Mohammad Soltanieh

REVIEW OF REVERSE OSMOSIS MEMBRANES AND TRANSPORT MODELS

Abstract 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 ...

Multicomponent transport across nonporous polymeric membranes

Abstract The theoretical description of multicomponent transport across nonporous polymeric membranes was investigated using two alternative frameworks: the phenomenological approach of irreversible thermodynamics and the mechanistic Stefan—Maxwell formulation. The transport models developed account for potential equilibrium and/or kinetic coupling of fluxes and the contribution of diffusion induced non-selective flow within the polymer. The models were validated against transient dialysis and pervaporation data for the {ethanol-water}/silicone rubber system. A critical assessment was obtained by recovering the model parameters from the dialysis data and using the same parameters to predict the transient pervaporation performance. An empirical modification of the Flory—Huggins model was developed to describe the sorption of small polar solutes into hydrophobic membranes, which provided a physically realistic description of the sorption equilibria for the {ethanol-water}/silicone rubber system. The irreversible thermodynamics approach was used to develop transient models of dialysis and pervaporation. Average phenomenological diffusion coefficients recovered from dialysis data can give a good qualitative prediction of pervaporation performance. However, a quantitative prediction requires the explicit inclusion of the concentration dependence of the diffusivities, which is best achieved within the mechanistic Stefan—Maxwell formulation. A generic model of membrane transport was formulated using the mechanistic Stephan—Maxwell approach and generalised driving forces, which included the contribution from the various internal and external driving forces. The results obtained indicate that the generic model is capable of describing the transient dialysis and pervaporation of the {ethanol-water}/silicone rubber system with an identical set of concentration dependent equilibrium and diffusive parameters.

A GENERAL MODEL FOR MULTICOMPONENT TRANSPORT IN NONPOROUS MEMBRANES BASED ON MAXWELL-STEFAN FORMULATION

A “general” model of membrane transport was formulated using the mechanistic Maxwell-Stefan approach and generalized driving forces, which included the contribution from the various internal and external driving forces. Transient models of dialysis and pervaporation were developed that used exactly the same general model to describe the transport through the membrane. In this model, the bulk solution/polymer equilibria were described by a modified Flory-Huggins model, and the concentration dependence of ternary Maxwell-Stefan diffusivities was described by a natural extension of the binary Vignes relationship to a multicomponent system. A notable advantage of the general model lies in the fact that the Maxwell-Stefan diffusivities retain their physical significance irrespective of the number of components present. This offers the opportunity of recovering many of the model parameters from relatively simple binary experiments. The results obtained indicate that the general model is capable of describing the transient dialysis and pervaporation of the {ethanol-water}/silicone rubber system with an identical set of concentration dependent equilibrium and diffusive parameters. The general model provides a solid framework for the theoretical description of diverse processes employing a nonporous polymer as the selective separation barrier.

Transport of small polar molecules across nonporous polymeric membranes. I. Experimental procedures and data analysis

Abstract The transient measurement of concentration profile within the liquid boundary layer close to the membrane interface and the flux of permeating species across the membrane coupled with transient model of membrane allows a more critical evaluation of membrane transport performance. The experimental procedure for transient measurement of pervaporation fluxes and data obtained for the {ethanol–water}/silicone rubber system and experimental set up for transient dialysis measurement by interferometry technique for the same system was described. A detailed analysis of optical effect accounting for the light deflection in a medium of varying refractive index profile was presented. A numerical procedure was described which is capable to handle the transient models consist of highly nonlinear partial differential equations. The potential of recovering the transport model parameters from the interference fringes was tested by using a hypothetical model system. The results obtained confirm that both the diffusive and equilibrium parameters can be recovered from the interference fringes. The possibility of recovering the transport model parameters for the {ethanol–water}/silicon rubber system from dialysis data and using those parameters for predicting pervaporation performance for the purpose of model validation will be described in forthcoming articles.

Application of charged membranes in water softening : modeling and experiments in the presence of polyelectrolytes

Abstract In this paper theoretical and experimental results for water softening by bipolar membranes in the presence of polyelectrolytes have been presented. A modified capillary model is introduced for flow of a multiion solution through the membrane. The most important modifications are: an integral boundary condition in Poisson equation and a coupling coefficient in the convective molar flux by using the modified Faxen equation. In addition, electrical permittivity of solution has not been considered as a constant. The predictions of the model were compared well with the experimental data obtained by using bipolar membranes in a recirculating test system in the presence of polyelectrolytes.

Interaction effects in multicomponent separation by reverse osmosis

Abstract Separation of multicomponent mixtures, in particular ternary systems, was investigated theoretically and experimentally. The interactions in various multicomponent mixtures were determined. Using data from literature as well as the limited data obtained in our laboratory, we identified the situations where the multicomponent effects are strong. A correlation between the coupled permeability coefficients and straight permeability coefficients and concentration of components in ternary systems was obtained. Capabilities of thermodynamic models in describing the electrolyte–nonelectrolyte systems consisting of a weak acid were also investigated. The results of this work show that the multicomponent effects can be used in improving the separation properties of membranes. The findings of this study may be applied to several processes including recovery of small amounts of metals from wastes, separation of ionic compounds from organic, and separation of weak and strong electrolytes.

A MODIFIED SOLUTION-DIFFUSION MODEL FOR SEPARATION OF ETHANOL-WATER AZEOTROPIC MIXTURES IN PERVAPORATION

A modified solution-diffusion model is presented which describes separation of ethanol-water mixtures. The model is particularly useful in predicting the solute (ethanol) flux as the mixture approaches the azeotrope point where ethanol activity is greater than 0 6. Based on the experimental observations obtained from the literature, the model assumes that polymers of about seven molecules of ethanol are formed, which are then transported through the membrane along with water and ethanol monomers and dimers. It is shown that the ethanol flux can be predicted more accurately as compared with the existing model. Comparisons with experimental data from the literature confirms this model.

Transport of small polar molecules across nonporous polymeric membranes. II. Shortcomings of phenomenological models of membrane transport

A molecule within the nonporous polymeric membrane moves in response to the local driving force and has no memory of how it entered the membrane or how the local gradients were generated. This means that a properly formulated model of transport within the membrane should be equally applicable to dialysis, pervaporation or vapour permeation. The phenomenological approach of irreversible thermodynamics was used to develop transient models of dialysis and pervaporation. The model developed in this study were validated against transient dialysis and pervaporation data for ethanol–water/silicone rubber system. A critical assessment was obtained by recovering the model parameters from the dialysis data and using the same parameters to predict the transient pervaporation performance. The equilibria for the system under study was separately described in terms of Flory–Huggins model with constant interaction parameters where the interaction parameters were found from a nonlinear fit to the available relative sorption data. It was shown the average phenomenological diffusion coefficients recovered from dialysis data can give a good qualitative prediction of pervaporation performance provided the diffusion coefficients satisfy the Onsagar reciprocal relationships. However, a quantitative prediction requires the explicit inclusion of the concentration dependence of the diffusivities as well as a better description of polymer phase equilibria, which is difficult to handle in the framework of irreversible thermodynamics formalism and best achieved within the mechanistic Stefan–Maxwell formulation and deferred to the forthcoming article.

Influence of crossflow microfiltration on ceramic membrane fouling and beer quality

Abstract In this article, an experimental investigation has been carried out to determine the types of fouling phenomena that occur during clarification of dilute malt extract (DME) and pasteurization of clarified beer (CB) by a tubular ceramic membrane in a crossflow pilot plant. Using the classical models, the predominant fouling mechanism responsible for flux decline was found to be complete blocking of the membrane pores followed by formation of a compressible cake layer of yeast cell in the case of DME clarification, whereas the internal fouling of the membrane occurs during pasteurization of CB. The effects of operating parameters, including temperature, transmembrane pressure, and crossflow velocity, on the steady-state permeate flux, as the key factor of crossflow microfiltration processes, were examined. For CB microfiltration, the steady-state permeation flux increased almost linearly with transmembrane pressure and the membrane could reduce the turbidity by 60%. For DME filtration, the maximum ...

A simplified model for prediction of time-dependent axial dispersion coefficient

Abstract A simple model is proposed for prediction of the axial dispersion coefficient as a function of time. The model contains only a single parameter called the decay time, which is the time required for the mean concentration to approach 1 e of its initial value. The asymptotic value of this coefficient for large times approaches the value predicted by the Taylor dispersion theory. The model is valid for laminar and turbulent flow in closed and open conduits. It is shown that the dispersion coefficient determined from Gill and Subramanian can be approximated very well by the present model.