Modelling Flocculated Cell Suspensions using a Population Balance Approach: Applications to Microfiltration
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Modelling Flocculated Cell Suspensions using a Population Balance Approach: Applications to Microfiltration S. Ranil Wickramasinghe, Binbing Han, Saengchai Akeprathumchai, and Xianghong Qian1 Department of Chemical Engineering, Colorado State University, Fort Collins, CO 80523, U.S.A. 1 Department of Physics, Colorado State University, Fort Collins, CO 80523, U.S.A. ABSTRACT Experimental results for flocculation of yeast and CHO cells using cationic polyelectrolytes are presented. These results suggest the existence of a self-similar floc size distribution. The experimentally determined floc size distributions have been modelled using a population balance approach. For flocculated yeast suspensions, the variation of the floc volume fraction with dimensionless particle diameter is predicted by the population balance model assuming a binary fragment distribution function. However, for CHO cell flocs, the floc volume fraction is predicted using a log normal fragment distribution function. Since the efficiency of unit operations such as microfiltration may be improved by flocculation of the feed suspension characterization of the particle size distribution is of great importance. INTRODUCTION Tangential flow microfiltration is frequently used for bioreactor harvesting in the biotechnology industry. Cells, cell debris and other insoluble particulate matter (typically 0.0210 µm in diameter) are removed from the suspending medium. Often the protein of interest is excreted by the cells into the suspending medium. The tangential flow microfiltration product stream is therefore usually the permeate stream which contains the protein of interest. In tangential flow microfiltration, the feed flows tangentially to the microporous membrane. The driving force for permeate flow through the membrane pores is the transmembrane pressure drop (TMP). During tangential flow microfiltration, the rejected species deposit on the membrane surface forming a compressible cake [1]. The formation of the cake layer results in an additional resistance to permeate flow which leads to a decrease in the permeate flux for a given feed flow rate and transmembrane pressure drop. Previous studies have shown that the addition of flocculants to a feed stream prior to microfiltration can lead to enhanced permeate fluxes [2-3]. These studies indicate that the improvement in the permeate flux is due to an altered particle size distribution. Further the improvement in permeate flux after flocculation may be estimated by determining the particle size distribution of the flocculated feed stream. Flocculation of cell suspensions will lead to a distribution of particle sizes. The existence of a steady state floc size distribution has been demonstrated experimentally by a number of investigators [4-7]. Further, if the dimensionless steady state floc size distributions obtained under different conditions can be collapsed on to the same curve, the distribution is said to be self-similar [8]. Obtaining such a distribution is of considerable value not only in
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