Ultrafiltration macrosolute

Autofiltration The retention of any material at the surface of the membrane gives rise to the possibility of a secondaiy or a dynamic membrane being formed. This is a significant problem for fractionation by ultrafiltration because microsolutes are partially retained by almost all retained macrosolutes. The degree of retention is quite case-specific. As a rule of thumb, higher pressure and more polarization resiilts in more autofiltration. Autofiltration is particularly problematic in attempts to fractionate macromolecules. 

Microfiltration (MF) and ultrafiltration (UF) involve contacting the upstream face ofa porous membrane with a feed stream containing particles or macromolecules (B) suspended in a low molecular weight fluid (A). The pores are simply larger in MF membranes than for UF membranes. In either case, a transmembrane pressure difference motivates the suspending fluid (usually water) to pass through physically observable permanent pores in the membrane. The fluid flow drags suspended particles and macrosolutes to the surface of the membrane where they are rejected due to their excessive size relative to the membrane pores. This simple process... 

Diafiltration is a variation of ultrafiltration, in which fresh solvent is added to the feed solution to replenish the volume ultrafiltered, and in the process washes small molecules such as salts away from the retained macromolecules. Using appropriate replenishing solutions, diafiltration is a common procedure to perform buffer exchange of proteins. Alternatively, a dilute solution may be first ultrafiltered to concentrate the feed material, then diafiltered to purify the retentate. It is sometimes possible to fractionate a mixture of macrosolutes by sequential diafiltration with a series of membranes of progressively lower molecular weight cutoff ratings. 

In practice, however there could be differences between the observed and estimated flux. The mass transfer coefficient is strongly dependent on diffusion coefficient and boundary layer thickness. Under turbulent flow conditions particle shear effects induce hydrodynamic diffusion of particles. Thus, for microfiltration, shear-induced difflisivity values correlate better with the observed filtration rates compared to Brownian difflisivity calculations.Further, concentration polarization effeets are more reliably predicted for MF than UF due to the fact diat macrosolutes diffusivities in gels are much lower than the Brownian difflisivity of micron-sized particles. As a result, the predicted flux for ultrafiltration is much lower than observed, whereas observed flux for microfilters may be eloser to the predicted value. 

Amicon Diaflo ultrafiltration membrane offer a selection of macrosolute retentions ranging from 500 to 300,000 molecular weight as cahbrated with globular macrosolutes. These values correspond to pore sizes between about 1 and 15 nm. Each membrane is characterized by its nominal out-off, that is, its abihty to retain molecules larger than those of a given size. 

For effective ultrafiltration, equipment must be optimized to promote the highest transmembrane flow and selectivity. A major problem which must be overcome is concentration polarization, the accumulation of a gradient of retained macrosolute above the membrane. The extent of polarization is determined by the macrosolute concentration and diffusivity, temperature effects on solution viscosity and system geometry. If left undisturbed, concentration polarization restricts solvent and solute transport through the membrane and can even alter membrane selectivity by forming a gel layer on the membrane surface—in effect, a secondary membrane — increasing rejection of normally permeating species. 

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). 

Consider now a porous membrane for the process of ultrafiltration separation of a protein solution (Section 3.4.2.S). Suppose the regions on the two sides of the membrane have become filled with liquid (from the feed region 1 to product region 2). If the membrane does not reject the protein (a macrosolute) completely, the solute protein will slowly diffuse from region 1 to region 2. Ultimately, both sides will have the same protein concentration. The separation achieved initially will be lost Therefore, in practice, it is necessary to have an open system so that any permeate appearing from the feed side into the permeate side is immediately withdrawn. The same eugument is equally valid if the membrane in reverse osmosis (Section 3.4.2.1) has some permeability of the microsolute present in the feed side. 

Figure 6.3.26. Ultrafiltration, (a) UF in a batch cell macrosolute concentration profile infeed side (b) Piston driven UF in a batch cell bulk flow parallel to the force, (c) Observed behavior ofsolvent flux vs. AP in macrosolute ultrafiltration. For an explanation of (l)-(4), see the text.

Such an analysis assumes that electrostatic and electroki-netic interactions are not important in macrosolute transport through the membrane. Pujar and Zydney (1994) have considered such effects in protein ultrafiltration through narrow pore membranes. 

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. 

Suppose now that is sufficiently small compared to i.e. the membrane allows a substantial amount of species 2 to pass through. Therefore, unless rj and V2 are far apart, the integral in the numerator on the right-hand side of (6.3,147e) is small compared to the denominator. The selectivity of a "diffuse cut off microporous ultrafilter is not very high unless the macrosolutes differ considerably in the values of their solvated radii. Traditionally, therefore, fractionation of macrosolutes like proteins by ultrafiltration is limited to systems where the two macrosolutes differ in size by about seven to ten times (Cherkasov and Polotsky, 1996). 

Consider Figure 6.4.9(a), where, at time t = 0, a batch solution of volume, Vp, is introduced as feed to the vessel on top of the membrane this well-mixed solution has a molar concentration, C,o, of macrosolute species i. If after some time the well-mbced batch feed solution volume is reduced to Vjr, the volume of the retentate, by means of ultrafiltration, what is the macrosolute concentration Qr in the retentate It may be assumed that the observed macrosolute rejection for the species i remains constant during this concentration process (assuming that the macrosolute is substantially rejected). The extent of volume reduction in the well-mbced feed solution is often identified as the... 

If, in a differentially small interval of time. At, a differentially small volume of magnitude dV/7) permeates through the membrane, and the concentration of the macrosolute in the ultrafiltrate is C,p, whereas the macrosolute concentration in the retentate at this time is Qr, then a simple macrosolute balance leads to... 

Consider a time interval dt over which a differential volume dV(, of the buffer is added to the well-stirred feed vessel containing a solution volume Vfo to start with, this solution has a solute concentration Cg, (the lower molecular weight impurity or the macrosolute of interest). Continuous diafiltration is carried out such that the solution volume in the feed vessel remains constant at V/q. Therefore the volume of ultrafiltrate produced in time dt is dVb- it has a species i concentration of Cip at time t. A molar balance on species i leads to... 

An alternative strategy is often adopted it is called discontinuous diafiltration. Consider Figure 6.4.9(c), which shows three identical well-stirred vessels (vessels 1, 2 and 3) having the same ultrafiltration membrane. At time t = 0, a volume Vfo of the feed solution containing a macrosolute i and a microsolute (say, salt) j is present in vessel 1. Assume for the time being that iJj = 1 and / ,= 0. Let the value of the VCR in batch ultrafiltration be 10. Then Cifll, = lOCioandCjfil = Cjo (from equation (6.4.101)). Now let this small volume of concentrate (volume = Vyo/10) be transferred to the next well-stirred vessel (vessel 2), where an amount of fresh buffer solution is added to bring the total solution volume to Vfo- Therefore the two solute concentrations in this vessel 2 are now ... 

Consider ultrafiltration based separation of a protein in the configuration of Figures 6.3.26(a) and (b). Suppose now another membrane, identical to the first membrane, is located below the first membrane at some distance from it. Permeate generated from the first membrane having a protein concentration of Cip becomes the feed to the second UF membrane. The protein concentration in the permeate from the second membrane is Cjp. The protein concentration in the feed to the first membrane is Assume a pseudosteady state the macrosolute observed rejection value Ri for the first membrane may be assumed to be valid for the second membrane as well, in relation to its feed and permeate. 

---