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where i* is the species maximum growth rate constant (t-1); S is the local dissolved substrate concentration (MsubstrateL-3); KS is the saturation kinetics half-saturation constant (MsubstrateL-3); and B is the local biofilm cell concentration (McellL-2).

Some differences in biofilm kinetics versus typical suspended cell microbial kinetics include the following:

• The concentration of active bacterial cell mass metabolizing the substrate, B, is a per area concentration and may also be a function of time and space, B = B(t, z). In a mixed culture biofilm, each bacterial species could exhibit a different dependency on time and space.

• The concentration of substrate S in the biofilm will be affected by mass transfer resistances and biological reaction rates, such that S may also be a function of time and space.

• Endogenous decay, maintenance energy, or death terms for cells not receiving adequate nutrients are treated as simple first-order functions of the biofilm population, for example,

where kd is the cell death specific rate constant (t-1). Thus the local, instantaneous net production of a species biomass in the biofilm can be modeled as

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