Ultrafiltration membranes curves

The Ferry-Renkin equation can be used to estimate the pore size of ultrafiltration membranes from the membrane s rejection of a solute of known radius. The rejections of globular proteins by four typical ultrafiltration membranes plotted against the cube root of the protein molecular weight (an approximate measure of the molecular radius) are shown in Figure 2.33(a). The theoretical curves... 

Figure 2.33 (a) Rejection of globular proteins by ultrafiltration membranes of increasing pore size (b) calculated rejection curves from the Ferry-Renkin equation (2.106) plotted on the same scale [52]... 

Equations (22-86) and (22-89) are the turbulent- and laminar-flow flux equations for the pressure-independent portion of the ultrafiltration operating curve. They assume complete retention of solute. Appropriate values of diffusivity and kinematic viscosity are rarely known, so an a priori solution of the equations isn t usually possible. Interpolation, extrapolation, even prediction of an operating curve may be done from limited data. For turbulent flow over an unfouled membrane of a solution containing no particulates, the exponent on Q is usually 0.8. Fouhng reduces the exponent and particulates can increase the exponent to a value as high as 2. These equations also apply to some cases of reverse osmosis and microfiltration. In the former, the constancy of C aji may not be assumed, and in the latter, D is usually enhanced very significantly by the action of materials not in true solution. 

Together, fractional rejection curve (Rjj.) and traditional cut off curve will give more information on the rejection characteristics of ultrafiltration membranes. 

Recently, Ulbricht and coworkers [131] have reported the preparation of low-fouling ultrafiltration membranes by simultaneous photograft copolymerization of hydrophilic poly(ethylene glycol) methacrylate onto a polyethersulfone (PES) membrane. A broad characterization using flux measurement and sieving curve... 

FIGURE 5.24 Pore size distribution curves of PL (curves 1-3) and PB (curves 4-6) series of membranes with 5, 10, and 30 kDa. (Adapted from J. Membr. ScL, 309, Jeon, J.-D., Kim, S. J., and Kwak, S.-Y., H nuclear magnetic resonance (NMR) cryoporometry as a tool to determine the pore size distribution of ultrafiltration membranes, 233-238, 2008, Copyright 2008, with permission from Elsevier.)... 

At the lowest pressures the largest pores will be filled with mercury. On increasing the pressure, progressively smaller pores will be filled according to eq. IV - 3. This will continue until ail the pores have been filled and a maximum intrusion value is reached. It is possible to deduce the pore size distribution from the curve given in figure IV - 10, because every pressure is related to one specific pore size (or entrance to the pore ). The pore sizes covered by this technique range from about 5 nm to 10 pm. This means that all microfiltration membranes can be characterised as well as a substantial proportion of the ultrafiltration membranes. 

Figure I - 20 gives the cumulative pore volume and the pore size distribution for a PPO poly(phenylene oxide) ultrafiltration membrane determined by thermoporometry [12]. Figure I - 21 gives the pore size distribution of a ceramic membrane determined by two methods gas adsorption-desorption and thermoporometry [13]. Both curves (and hence both methods) are in good agreement with each other. Similar results were found by Cuperus for Y-aJumina membranes [14].

Figure 6.1 Schematic illustrating in vivo membrane separation processes. Left microdialysis sampling probe with curved lines indicating analyte tortuous diffusion through the tissue into and out of the probe. Right ultrafiltration representing interstitial fluid flow into the membrane device. Tissue is represented with cells and hlood vessels (dark circles in light circles).

It is apparent from all these results that the Spiegler and Kedem equations, Eqs. (11) and (12), were suitable as transport equations of ultrafiltration and the curve-fitting method was the best for the determination of the membrane parameters, O and P. 

Even though enzymatic conversion is not too effective, it is possible to prepare semipermeable membranes whose ultrafiltration yields are higher than those of passive membranes.74 75 Ultrafiltration experiments of cheese whey through cellulosic membranes to which papain was covalently bound, show that flux decay curves of enzymatic membranes are even less sensitive to pH changes.74... 

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