Kinetics of the Steady State Bacterial
Culture IV. Transfer Rates
EDWARD J. MARTIN, Technical Assistant to the Chief
Basic and Applied Sciences Branch
Division of Water Supply and Pollution Control
Public Health Service
U.S. Department of Health, Education, and Welfare
Washington, D. C.
DONALD R. WASHINGTON, Associate Professor
Environmental Engineering
Rensselaer Polytechnic Institute
Troy, New York
ABSTRACT
Through the use of pure bacterial cultures in the continuous flow or steady
state apparatus and carbon-14 tracer techniques, overall carbon transfer rates and
the relationship to the metabolic activity of organisms in this growth condition
have been studied.
Pseudomonas fluorescens has been fed by injecting uniformly labeled glutamic acid carbon-14 as the organic substrate. The steady state system is treated
as being composed of compartments, i.e., "carbon pools" which can be described for purposes of mathematical analysis by sets of linear differential equations. Oscillations within compartments with respect to feed, cells, organic and
inorganic phases of the liquid effluent and gaseous effluent (C02) are described by
two equations, the rate of change of radioactivity with time and the rate of
change of carbon with time. These equations for the steady state case were
solved for the constant coefficient-carbon transfer rates between the various compartments.
The rates were incorporated within the existing theoretical description of
growth kinetics.
The carbon transfer rate of cells to soluble organic substrate was observed to
exhibit a minimum value at or near Dilution Rate, D = 0.5hr."l.
A maximum effective yield coefficient (Y) was observed at the same value
of D. At dilution rates greater and less than D = 0.5 hr."1, the cell-substrate
transfer rate (r2^) increased, and effective yield coefficient was observed to decrease. The former showed increases of from 50 to 200 per cent and the latter
exhibited decreases in the order of 10 per cent. The magnitude of these variations would seem to be significant in industrial fermentation processes which utilize continuous microbiological cultures.
SUMMARY OF THEORY
If Ej is designated as the amount of carbon in any compartment (i), at any
time (t), for each compartment a balance of transfer rates in and out of the compartment may be written
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