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in tower fermenters, in which immobilized cells and enzymes or microbial flocculants are retained in the vessel by a sedimentation zone within the vessel. Unlike the ideal CSTR, tower fermenters may exhibit spatial variations in nutrient concentrations and broth properties along the height of the tower that can significantly influence reactor performance. In addition, the productivity in these reactors may be limited by the need to maintain low upward velocities (e.g., low aeration or CO2 evolution) to allow adequate cell sedimentation.

Centrifugation. The operating principle behind centri-fugation is the same as that of sedimentation; however, much higher settling velocities than in sedimentation may be obtained in the centrifugal field. Centrifugal separators enable high-volume continuous processing of fluids containing many particles, with short retention times and small space requirements. To determine the unhindered particle velocity in a centrifugal field (u0C), equation 40 is multiplied by the centrifugal coefficient (C), also known as the G-value, which describes the increase in sedimentation rate due to centrifugation relative to gravitational settling:

where r is the radial distance from the axis of rotation and x is the angular velocity.

Industrial centrifuges are most often classified by internal structure (e.g., disk stack, tubular bowl) and mode of operation (e.g., solids retaining, continuous or intermittent solids ejecting). The selection of sturdier construction and materials will enable higher rotation speeds for separation of smaller particles. The equation describing throughput in a centrifuge is analogous to equation 42, except that the centrifuge area is expressed using the R value, which is the area equivalent for a given centrifuge and rotation speed. Centrifuge manufacturers will often provide machine-specific R values, although the R value for simple disk-stack and tubular-bowl centrifuges can be calculated directly.

Filtration. Filtration is separation based on size, allowing retention of molecules larger than the pore size of the filter and passage of smaller molecules. Membrane filtration thus offers the twin benefits of cell retention and inhibitory by-product removal. In cell recycle systems, the most common arrangements are internal filters for cell and enzyme retention (52,53) or external membrane filters (54,55) in plate and frame, spiral cartridge, and hollow fiber configurations. In all these configurations, flow patterns tangential to the membrane surface can reduce fouling and improve the filtrate flux across the membrane. Compared to internal filters, external filters have higher surface-area-to-volume ratios and may be easier to maintain; however, they may be less easily sterilized (particularly for some polymer membranes) and could introduce problems of nutrient depletion in the external recycle loop. Membrane selection depends primarily on the critical particle size, with other criteria being cost, mechanical stability, and susceptibility to plugging and fouling. Because membranes have the potential for complete cell recycle, a purge or bleed stream is typically split from the recycle stream to prevent accumulation of inert particles and debris in the vessel.

Material Balances. A schematic of a CSTR with recycle of cells is shown in Figure 4. A material balance on cell mass for the CSTR with recycle system, neglecting cell death, may be written

F • X0 + a • F • C • X1 - (1 + a) • F • X1

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