By T.K. Ghose ,A. Fiechter, N.Blakebrough
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Extra resources for Advances in Biochemical Engineering, Volume 008: Mass Transfer in Biotechnology
I la s ) MA G- KLaGICA _ CA ) / / " - G A S / - aUBBLE( aG ) SURFACE \ \ \ /~IAL- k'LaS(CA'CAsl \ / Fig. 30. Diffusion model for three phase interphase mass transfer where KL is the mass transfer coefficient for this interphase transport process, a G is the surface area of the gas phase (bubbles), C~, is the maximum concentration of the solute (the concentration of A when the liquid is saturated with A at the prevailing partial pressure of A in the gas phase), and CA is the actual concentration of A in the liquid phase.
Nagata [91 ] has also Technical Aspects of the RheologicalProperties of Microbial Cultures 37 shown that one can obtain a rough approximation of mixing time from NOm - 3V NQ-d~' (45) where V is the liquid volume. For other correlations the reader is referred to the literature [80-89], the reviews of Wang and Humphrey  and Hyman  and in particular to the comprehensive treatise of Nagata. However, in all cases the reader should be aware that these correlations for Newtonian fluids were developed for unsparged systems containing no cell mass and may not be applicable to aerated reactors (see below).
Before going on it is worth noting that the apparent viscosity reported by LeDuy et al. 0 s-1. They refer to this as the fieM apparent viscosity (Pap). It is important to recognize that this is not necessarily equal to the consistency index (K) in the power law model as the latter is an extrapolated value which need not have a real physical significance at a shear rate of 1 s- l . Finally, LeDuy et al. /" 30 i01 . '//; M. Charles i0 ° /,_2,,8_/// Im tud i(~t. ' IJJ "t" 03 ~O~B- 1459 id 2. _B_1973 4''\ !