Biochemical Engineering Fundamentals, Part 1 - Bailey J., Ollis D. 1989

Kinetics of substrate utilization, metabolite production, and biomass formation in cell cultures
Kinetics of balanced growth

We will begin our modeling and analysis of Cell population growth kinetics with Unstructured models, in which the biological phase is characterized solely by cell mass or numerical concentration. The overall growth rate of cell mass rх is frequently expressed as μх, where х represents The Cell mass per unit volume of culture, and μ is the specific Cell Growth Rate expressed in units of reciprocal time. In terms of these parameters, the mass balance equation for cell mass in a continuous culture at steady state takes the following form:

Class="center">Dxf = (D - μ)х      (7.8)

The nutrient solution entering a flow Reactor often consists exclusively of sterile medium, meaning that xf = 0. In this case, it follows from equation (7.8) that a non-zero cell population can persist at steady state only when

D = μ      (7.9)

i. e., when the specific cell growth rate equals the dilution rate. When the condition of equation (7.9) is satisfied with a sterile nutrient feed, equation (7.8) no longer determines х. This indeterminacy of the population level was confirmed in experiments involving a Bacillus linens culture in a flow reactor. In these experiments, a steady state was attained after 6 h (Fig. 7.4), after which the culture was subjected to two successive dilutions, where a portion of the reactor contents consisting of the cell population and medium was removed and replaced with fresh medium.

FIG. 7.4. As indicated by equation (7.9), at a constant μ, the cell mass concentration in continuous culture is indeterminate (B. linens at 26 °C and D = 0.417 h-1). [Reproduced from: Finn R. К., Wilson R. Е., Population Dynamics of a Continuous Propagator for Microorganisms, J. Agri. Food Chem,, 2, 66 (1954). © American Chemical Society.]

Following each such dilution, a new steady state characterized by a different cell mass concentration was established in the system after some time.



Last update: 06/08/2026

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