Nonideality in Retardation

In groundwater, as in surface waters, biofilms can be very effective in transforming pollutant chemicals. Modeling the behavior of biofilms is more complex than modeling batch or continuous cultures (Section 2.6.3), although 

A mathematical model of a biofilm is more complex than a model of a batch or a continuous culture, mainly because the pertinent mass balance equations contain diffusive mass transport terms. (Recall from Section 2.6.3 that a model of a batch culture contains no mass transport equations at all, while a continuous culture, or chemostat, model contains only simple mass inflow and mass outflow.) The following set of equations characterizes the biofilm of Fig. 3-29 at steady state  

Conservation of mass in the stagnant boundary layer requires that the diffusive flux into the stagnant water layer from bulk water equals the diffu- 

FIGURE 3-29 Diagram of a fully penetrated biofilm. The rate of uptake of a chemical is governed by the uptake capabilities of the microbial cells composing the biofilm as well as by Fickian transport limitations in both the biofilm and the stagnant boundary layer. In a partially penetrated biofilm, Cj would decrease to zero at some point in the bio film. In a shallow bio film, Cj would be approximately equal to C/s throughout the bio film. 

Mass balance within an arbitrarily chosen biofilm section, or slice, taken parallel to the surface of attachment, is described by the one-dimensional, advection-dispersion-reaction equation, Eq. [1-5], with steady-state conditions and no advection. The sink term is microbial uptake, modeled using the parameters discussed in Section 2.6.3 see Eqs. [2-71 a] and [2-72], 

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