Ultrafiltration pressure-independent

The explanation of the pressure-independent region during the ultrafiltration of macromolecules requires the arbitrary introduction of the concept of a gel-layer in the film model. A more complete description of the dependence of the membrane permeation rate on the applied pressure may be given by considering the effect of the osmotic pressure of the macromolecules as described by Wijmans et alS18 Equation 8.2 may then be written as ... 

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. 

Pressure-Independent Ultrafiltration—Is It Gel Limited or Osmotic Pressure Limited ... 

In the ultrafiltration of macromolecular solutions, a large number of investigators have observed that as pressure is increased, permeate flux first increases and then remains more or less pressure independent. Blatt, (1970), among others,... 

Gel polarized ultrafiltration was recently analyzed for cross flow and unstirred batch cell systems by Trettin and Doshi (1980 a,b). We have shown in these papers that the widely used film theory does not predict the limiting flux accurately. The objective of this paper is to derive an expression for the permeate flux when the pressure independent ultrafiltration of macro-molecular solutions is osmotic pressure limited. We will also attempt to distinguish between gel and osmotic pressure limited ultrafiltration of macromolecular solutions. 

It is theoretically shown for the unstirred batch cell that, in limiting cases, the assumption of constant wall (membrane) concentration with respect to time may be made even in the absence of gel formation. Although the assumption of constant wall concentration is similar in both gel and osmotic pressure limited ultrafiltration, it is important to recognize that in gel polarized ultrafiltration, wall concentration is also pressure independent since it corresponds to the solute solubility limit. This is not the case in osmotic pressure limited ultrafiltration... 

In macromolecular ultrafiltration, 2is pressure is increased, permeate flux first Increases and then In a large number of cases levels out and remains more or less pressure Independent. This could be due to the increase In solute concentration at the membrane surface such that either gel formation occurs or the corresponding osmotic pressure approaches the applied pressure. Limiting flux for the gel polarized case was recently analyzed for cross flow and unstirred batch cell systems by Trettln and Doshi (1980,a, b). In this paper we have analyzed the osmotic pressure limited ultrafiltration for the two systems. Our unstirred batch cell data and the literature cross flow data agree quite well with the theory. We have further shown that an unstirred batch cell system can be used to determine whether pressure Independent ultrafiltration of macromolecular solution is gel or osmotic pressure limited. Other causes for the observed pressure Independence may be present but are not considered in this paper. 

TAYLOR, G.L 1969. Motion of axisymmetric bodies in viscous fluids. In Problems of Hydrodynamics and Continuum Mechanics, pp. 718—724. Philadelphia SIAM. TRETTIN, D.R. 8c DOSHl, M.R. 1981. Pressure-independent ultrafiltration—Is it gel limited or osmotic pressure limited In Synthetic Membranes-, vol. II Hyper- and Ultrafiltration Uses (ed. A.F. Turbak), pp. 373-409. ACS Symp. Series 154. Washington Am. Chem. Soc. 

Transmembrane pressures during ultrafiltration are generally higher than for microfiltration, but pressures in excess of 6 bar are rarely used. Equilibrium fhix rates become pressure independent as illustrated in Figure 10.4, often because of a gel layer which is described in greater detail in Section 10.5. Permeate flux rates from ultrafiltration membranes are usually less than 501 nih ... 

For experiments with proteins, this theory, together with data for osmotic pressure, also aids in explaining the rather unusual response of ultrafiltration rate to pressure and the virtual Independence of this response from fiber length and axial flow velocity. Osmotic pressure data are available in the literature for bovine serum albumin at pH 7.4 ( ), and osmotic pressure measurements of moderate accuracy were made by the authors on bovine calf serum. 

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