Concepts from Chemical Reaction Kinetics - Elements of Environmental Engineering: Thermodynamics and Kinetics - page 252

a given fixed enzyme concentration. We know that food metabolism in biological
species leads to growth and reproduction. As cells grow rapidly and multiply in
number, the concentration of the enzyme and the substrate degradation rate will vary.
These aspects come under growth kinetics or cell kinetics .
Generally the growth of microorganisms occurs in phases. Figure 5.21 is a typical
growth curve. A measure of the microbial growth is the cell number density (number
of cells per unit volume) denoted [X]. During the initial stage the change in cell
density is zero for some time. This is the lag phase . Subsequent to the lag phase is
the phase of growth and cell division. This is called the accelerated growth phase .
This is followed by the exponential growth phase in which the growth rate increases
exponentially. Further the growth rate starts to plateau. This is called the decelerated
growth phase . This leads to a constant maximum cell density in what is called the
stationary phase . As time progresses, the cells deplete the nutrient source and begin
to die. The cell density rapidly decreases during the final stage called the death
phase .
The rate of cell growth per unit time is represented by the following equation:

d [ ]

d t = ζ[

X

r g = X ] , (5.203)

is the specific growth rate (h − 1 ) . The effect of substrate concentration [S] on

where ζ

ζ is described by the Monod equation :

ζ = ζ max [

S ]

. (5.204)

K s +[ S ]

ζ = ζ max . The above equa-
tion is an empirical expression and states that if the nutrient concentration [S] reaches

Note that when [ S ] K s , ζ ∝[ S ] and when [ S ] K s ,

Constant
growth
phase

Death
phase

Accelerated
growth
phase

Exponential
growth phase

Lag phase

t /h

FIGURE 5.21 A typical growth curve for microorganisms.