only for describing the specific growth rate of suspended cells in simple situations (e.g.,
without substrate or product inhibition, in dilute solutions). Therefore, the application of
such a model to a system where cells are entrapped within a polymeric matrix built by
themselves, should be carried out with extreme caution, since the environment around the
cells can be totally different from the one encountered by dispersed cells in solution.
The original Monod equation is:
(4)
where Ks is the affinity (or “saturation”) constant of the suspended cell culture; it can be
interpreted as the substrate concentration for which the specific growth rate (μ) will be
equal to half the maximum specific growth rate (μmax) and the higher is its value, the
lower is the affinity of the micro-organism with the substrate. The specific growth rate is
defined as the mass of new cells produced per unit mass of existing cells and per unit
time (kg.kg−^1 .s−^1 ). S is the bulk substrate concentration in the solution.
The adaptation of the Monod concept to biofilms implies the introduction of a few
modifications. Since the active cells in a biofilm produce not only new cells but also a
substantial amount of exopolymers, a new variable, called “specific biofilm production
rate” (μp), should be defined: it represents the mass of cells and exopolymers (dry
biofilm) produced per unit time and per unit mass of the biofilm. Then, the Monod
equation will be transformed into:
(5)
(μp)max being the maximum value of the specific biofilm production rate and Sf the
substrate concentration inside the biofilm. Note that the value of Ks in a biofilm is not
necessarily the same as in a suspended culture.
If (Xf)a is the active cell density in the microbial film (that is, the mass of active cells
per unit volume of wet biofilm, kg.m−^3 ), and Yf/s is the mass of dry biofilm (cells plus
exopolymers) produced per unit mass of substrate consumed in the biofilm (kg of dry
biofilm/kg substrate), the following relationship applies:
(6)where (μp)a is the mass of dry biofilm produced per unit time and per unit mass of active
cells in the biofilm. If the whole biofilm is biologically active, then (μp)a=μp.
The biofilm reaction rate equation will then be given by:
(7)
In this equation, (rf)max is the maximum substrate consumption rate per unit volume of
wet biofilm. Substitution of Equation (7) into Equation (1) results in the following
equation, which has to be integrated to obtain rf:
Biofilm reactors 303