Biofilm kinetics

While pseudohomogeneous rates of biokinetics follow the equation for [kgm h i] 

The parameters k and dp are responsible for heterogeneity, dp being the particle diameter and kj a process kinetic constant, defined by Atkinson (1974) as 

The BRE (cf Equ. 5.239) is valid for heterogeneous microbiological and biochemical systems, including fermentations and enzyme engineering systems. The model uses the same ty e of equation as Equ. 4.60 with limiting boundary conditions Equ. 4.61a and b, with the exception that the substrate utilization rate is referred to the surface area of the biological mass, which is a quantity more easily measured. The connection with the specific rate, [hr ], is through the relationship 

The complete computer simulation of the BRE is given by dotted lines for various film thicknesses d, and the area of experimental verification is indicated with solid lines. Obviously, high S concentration cannot be attained with thick films. As can be seen from Fig. 5.69, the appearance of a simple first-order reaction rate in cases of biofilm processing can often be understood as an observed case of pseudokinetics. 

With biological floes, reaction rates should be plotted as illustrated in Fig. 5.70 (Atkinson, 1974). With increasing film thickness, and with larger particles, the curve moves to higher S values. Again, dotted lines represent the computer simulation, while solid lines correspond to experimental situations. 

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Rittmann, B.E. and McCarty, P.L., Model of steady-state biofilm kinetics, Biotech. Bioeng., 22, 2343-2357, 1980. 

Livingston, A. G., Biodegradation of 3,4-Dichloroaniline in a Fluidized Bed Bioreactor and a Steady-State Biofilm Kinetic Model Biotechnol. Bioeng., 38 260 (1991)... 

The biological processes in biofilms are either described by 1-order or 0-order kinetics. However, the 0-order reaction is of specific importance for sewer biofilms as is also the case for treatment processes of wastewater in biofilters. The saturation constant, Ks, is normally insignificant compared with the substrate concentration, and the biofilm kinetics [cf. Equation (2.20)], is therefore 0-order. As shown in Figure 2.8, two different conditions exist the biofilm is either fully penetrated or partly penetrated, corresponding to either a fully effective or a partly effective biofilm. The distinction between these two situations can be expressed by means of a dimensionless constant, P, called the penetration ratio (Harremoes, 1978). For each of these two situations, the flux of substrate across the biofilm surface can neglect the stagnant liquid film being calculated [Equations (2.23) and (2.25)] ... 

FIGURE 2.9. Biofilm kinetics with respect to the bulk water phase. Typically, only conditions corresponding to 1/2-order kinetics are observed in a sewer biofilm. 

Harremoes, P. (1978), Biofilm kinetics. In R. Mitchell (ed.), Water Poll. Microbiol., 2, Wiley Interscience, New York, pp. 71-109. 

Thus, ATR spectra can provide chemical and structural information about the processes in the biofilm, kinetic data on the biofllm growth, and penetration of another agent into the biofilm. 

In the case of a zero-order reaction (r = feof) fhe Thiele modulus jS has been modified to suit the interpretation for biofilm kinetics. It is then the reciprocal of the normal Thiele modulus for a zero-order reaction,... 

Recently, the application of fluidized beds to bioprocessing stimulated the modeling of FBBRs. In this complex case, however, models of the hydraulics must be combined with a model of biofilm kinetics, including mass transport-affected substrate conversion. This truly heterogeneous case of reactor operation will be presented here. 

Rittmann BE, McCarty PL. Evaluation of steady-state biofilm kinetics. Biotechnol Bioeng 1980 22 2359-2373. 

In this chapter, boundaries are calculated on maximum current densities achievable by bacteria in biofilms by examining the upper limits to biofilm kinetics and comparing these to limits imposed by substrate mass transfer to the biofilm. With this information, we can calculate maximum power densities (power per surface area). We have already seen in chapter 5 that there are limits on current and power densities imposed by internal resistance. Here, we examine the limits based on mass transfer calculations so that in a... 

We can examine two limits of the rate equation to make our calculations of biofilm kinetics easier very high and very low substrate concentrations. When the substrate concentration is high (r. e., non-limiting for growth), the bacteria grow at their maximum rate. Under these conditions, c X and cq. i-4 becomes equivalent to a zero-order rate constant, or... 

First-order biofilm kinetics. If we assume first-order biofilm kinetics, with a rate constant k, then the maximum flux of substrate into the biofilm can be calculated Logan 1999) as... 

Zero-order biofilm kinetics. For this case, we have two different solutions for the substrate flux depending on the thickness of the biofilm. For a shallow biofilm, meaning that the substrate completely penetrates the biofilm and reaches the support surface (what is needed for electrochemical activity at the electrode surface), the flux is... 

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