Ultrafiltration solvent flux

The concentration polarization effects for hollow fibers is often quite small because of the low solvent flux. Hence, Eq. (13.11-1) describes the flux. In order to increase the ultrafiltration solvent flux, cross-flow of fluid past the membrane can be used to sweep away part of the polarized layer, thereby increasing in Eq. (13.11-4). Higher velocities and other methods are used to increase turbulence, and hence, k. In most cases the solvent flux is too small to operate in a single-pass mode. It is necessary to recirculate the feed by the membrane with recirculation rates of 10/1 to 100/1 often used. 

Mass-transport limitations are common to all processes involving mass transfer at interfaces, and membranes are not an exception. This problem can be extremely important both for situations where the transport of solvent through the membrane is faster and preferential when compared with the transport of solute(s) - which happens with membrane filtration processes such as microfiltration and ultrafiltration - as well as with processes where the flux of solute(s) is preferential, as happens in organophilic pervaporation. In the first case, the concentration of solute builds up near the membrane interface, while in the second case a depletion of solute occurs. In both situations the performance of the system is affected negatively (1) solute accumulation leads, ultimately, to a loss of selectivity for solute rejection, promotes conditions for membrane fouling and local increase of osmotic pressure difference, which impacts on solvent flux (2) solute depletion at the membrane surface diminishes the driving force for solute transport, which impacts on solute flux and, ultimately, on the overall process selectivity towards the transport of that specific solute. 

In the absence of suspended solutes or colloids, the pure solvent flux through an ultrafiltration membrane is directly proportional to the applied pressure difference and inversely proportional to the viscosity of the solvent and the membrane thickness. Transport within the pores occurs in the creeping flow regime, since kinematic viscosities of liquids are sufficient to make Re < C 1 for practical pore sizes. In the simplest case, the membrane can be considered to be a packed array of straight, equal diameter nonintersecting capillary tubes. The observed volumetric flux, nAvA (cc/sec cm2), equals the product of the mass flux of solvent based on the total membrane area, nA... 

Almost all reported OSN data have been obtained at the lab scale and with dilute solutions (<1 wt% solute in solvent), whereas in actual appHcations, solutes will be more concentrated (>5 wt%). Under these conditions, concentration polarization and osmotic pressure may contribute to the solvent flux, as they do in well-studied aqueous systems. There are several studies on concentration polarization in aqueous systems, mainly concerning ultrafiltration [38-42]. We as-... 

In the absence of any concentration polarization, and Cfi are equal to Cg and respectively. The extent of concentration polarization and its effects on the solvent flux and solute transport for porous membranes and macrosolutes/proteins can be quite severe (see Section 6.3.3). This model is often termed the combined diffusion-viscous flow model (Merten, 1966), and it can be used in ultrafiltration (see Sections 6.3.3.2 and 7.2.1.3). The relations between this and other models, such as the finely porous model, are considered in Soltanieh and Gill (1981). 

The above analysis/description of solvent flux and macrosolute rejection/retention/ttansmission far an ultra-flllration membreme was carried out in the context of a pseudo steady state analysis in a batch cell (Figure 6.3.26 (a)). Back diffusion of the macrosolute from the feed solution-membrane interface to the bulk solution takes place by simple difflision against the small bulk flow parallel to the force direction. The resulting mass-transfer coefficients for macrosolutes will be quite small the solvent flux levels achievable will be quite low. For practically useful ultrafiltration rates, the mass-transfer coefficient is increased via different flow configurations with respect to the force. 

There is an important consideration in the separation of a gas mixture through a membrane, as shown in Figure 6.3.32. For a similar configuration, we have seen in Figure 6.3.26 for ultrafiltration that the concentration of the rejected species builds up on the feed side of the membrane the extent of the buildup is dependent on the solvent flux through the membrane and the rate of back diffusion of the species, specifically the ratio ( Vz /ku). The lower the value of this ratio, the lower the buildup of the rejected species on the feed surface of the membrane. If we employ the same analogy here, then we should determine the... 

Obviously batch ultrafiltration or one-stage discontinuous diafiltration is a more efficient technique for puriiying the protein of a low molecular weight impurity. However, one must ensme that the required solvent flux level is achievable in batch UF when the volume is reduced. 

In a stirred ultrafiltration cell using a flat UF membrane, an aqueous solution of the polymer Dextran 20 was ultrafiltered. Data were gathered at different values of the water flux, and the solute rejection was measured. Dextran 20 is a linear polymer, and, as the solvent flux was increased, the rejection observed for Dextran 20 decreased. A plot of the solvent flux against the quantity (1 —Robs)/K>bs in a semilogarithmic plot (logarithmic on the abscissa for (1 ilobs)/fiobs) yielded a straight line with a positive slope and an intercept of 0.05 on the abscissa. 

The solution of such an equation for an actual membrane device for ultrafiltration is difficult to obtain (see Zeman and Zydney (1996) for background information). One therefore usually falls back on the stagnant film model for determining the relation between the solvent flux and the concentration profile (see result (6.3.142b)). To use this result, we need to estimate the mass-transfer coefficient kit = Dit/dt), for the protein/macromolecule. One can focus on the entrance region of the concentration boundary layer, assume to be constant for a dilute solution, V = V, Vj, = 0 in the thin boundary layer, v = y ,y (where is the wall shear rate of magnitude AVz/Ay ) and obtain the result known as the Leveque solution at any location z in terms of the Sherwood number ... 

Ultrafiltration of latex solutions, (e.g., PVC (polyvinyl chloride) latex) may be carried out in a tubular device containing membrane tubes of 2.54 cm I.D. The solvent flux Vso was found in a few experiments to be proportional to Q , where Qf is the volumetric latex flow rate through the tube and bj > 1.0. Assume that the Sherwood number kuo di/Du) for the mass-transfer process is such that Sh = (kuodi/Du) oc (/Je) . 

It has been observed that particle flux expressions developed based on shear-induced particle diffusivity describe the observed solvent flux through a microflltration membrane much better than those based on Brownian diffusivity of a particle. For the following system properties, determine the ratio of the solvent fluxes based on shear-induced particle diffusivity and Brownian diffusivity. You should employ the particle volume fraction based solvent flux expression based on the gel polarization model used in ultrafiltration (equation (7.2.72)) ... 

Membrane Properties. The performance range of ammonia-modified membranes in low pressure operation is indicated in Figure 6 along with the performance of the reference membrane (I, reference membrane IV, ammonia-modified membrane). The lower boundary of the performance range refers to a solvent-to-polymer ratio of 3, the upper boundary to a ratio of 4. While the salt rejection towards univalent ions of the ammonia-modified membrane is limited to below 80 %, the maximum low pressure flux is over 15 m /m d (approaching 400 gfd) at a sodium chloride rejection of the order of 10 %. This membrane thus exhibits the flux capability of an ultrafiltration membrane while retaining the features of reverse osmosis membranes, viz. asymmetry and pressure resistance. 

In ultrafiltration and reverse osmosis, in which solutions are concentrated by allowing the solvent to permeate a semi-permeable membrane, the permeate flux (i.e. the flow of permeate or solvent per unit time, per unit membrane area) declines continuously during operation, although not at a constant rate. Probably the most important contribution to flux decline is the formation of a concentration polarisation layer. As solvent passes through the membrane, the solute molecules which are unable to pass through become concentrated next to the membrane surface. Consequently, the efficiency of separafion decreases as fhis layer of concentrated solution accumulates. The layer is established within the first few seconds of operation and is an inevitable consequence of the separation of solvent and solute. 

The same nanofiltration experiments were performed with a 50-A ultrafiltration membrane (available from US Filter/Membralox, Warrendale, PA,USA), this time with a monodentate phosphite ligand (24) used for comparison and toluene as the solvent (Table V). Both higher retentions and flux rates for the dendrimers were obtained relative to what was observed with the reverse osmosis membranes. Dendrophite G4 was used in three subsequent reactions carried out with this procedure. 

The production by Loeb and Sourirajan of the first successful anisotropic membranes spawned numerous other techniques in which a microporous membrane is used as a support for a thin, dense separating layer. One of the most important of these was interfacial polymerization, an entirely new method of making anisotropic membranes developed by John Cadotte, then at North Star Research. Reverse osmosis membranes produced by this technique had dramatically improved salt rejections and water fluxes compared to those prepared by the Loeb-Souri-rajan process. Almost all reverse osmosis membranes are now made by the interfacial polymerization process, illustrated in Figure 3.20. In this method, an aqueous solution of a reactive prepolymer, such as a polyamine, is first deposited in the pores of a microporous support membrane, typically a polysul-fone ultrafiltration membrane. The amine-loaded support is then immersed in a water-immiscible solvent solution containing a reactant, such as a diacid chloride in hexane. The amine and acid chloride react at the interface of the two immiscible... 

Metal oxides, used for manufacturing of ceramic nanofiltration membranes, are intrinsically hydrophilic. This limits the use of these membranes to polar solvents filtration of nonpolar solvents (n-hexane, toluene, cyclohexane) usually yields zero fluxes. Attempts have been made to modify the pore structure by adding hydrophobic groups, for example, in a silane coupling reaction [38, 43]. This approach is similar to modifications of ultrafiltration and microfiltration membranes... 

In the presence of solutes with small molecular weights, concentration polarization is likely to occur but with much less effect than in the case of ultrafiltration as explained in Section 12.2.1. A theoretical model concerning separation of sucrose and raffinose by ultrafiltration membranes has been proposed by Baker et al. [53] which assumes transport of solvent and solute exclusively through pores. This model can apply to ceramic nanofilters as they exhibit a porous structure with a pore size distribution. The retention characteristics of a given membrane for a given solute is basically determined by its pore-size distribution. The partial volume flux jy through the pores which show no rejection to the solute can be expressed as a fraction of the total volume flux fy. 

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