Membranes driving force

Figure 20.2 Different types of membrane contactors, (a) stripper/ scrubber, driving force difference of concentration (b) liquid-liquid extractors, driving force difference of concentration (c) removal of volatiles/gases from liquids, driving force difference of partial pressures (d) direct contact membrane distillation, driving force difference of partial pressures (e) supported liquid membranes, driving force difference of concentrations.

The initial distribution ratios Kc = E-p/E (internal or liquid membrane driving force coefficients) are... 

When there is concentration difference of solutes across an ion exchange membrane (driving force difference of chemical potential) the solute diffuses through the membrane. Thus, a diffusion potential corresponding to the concentration gradient is generated across the membrane. The flux of i through the membrane, J is expressed by the Nemst-Planck equation as... 

In our case, current is the flux of substrate across the membrane (/), driving force is the concentration of the substrate (C), conductance is the membrane conductance (PS), and Eq. (2) can be rewritten as... 

Bulk phase solute concentration, M Internal phase solute concentration, M Membrane phase solute concentration, M Internal phase reagent concentration, M Internal phase product concentration, M Effective solute dlffusivlty In the emulsion globule based on the membrane driving force and Including... 

The performance of all membranes is typically described by the permeability and permselectivity parameters. Permeability, or the permeability coefficient, is the flux normalized against the cross-membrane driving force (pressure difference) and the membrane thickness (mohm m 2 s i Pa i). However, the membrane thickness is not readily available for silica membranes, and so permeance, Q (mol m -s npa i), is normally employed instead. Permselectivity, or ideal selectivity S >, is the ratio of the permeability of two different gas species as given by ... 

Nonporous Dense Membranes. Nonporous, dense membranes consist of a dense film through which permeants are transported by diffusion under the driving force of a pressure, concentration, or electrical potential gradient. The separation of various components of a solution is related directiy to their relative transport rate within the membrane, which is determined by their diffusivity and solubiUty ia the membrane material. An important property of nonporous, dense membranes is that even permeants of similar size may be separated when their concentration ia the membrane material (ie, their solubiUty) differs significantly. Most gas separation, pervaporation, and reverse osmosis membranes use dense membranes to perform the separation. However, these membranes usually have an asymmetric stmcture to improve the flux. 

The fourth fully developed membrane process is electrodialysis, in which charged membranes are used to separate ions from aqueous solutions under the driving force of an electrical potential difference. The process utilizes an electrodialysis stack, built on the plate-and-frame principle, containing several hundred individual cells formed by a pair of anion- and cation-exchange membranes. The principal current appHcation of electrodialysis is the desalting of brackish groundwater. However, industrial use of the process in the food industry, for example to deionize cheese whey, is growing, as is its use in poUution-control appHcations. 

Gas Separation. During the 1980s, gas separation using membranes became a commercially important process the size of this appHcation is stiH increasing rapidly. In gas separation, one of the components of the feed permeates a permselective membrane at a much higher rate than the others. The driving force is the pressure difference between the pressurized feed gas and the lower pressure permeate. 

This system utilizes specific membranes, between which the dmg reservoir is enclosed (Fig. 4). A tiny ehiptical disk, inserted into the cul-de-sac of the eye, releases pilocarpiae steadily. The dmg is deUvered through selected polymeric membranes. The dmg reservoir maintains a saturated solution between the membranes which acts osmoticaHy as the driving force for the dmg to diffuse through the rate-limiting membranes. 

A reverse osmosis membrane acts as the semipermeable barrier to flow ia the RO process, aHowiag selective passage of a particular species, usually water, while partially or completely retaining other species, ie, solutes such as salts. Chemical potential gradients across the membrane provide the driving forces for solute and solvent transport across the membrane. The solute chemical potential gradient, —is usually expressed ia terms of concentration the water (solvent) chemical potential gradient, —Afi, is usually expressed ia terms of pressure difference across the membrane. 

The pressure difference between the high and low pressure sides of the membrane is denoted as AP the osmotic pressure difference across the membrane is defined as Att the net driving force for water transport across the membrane is AP — (tAtt, where O is the Staverman reflection coefficient and a = 1 means 100% solute rejection. The standardized terminology recommended for use to describe pressure-driven membrane processes, including that for reverse osmosis, has been reviewed (24). 

Solution—Diffusion Model. In the solution—diffusion model, it is assumed that (/) the RO membrane has a homogeneous, nonporous surface layer (2) both the solute and solvent dissolve in this layer and then each diffuses across it (J) solute and solvent diffusion is uncoupled and each is the result of the particular material s chemical potential gradient across the membrane and (4) the gradients are the result of concentration and pressure differences across the membrane (26,30). The driving force for water transport is primarily a result of the net transmembrane pressure difference and can be represented by equation 5 ... 

Membrane Filtration. Membrane filtration describes a number of weU-known processes including reverse osmosis, ultrafiltration, nanofiltration, microfiltration, and electro dialysis. The basic principle behind this technology is the use of a driving force (electricity or pressure) to filter... 

Reverse Osmosis. Osmosis is the flow of solvent through a semipermeable membrane, from a dilute solution to a concentrated solution. This flow results from the driving force created by the difference in pressure between the two solutions. Osmotic pressure is the pressure that must be added to the concentrated solution side to stop the solvent flow through the membrane. Reverse osmosis is the process of reversing the flow, forcing water through a membrane from a concentrated solution to a dilute solution to produce pure water. Figure 2 illustrates the processes of osmosis and reverse osmosis. 

Osmotic Control. Several oral osmotic systems (OROS) have been developed by the Alza Corporation to allow controUed deHvery of highly water-soluble dmgs. The elementary osmotic pump (94) consists of an osmotic core containing dmg surrounded by a semi-permeable membrane having a laser-drilled deHvery orifice. The system looks like a conventional tablet, yet the outer layer allows only the diffusion of water into the core of the unit. The rate of water diffusion into the system is controUed by the membrane s permeabUity to water and by the osmotic activity of the core. Because the membrane does not expand as water is absorbed, the dmg solution must leave the interior of the tablet through the smaU orifice at the same rate that water enters by osmosis. The osmotic driving force is constant until aU of the dmg is dissolved thus, the osmotic system maintains a constant deHvery rate of dmg until the time of complete dissolution of the dmg. 

If the dmg itself cannot provide the osmotic driving force, then a push-puU design of the osmotic system is available with other salts as the osmotic force. This system is schematized in Eigure 5. The outer surface is a rigid semi-permeable membrane that surrounds the osmotic layer of salt (propeUant). Inside the osmotic layer is a compressible membrane that surrounds the dmg solution. As the salt layer sweUs with water, the inner membrane compresses and pushes out the dmg solution. 

Equation (22-106) gives a permeate concentration as a function of the feed concentration at a stage cut, 0 = 0, To calculate permeate composition as a function of 0, the equation may be used iteratively if the permeate is unmixed, such as would apply in a test cell. The calculation for real devices must take into account the fact that the driving force is variable due to changes on both sides of the membrane, as partial pressure is a point function, nowhere constant. Using the same caveat, permeation rates may be calciilated component by component using Eq. (22-98) and permeance values. For any real device, both concentration and permeation require iterative calculations dependent on module geometiy. 

Driving Force Gas moves across a membrane in response to a difference in chemical potential. Partial pressure is sufficiently proportional to be used as the variable for design calculations for most gases of interest, but fugacity must be used for CO9 and usually for Hg... 

Membrane System Design Features For the rate process of permeation to occur, there must be a driving force. For gas separations, that force is partial pressure (or fugacity). Since the ratio of the component fluxes determines the separation, the partial pressure of each component at each point is important. There are three ways of driving the process Either high partial pressure on the feed side (achieved by high total pressure), or low partial pressure on the permeate side, which may be achieved either by vacuum or by introduc-... 

Partial Pressure Pinch An example of the hmitations of the partial pressure pinch is the dehumidification of air by membrane. While O9 is the fast gas in air separation, in this apphcation H9O is faster still. Special dehydration membranes exhibit a = 20,000. As gas passes down the membrane, the pai-dal pressure of H9O drops rapidly in the feed. Since the H9O in the permeate is diluted only by the O9 and N9 permeating simultaneously, p oo rises rapidly in the permeate. Soon there is no driving force. The commercial solution is to take some of the diy air product and introduce it into the permeate side as a countercurrent sweep gas, to dilute the permeate and lower the H9O partial pressure. It is in effect the introduction of a leak into the membrane, but it is a controlled leak and it is introduced at the optimum position. 

For rubbeiy membranes (hydrophobic), the degree of swelling has less effect on selectivity. Thus the permeate pressure is less critical to the separation, but it is critical to the driving force, thus flux, since the vapor pressure of the organic will be high compared to that of water. 

Filtration Cross-flow filtration (microfiltration includes cross-flow filtration as one mode of operation in Membrane Separation Processes which appears earlier in this section) relies on the retention of particles by a membrane. The driving force for separation is pressure across a semipermeable membrane, while a tangential flow of the feed stream parallel to the membrane surface inhibits solids settling on and within the membrane matrix (Datar and Rosen, loc. cit.). 

Table 2 provides a comparison of membrane structures. Between these two tables, you should get an idea of the operating conditions viz., membrane structural types, the driving forces involved in separation, and the separation mechanisms. 

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