Unstirred batch cell

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. 

Consider the unstirred batch cell geometry shown in Fig. 1 where the general solute mass balance equation of... 

An analogous treatment to the unstirred batch cell may be performed for the thin channel system where... 

Introducing the similarity coordinate, analogous to unstirred batch cell problem, Eq. (20),... 

When the criterion of Eq. (46) for the unstirred batch cell, or Eq. (77) for the cross flow parallel plate system, is satisfied, it is possible to make the simplifying assumption of constant wall concentration (c c ). Consequently, Eq. (36) becomes... 

As can be seen, the unstirred batch cell technique represents a unique method for characterizing macromolecular solutions as to the pressure range in which gel polarization occurs. One must be cautious in using the batch cell technique, however, to select AP increments which are large enough to cause a discernible... 

Figure 4. Unstirred batch cell UF of 0.15M NaCl BSA solution fT =-= 21°-24°C, pH 7.4) at various solute concentrations and applied pressures...

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... 

When the assumption of constant wall concentration is justified, data for the unstirred batch cell and thin channel systems may be interpreted using models presented in Trettln and Doshi (1980a, 1980b). Such an analysis is performed where agreement is shown to be very good between theory and osmotic pressure limited ultrafiltration experiments. 

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. 

Tietjen, K. G. Hunkier, D. Matem, U. "Differential Response of Cultured Parsley Cells to Elicitors from Two Non-pathogenic Strains of Fungi, 1. Identification of Induced Products as Coumarin Derivatives" Eur. ]. Biochem. 1983,131, pp 401-407. Devereux, N. Hoare, M. Duimill, P. "Membrane Separation of Protein Precipitates Unstirred Batch Studies" Biotech, and Bioeng. 1986, 28, pp 88-96. Mateus, M. Cabral, J. M. S. "Recovery of 6-a-methylprednisolone from biotransformation medium by tangential flow filtration" In Bioprocess Engineering. 1989, Springer Verlag, (in press). 

Exceptions to the practice of not adding buffer to plant tissue samples are numerous. Root tissues must be maintained moist and consequently are examined while in close contact with buffer-saturated filter paper disks [34, 35]. Immersing root tissue in water does not yield satisfactory data. Callus tissue cells and cell cultures are commonly measured while being maintained on agar or in liquid media. Marine tissues may be examined in water suspension by flow calorimetry, but unstirred samples rapidly settle to the bottom of the ampule and become O2 limited during batch calorimetry. 

A means of measuring plant cell culture activities in liquid media by unstirred batch calorimetry was demonstrated by Fontana et al. [47]. Cells were floated on liquid media supplemented with an inert, high density preparation of Percoll. Other additives could also be used to increase media density. Cells at the air-media interface were able to obtain adequate supplies of both O2 and nutrients for rapid metabolism without diffusion rate limitations. 

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