The mechanism of liquid transport through swollen polymer membranes

The pressure-driven transport of liquids employed in reverse osmosis has been shown to occur by a solution-diffusion mechanism in highly swollen polymer membranes. A theory based on this mechanism was successfully used earlier to correlate permeation fluxes for such membranes. Positive confirmation of this theory is provided here by direct measurement of the proposed concentration gradient. A study of the temperature dependence of the liquid diffusion coefficient in the polymer membrane has provided additional evidence of a hydrodynamic regime of diffusion in highly swollen membranes. It is also shown that the proposed ceiling flux in reverse osmosis is equal to the pervaporation flux.     

REVIEW OF REVERSE OSMOSIS MEMBRANES AND TRANSPORT MODELS

After a brief introduction to membrane processes in general, and the reverse osmosis process in particular, the structure and properties of membranes and membrane transport theory are described. The mechanism of salt rejection and transport properties of membranes are discussed in detail. Solubility, diffusivity, and permeability of membranes to solutes and solvents are reviewed critically and compared with each other. Special attention is given to two particular types of membranes, cellulose acetate (CA) and aromatic polyamide (AP) membranes, which are often used for water desalination.

The major portion of this article is devoted to the review and discussion of membrane transport theory with application to the reverse osmosis and ultrafiltralion processes. It is shown that the solvent flux can be represented reasonably well by linear models such as the solution-diffusion model (Lonsdale, et al., 1965). The contribution of pore flow to the solvent flux is small. The solute flux, however, is not linearly dependent on the driving forces and one has to solve the differential equation of transport within the membrane which results in models such as the Spiegler-Kedem (1966) or the finely-porous (Merten, 1966) models. When the wall Peclet number is small, Pe_w =uτδ/D_sw ?1, (D_sw = bD_e one can linearize the nonlinear models. This requirement is not satisfied in most practical cases. Furthermore, the pore flow has significant effect on the solute flux equation and thus it can not be neglected.

The ambiguities that exist in the literature concerning the types of fluxes are discussed. The fluxes used in models derived from irreversible thermodynamics are purely diffusive (concentration and pressure diffusion) and they do not contain any convective effects; whereas the experimentally observed fluxes are the total fluxes with respect to the membrane which consist of a diffusive flux and a convective flux. A new model, based on irreversible thermodynamics, is derived which includes a convective term.

A membrane model is especially useful when the transport coefficients which define the model are not functions of the driving forces, i.e., pressure and concentration gradients. The coefficients in the solution diffusion and sotution-diffusion-imperfection (Sherwood, et al., 1967) models are functions of both pressure and concentration, while the coefficients in the Kedem-Katchalsky (1958) model are relatively insensitive to pressure and concentration. The nonlinear model of Spiegler-Kedem (1966) further improves the Kedem-Katchalsky model.     

Transportvorgänge in Membranen zur umgekehrten Osmose

Transport processes in membranes for reverse osmosis . The transport processes of electrolytes and undissociated polar organic compounds in membranes for reverse osmosis in individual or mixed systems are described with the aid of model equations. In addition the influence of the structure of the polymer used as membrane on the transport of the dissolved material is discussed from the viewpoint of interaction of dissolved material, solvent and membrane surface.     

Pressure-induced diffusion of organic liquids through highly swollen polymer membranes

The transport of twelve organic liquids through a highly swollen rubbery membrane has been studied. The transport was caused by a pressure applied to the liquid above the membrane (reverse osmosis). The flux was found to be a highly nonlinear function of the driving pressure. Detailed thermodynamic and diffusion theories are proposed to describe the transport in terms of the concentration gradient of the swelling liquid within the membrane induced by the applied pressure. The data and the theory appear to be in very good agreement. The diffusion coefficients deduced from the data are explained in terms of a hydrodynamic mechanism of diffusion. Highly swollen membranes can yield very high liquid fluxes at moderate pressure and consequently may have applications for performing certain separations.     

Concentration and pressure dependence of rate of membrane permeation

The permeation of water and sodium chloride in cellulose acetate membranes has been examined over a wide range of concentration and pressure. The results obtained from reverse osmosis experiments have been used to evaluate relations derived on the assumption that permeation of both solution components takes place by diffusion down a concentration gradient in the membrane. With the aid of equilibrium and raidoactive tracer measurements, most of the deviations could be attributed to nonconstancy of the diffusion, and, especially, the distribution coefficients of water. A comparison of the net flux in reverse osmosis with the rate of tracer permeation in the same membrane provided positive evidence to show that hydrodynamic flow under pressure cannot account for the water flux through the membrane. Differences in the shape of the distribution isotherms for salt and water between solution and membrane provide an explanation for the high selectivity of cellulose acetate membranes in favor of water.     

Structure of porous cellulose acetate membranes and a method for improving their performance in reverse osmosis

Experimental data support the hypothesis that the surface layer of the asymmetric Loeb-Sourirajan type porous cellulose acetate membranes has a heterogeneous microporous structure. A general method is proposed for improving the performance of the above membranes in reverse osmosis, by which product rates are increased without decreasing solute separation. The method consists in pumping pure water past the back side of the membrane under just enough pressure for a sufficiently prolonged period of time; after such pretreatment, the membrane is used in the reverse osmosis experiments in the normal manner with the surface layer facing the feed solution. Back-pressure treatment at 400 psig for 85 hr on preshrunk and normally pressure-treated membranes increases the product rate by over 20% without decreasing solute separation in reverse osmosis experiments at 600 psig with the use of 0.5 wt-% NaCl–H₂O feed solutions; with a different sequence of back-pressure treatment, similar results have been obtained in reverse osmosis experiments at 1500 psig also. The compaction effect of a normal membrane and that of a back pressure treated membrane are the same during continuous reverse osmosis operation under 600 psig; the effects of back-pressure treatment on a normal membrane and a compacted membrane are also the same. The pure water permeability data obtained in cyclic experiments show that the smaller pores on the surface layer are opened more than the bigger ones during the back side operation. The probable structural changes taking place in the film during back-pressure treatment are discussed.     

A study on pore size distribution of modified ultrathin membrances

An equation to estimate the thickness of ultrathin membranes obtained by Levich, assuming constant physical properties, was compared with the measured thickness in the range of 0.3–40 μ. The proportionality constant was found to be 0.4, and the equation is expressed as follows: The nitrogen gas adsorption isotherms at ?195°C on the modified ultrathin membranes were measured and the surface area of the pores was determined by the B.E.T. equation. Distribution of pore volume was calculated by the method of Cranston and Inkley. On the assumption of straight cylindrical pores in the membrane, the crosssectional area of pores and the mean pore radius were calculated. Symmetric structure of the modified ultrathin membranes was confirmed by reverse osmosis tests with both the air and glass sides of the membrane facing the pressure solution.     

Poly(vinyl) alcohol coating of the support layer of reverse osmosis membranes to enhance performance in forward osmosis

Membrane hydrophilicity influences the transport of water through the membrane in osmotically driven separations such as forward osmosis. In this paper, we coated the polysulfone support layer of two types of commercially available reverse osmosis membranes (brackish water and seawater) with hydrophilic polyvinyl alcohol (PVA). The aim of this was to increase the support layer hydrophilicity and, correspondingly, the rate of water transport through the membrane. Previous work with polydopamine coatings of the polysulfone support of reverse osmosis membranes has yielded promising results. In this work, we explore more readily available materials. Specifically, we studied the effects of two different PVA crosslinking agents – maleic acid and glutaraldehyde – on the resultant membrane properties and osmotic performance. For seawater membranes we found that PVA crosslinked to a limited degree with maleic acid creates a significant improvement in water flux in RO and FO systems, as compared to membranes with PVA crosslinked by glutaraldehyde. However, brackish water membranes did not have comparably significant changes in membrane performance. We conclude that the smaller pores of the brackish water membrane become clogged, and this effect is magnified by the lack of fractional free volume available within PVA that is highly crosslinked with glutaraldehyde.     

Theory of reverse osmosis and some other membrane permeation operations

The general permeation equations for various transport operations using membranes were correlated according to the solution-diffusion theory. It was shown that for some important conditions, the permeation properties for reverse osmosis can be generated from those of pervaporation. The use of reverse osmosis with pressure smaller than 2000 psi is calculated to be of limited use for the purification of water with small amounts of organic compounds.     

THERMODYNAMIC MODELING OF SOLUTE TRANSPORT THROUGH REVERSE OSMOSIS MEMBRANE

A new thermodynamic model is developed for water and solute transports through reverse osmosis membranes. The model is featured with rigorous derivations in theoretical development and clearly defined parameters for membrane transport properties. The new model can correctly describe not only the dependence of salt rejection on pressure and salt concentration, but also the non-linearity between water flux and pressure. Comparisons of model simulations with the reported reverse osmosis experiments demonstrate that the parameters in the new model are concentration-independent. This study shows that water and salt transports through reverse osmosis membranes can be satisfactorily described with irreversible thermodynamics.     

Precise measurement of membrane constants of cellulose acetate membranes by direct osmosis tests

A method for the determination of membrane constants by direct osmosis tests was studied using cellulose acetate membranes. A countercurrent type osmosis cell was designed and made for this study, and a method for precise measurements of permeated water and solutes through the membrane was established. Based on the membrane constants derived from direct osmosis tests, membrane performances of cellulose acetate membranes under pressure of 40 atm were predicted. The predicted values were in good agreement with the observed values in reverse osmosis experiments and it was confirmed that membrane performances under pressure could be predicted by the direct osmosis with considerably good accuracy.     

反渗透膜的研究进展与展望

反渗透具有低能耗、高效率等突出优点,是目前应用最为广泛的分离技术之一。反渗透膜的性能是影响反渗透过程效率的决定因素,反渗透膜的研制一直是国内外膜领域的研究热点。特别是近年来,石墨烯、碳纳米管等新型材料展现出优异的水传递行为,成为新型反渗透膜材料的研究热点。本论文回顾了反渗透膜的研制发展历程,介绍了不同单体通过界面聚合反应成膜的研究进展,综述了国内外新型混合基质膜和无机分子筛反渗透膜材料及其成膜研究,最后提出了新型反渗透膜的研究方向。     

On rigorous definition of ion transport process and accurate determination of membrane potential at steady state

Ion transport plays an important role in many fields, such as signal generation and transmission in neural systems, function of ion channel on bio-membranes, and water demineralization with nanofiltration and reverse osmosis. The electrical potential concurred with ion transport on a membrane not only reflects the properties of ions (e.g., charge, concentration, and mobility) but also regulates the transport rates of the ions. However, accurate determination of membrane potential remains a severe challenge because of the difficulties in specifying the appropriate boundary conditions for the governing Nernst–Planck–Poisson equations. An innovative boundary condition updating scheme was developed in this study to ensure that the boundary conditions are consistently imposed for both Nernst–Planck equation and Poisson's equation at any time. With this scheme, the general ion transport process can be rigorously defined and formulated for the accurate determination of membrane potential.     

Water and solute transport across cellulose acetate membranes in the treatment of soybean whey by reverse osmosis

In processing full-fat soy flour to produce an acid-precipitated lipid protein concentrate, there results a by-product whey fraction which, because of its high biological oxygen demand, represents a serious disposal problem. Processing of food waste streams by reverse osmosis has received considerable attention because of its low theoretical energy requirement, since no phase change is involved. A series of statistically designed and analyzed experiments were conducted on a pilot-plant reverse osmosis unit to study the effect of the operating parameters on solute and solvent transport in cellulose acetate membranes. Sucrose and sodium chloride solutions were tested in addition to soybean whey to relate the mixed solute system in whey to that of single-solute organic and inorganic feed solutions. Water flux was shown to have an Arrhenius dependency on temperature, and some membrane compaction was observed with the more porous membrane. Concentration polarization for sucrose and sodium chloride solutions increased linearly with water flux. Solute flux for soybean whey solutions decreased with molarity and was independent of pressure, whereas solute rejection increased with temperature and pressure and was independent of molarity. Good agreement was obtained using the derived parameters A, B, and τ for soy whey in the diffusion transport model when compared to the observed experimental values.     

Salt rejection and flux in reverse osmosis with compactible membranes

The theory of reverse osmosis in bilayer membranes is extended. At high fluxes the selectivity of the layer on the high pressure side dominates the salt rejection also in case this layer has the lowest selectivity. Theoretical concentration profiles are given for both orientations. Experimentally, irreversible compaction of the membrane is controlled by a pressure treatment. For the remaining reversible compaction the transport equations can be corrected. It turns out that reversible compaction affects the flux but not the salt rejection. Correspondingly structural changes occur in the layer of low selectivity.     

The role of membrane pressure in reverse osmosis

Liquid transport occurs through reverse osmosis membranes as a result of an applied pressure differential. The pressure within the membrane continuum is an important thermodynamic parameter in the formulation of solution-diffusion models for this process. It is shown that this membrane pressure is the same throughout the membrane for supported flat and tubular membranes and for hollow fibers. The use of this parameter in calculating the induced concentration differential is discussed.     

Stationary Mass Transfer in the Longitudinal Flow Past a Selectively Permeable Flat Wall

By numerically integrating the inverse Laplace transform, an approximate solution was obtained to the convective diffusion equation for stationary two-dimensional mass transfer on a selectively permeable surface (membrane) past which there is a flow with linear flow velocity distribution at constant suction velocity. The solution was the concentration distributions in the pressure channel, which depend on two coordinates and the membrane selectivity. The adequacy of the assumptions made for reverse osmosis and pregel ultrafiltration in describing the laminar and turbulent flows in plane channels was demonstrated.     

Studies on effect of irradiation on semipermeable membranes

The effect of γ irradiation on reverse osmosis (RO) semipermeable membranes has been studied in order to evaluate their performance under the radiation environment arising in the processing of various streams in nuclear industry by reverse osmosis process. Both cellulosic and noncellulosic membranes in dry as well as wet conditions were used. A Co⁶⁰ source was used for γ doses from kilorads to megarads. The transport properties, namely, salt retention and water flux of membranes determined before and after irradiation, suggested deterioration in the membrane properties due to irradiation. The tensile strength and viscosity of membrane polymer also suggested membrane degradation. Differential scanning calorimetry was taken to look into any structural changes in the membrane polymer as a result of irradiation. IR spectra and X-ray of membrane polymer was also undertaken to understand the changes on the molecular level.     

PEM燃料电池中质子交换膜内水和质子的迁移特性

质子交换膜的水含量及水和质子的迁移对PEM燃料电池的性能具有重要影响.提出了一个稳态两相流数学模型,用以研究质子交换膜中的水迁移和水含量及其与质子传递阻力的关系.模型耦合了连续方程、动量守恒方程、物料守恒方程和水在质子交换膜中的传递方程.通过与实验数据对比,验证了模型的有效性.分析模拟结果发现,当电流密度相同时,沿气体流动方向,质子交换膜中水的电渗拉力系数、反扩散系数和水力渗透系数逐步增大,而水的净迁移系数逐步减小;同时,质子交换膜的含水量增加,质子传递阻力逐步下降;增大电池的操作压力,电渗拉力系数、反扩散系数、水力渗透系数、水净迁移系数和质子膜的含水量增加,而质子传递阻力下降,使燃料电池的性能得到了提高.