Membrane separation flux modeling

Most of the general models for describing flux through porous media is given by the DGM. The term DGM, which was first described by Maxwell in 1860 [39], is relatively unfamiliar in the membrane separation field and has only recently been appearing in the membrane literature [33,39,41,60,61]. In this model, the porous medium is visualized as a collection of uniformly distributed dust particles, which are construed to be stationary. 

In the following discussion, we consider an ideal situation where the flux of a molecular species is localized to a single pore the membrane is otherwise impermeable to the molecule. Although this model is only an approximation of real samples, the resulting theory remains quite useful in the quantitative analysis of porous membranes, provided that the pores are not too closely spaced. The membrane separates donor and receptor solutions the donor solution contains an electroactive molecule that is transported across the membrane and detected by the SECM tip on the receptor side of the membrane (Fig. 1). 

If the organ is reasonably well perfused (i.e., the flow-limited conditions are not satisfied), the full physiological pharmacokinetic treatment may be reduced by assuming the organ is membrane limited. Here, the limitation on transport is assumed to occur at either the capillary membrane separating the vascular and interstitial compartments or the plasma membranes separating the interstitial and intracellular compartments. For example, when the net flux between the interstitial and intracellular compartments is much slower than the net flux between the vascular and interstitial compartments and the plasma flow rate, the three-compartment model can be reduced to a two-compartment model ... 

Fig. 14 Separation of C2H6/CH4 mixtures by permeation through a silicalite membrane, a Flux b selectivity. Continuous lines show the predictions of the Maxwell-Stefan model (Eq. 44) based on single-component diffusivities (Dqa> F>ob) with Dab from the Vignes correlation (Eq. 46). Dotted lines show predictions from the simplified Habgood model in which mutual diffusion effects are ignored (Eq. 45). From van de Graaf et al. [53] with permission...

In order to solve the MDPE in Equation 9.1, it is necessary to understand how y is related to x. There are numerous methods of describing this relationship. Gas separation involves the diffusion of a gaseous mixture through the membrane material. The rate at which a gas, or particular component of a gas mixture, moves through a membrane is known as the flux (total or individual). In order to obtain a general flux model for a gas separation membrane, the fundamental thermodynamic approach incorporating the solution-diffusion model [11] will be used at vacuum permeate conditions (itp 0) ... 

Solution diffusion — gas dissolves in the membrane material and diffuses across it. The membranes used in most commercial appHcations are non-porous in structure where separation is based on the SD mechanism. This mechanism involves molecular-scale interactions of the permeating gas with the membrane polymer. The model assumes that each component is sorbed by the membrane at one interface, transported by diffusion across the membrane through the voids between the polymeric chains (the so-called free volume ) and desorbed at the other interface. According to the SD model, the flux of gas through a membrane is given by... 

Liquid membrane separation systems possess great potential for performing cation separations. Many factors influence the effectiveness of a membrane separation system including complexation/ decomplexation kinetics, membrane thickness, complex diffusivity, anion type, solvent type, and the use of ionic additives. The role that each of these factors plays in determining cation selectivity and flux is discussed. In an effort to arrive at a more rational approach to liquid membrane design, the effect of varying each of these parameters is established both empirically and with theoretical models. Finally, several general liquid membrane types are reviewed, and a novel membrane type, the polymeric inclusion membrane, is discussed. 

The aim of this section is to present an innovative methodology modeling the permeate flux decay in membrane separation processes. An ANN was developed on the basis of the experimental results collected during the ultrafiltration of bovine serum albumin (BSA) solutions under pulsating conditions (Curcio et al, 2005). 

This condition has been recently used in a vaporization-exchange model for water sorption and flux in phase-separated ionomer membranes. The model allows determining interfacial water exchange rates and water permeabilities from measurements involving membranes in contact with flowing gases. It affords a definition of an effective resistance to water flux through the membrane that is proportional to... 

The first term on the right-hand side is the diffusive flux relative to the volume average velocity. The second term represents a contribution due to bulk flow. It should be emphasized here that the separation of the total flux into two contributions is always possible regardless of the actual transport mechanism through the membrane. In other words, Eq. (7) is purely phenomenological and does not require any specific transport model. 

This paper has provided the reader with an introduction to a class of polymers that show great potential as reverse osmosis membrane materials — poly(aryl ethers). Resistance to degradation and hydrolysis as well as resistance to stress Induced creep make membranes of these polymers particularly attractive. It has been demonstrated that through sulfonation the hydrophilic/hydrophobic, flux/separation, and structural stability characteristics of these membranes can be altered to suit the specific application. It has been Illustrated that the nature of the counter-ion of the sulfonation plays a role in determining performance characteristics. In the preliminary studies reported here, one particular poly(aryl ether) has been studied — the sulfonated derivative of Blsphenol A - polysulfone. This polymer was selected to serve as a model for the development of experimental techniques as well as to permit the investigation of variables... 

Reverse osmosis, pervaporation and polymeric gas separation membranes have a dense polymer layer with no visible pores, in which the separation occurs. These membranes show different transport rates for molecules as small as 2-5 A in diameter. The fluxes of permeants through these membranes are also much lower than through the microporous membranes. Transport is best described by the solution-diffusion model. The spaces between the polymer chains in these membranes are less than 5 A in diameter and so are within the normal range of thermal motion of the polymer chains that make up the membrane matrix. Molecules permeate the membrane through free volume elements between the polymer chains that are transient on the timescale of the diffusion processes occurring. 

Concentration polarization can dominate the transmembrane flux in UF, and this can be described by boundary-layer models. Because the fluxes through nonporous barriers are lower than in UF, polarization effects are less important in reverse osmosis (RO), nanofiltration (NF), pervaporation (PV), electrodialysis (ED) or carrier-mediated separation. Interactions between substances in the feed and the membrane surface (adsorption, fouling) may also significantly influence the separation performance fouling is especially strong with aqueous feeds. 

Similar to the approach for solvents, both diffusive and convective transport of solutes can be modeled separately. For dense membranes, a solution-diffusion model can be used [14], where the flux / of a solute is calculated as ... 

Important for practical implemetation of zeolitic membranes is the acquisition of permeation data of single components and mixtures and the interpretation of these data in the form of macroscopic models. These models describe the permeation flux of components as a function of partial pressure, composition and temperature. Once good models exist separation units can be designed for the separation of multicomponent mixtures. 

Generally, alcohols showed higher separation factors when present in model multicomponent solutions than in binary systems with water. On the other hand, aldehydes showed an opposite trend. The acmal tea aroma mixmre showed a rather different behavior from the model aroma mixmre, probably because of the presence of very large numbers of unknown compounds. Overall, the PDMS membrane with vinyl end groups used by Kanani et al. [20] showed higher separation factors and fluxes for most of the aroma compounds. Pervaporation was found to be an attractive technology. However, as mentioned above the varying selectivities for the different aroma compounds alter the sensory prohle and therefore application of PV for recovery of such mixmres needs careful consideration on a case-by-case basis. 

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