for pH changes only at lighter one, the critical Rayleigh number is larger the anion-exchange membrane, but the concept than For a 0. However, a rational approach in terms of reaction The theoretical conclusion, that gravitational con- kinetics demonstrated that the direct dissociation of vection cannot be responsible for destruction of the water is not nearly fast enough to yield the high unstirred layer above the limiting current, is sup- currents observed, and, on the other hand, a process ported by a simple experiment.

A cation-exchange does exist which can lead to relatively fast water membrane, consisting of sulfonated polysulfone, was splitting at the generally used anion-exchange mem- cast on filter paper.

Voltage—current curves were branes: protonationrdeprotonation of tertiary amines measured in both directions, and overlimiting current w5,15x. Subsequently, the absence of water splitting was obtained also when the uncoated filter paper at cation-exchange membranes was confirmed w9x, surface faced the diluate. Gravitational convection and it was shown that an anion-exchange membrane, cannot provide effective mixing within the filter not containing groups which can be protonated, does paper.

An alternative mechanism was suggested, which Accepting that the overlimiting current at cation- draws together the phenomena observed in all three exchange membranes is carried by the dissolved regions of the current—voltage curve: electroconvec- electrolyte, there must exist some mechanism of tion w13,19—25x.

Mixing as the cause of the overlimiting current low concentration of charged particles. This implies and of the related excess electric noise is confirmed a very large Debye length and thus a macroscopic by a straightforward experimental finding: if the space charge. Here we are dealing with electrocon- surface of the cation-exchange membrane facing the vection in a strong electrolyte solution, with an diluate is coated by a gel, a plateau is reached at abundance of ions of both signs.

The following three saturation, and the excess electric noise disappears modes of electroconvection may be distinguished. Classic electro-osmosis is due to charged surfaces It was suggested that gravitational convection, and the opposite charge in the liquid near the inter- brought about by the density gradients due to con- face: the equilibrium diffuse double layer.

Tangential centration polarisation, may destroy the unstirred electric fields acting on the space charges induce layer. It should however be remembered that the macroscopic flow of the electrolyte solutions. The theoretical descrip- motion by tangential electric field components acting tion of electroconvection near an ion-exchange mem- on the space charge of the non-equilibrium diffuse brane predicts the potential V at the inflexion w20,24x.

This is the so-called electro-osmosis of It is expected that the second kind w13x. Pe scopic scale in a locally electroneutral electrolyte is proportional to the reciproke of the diffusion solution. Local stoichiometric electroneutrality in coefficient. For the system studied, DAg s 1. From these one would pre- dict the width of the plateau in a silver salt to be 1. This may hold to a high degree of accuracy for every This cannot of course be considered experimental volume element, and at the same time the absolute proof by itself, but it does show that electroconvec- value of the space charge may be significant from tion as the mechanism of mixing is consistent with the point of view of volume forces w19—25x.

The bulk electroconvective instability may in principle other two modes may be crucial for mixing in the lead to mixing in the diffusion layer w21—25x. This diffusion layer at a permselective membrane with mechanism of mixing should appear also at high non-homogeneous surface conductance w13,20,21x. In currents at metal electrodes at which the cations are this case the field lines are concentrated into spots of reduced.

Thus, it cannot explain the difference be- higher conductance, the equipotential surfaces are no tween apparently smooth membranes and electrode longer parallel to the membrane, and tangential forces surfaces. Flow vortices of the size of the surface Electroconvection appears at high current density. Can this mix the whole diffusion layer, even mode of function of ion-exchange membranes, and if it is substantially thicker? Probably this can hap- therefore may contribute indirectly to process im- pen by the interaction between vortices of different provement, but practical currents are always kept in sizes.

Can one influence Thus both the dependence of the limiting current polarisation and local mixing by designed inhomo- on the nature of the membrane surface and the geneity, at practical current densities?