Fig. 2.8. Diagrammatic representations of chemostats with feedback (Pirt, 1975).

(a) Internal feedback.

f — flow rate of incoming medium (dm3 h~J) c = fraction of the outflow which is not filtered x = biomass concentration in the vessel and in theunfiltered stream hx = biomass concentration in the filtered stream

(b) External feedback.

F- flow rate from the medium reservoir (dm3 h"1) fs = flow rate of the effluent upstream of the separator * = biomass concentration in the vessel and upstream of the separator hx = biomass concentration in the dilute stream from the separator g= factor by which the separator concentrates the biomass a = proportion of the flow which is fed back to the fermenter s = substrate concentration in the vessel and effluent lines sr = substrate concentration in the medium reservoir filtered stream is (1 - c)F. The concentration of the biomass in the fermenter and in the unfiltered stream is x and the concentration of biomass in the filtered stream is hx. The biomass balance of the system is:

Change in biomass = Growth - Output in unfiltered stream - Output in filtered stream, which may be expressed as:

Ax/At = nx - D{c{ 1 - h) + h}x. At steady state Ax/At = 0, thus:

fix = D{c( 1 - h) + h}x and fi = £>{c(l - h) + h].

If the term 'c(l - h) + h' is represented by 'A', then-

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