Biofilm diffusion-reaction process

This example treats a diffusion-reaction process in a spherical biocatalyst bead. The original problem stems from a model of oxygen diffusion and reaction in clumps of animal cells by Keller (1991), but the modelling method also applies to bioflocs and biofilms, which are subject to potential oxygen limitation. Of course, the modelling procedure can also be applied generally to problems in heterogeneous catalysis. 

The conversion process within the biofilm is described by a substrate diffusion-reaction model. 

Equation (2.19), which concerns a situation without processes in the biofilm, can be extended to include transformation of a substrate, an electron donor (organic matter) or an electron acceptor, e.g., dissolved oxygen. If the reaction rate is limited by j ust one substrate and under steady state conditions, i.e., a fixed concentration profile, the differential equation for the combined transport and substrate utilization following Monod kinetics is shown in Equation (2.20) and is illustrated in Figure 2.8. Equation (2.20) expresses that under steady state conditions, the molecular diffusion determined by Fick s second law is equal to the bacterial uptake of the substrate. 

The use of continuous immobilized cell biofilm reactors eliminates downtime and hence results in superior reactor productivity (2,3). Adsorbed cell continuous biofilm reactors have been shown to favorably affect process economics (4). Application of these reactors reduces capital and operational cost, thus making the process simpler. Within these reactors, cells are immobilized by adsorption, which is a simpler technique than other techniques such as entrapment and covalent bonding (5). Adsorption is a simple technique and can be performed inside the reactors without the use of chemicals, whereas entrapment and covalent bonding are complicated techniques and require chemicals for bond formation. In anaerobic systems, such as butanol production, adsorption can be performed anaerobically within the reactor. An additional advantage of adsorption is that cells form uniform biofilm layers around the support, which lessens diffusion resistance compared to entrapped and covalently bonded cells. Hence, these reactors are called biofilm reactors. Because of reduction in diffusion resistance, the reaction rate is enhanced. For this reason, adsorption was chosen as the technique to be employed for Clostridium beijerinckii BA101 cell immobilization to produce butanol. In addition to being simple, it has the potential to be used in large-scale reactors. In the present study, clay brick was chosen as the cell adsorption support. It is available at a low cost and is easy to dispose of after use. 

Three dominant processes in the reaction diffusion in biofilms and cellular systems are (1) diffusion in a continuous extracellular phase B, (2) transport of solutes across the membrane, and (3) diffusion and reaction in the intracellular phase A. Consider aerobic growth on a single carbon source. The volume-averaged equations of a substrate S and oxygen O (electron acceptor) transport are... 

Many food processes, which affect food quality and stability, are diffusion controlled (Karel et al., 1994 Roos, 1995). Transport of key penetrants such as water into or out of a polymeric food matrix can play a critical role in food quality and stability. Water is one of the major components and a very good plasticizer in foods. The quality and stability of dehydrated products, multi-domain foods, and the performance of biofilms and encapsulation and controlled release technologies are affected by moisture transport. The rates of molecular mobility and diffusion-limited reactions strongly depend on the factors surrounding the food. Temperature and water activity (fl ) pl y significant roles in penetrant diffusion. The physical state of the carrier matrix, chemistry, size, and structure of diffusing molecule and specific... 

There is an implicit assumption, however, that EABs growing on electrode surfaces can be described as a well-controlled condition in which CV can be applied to study reaction mechanisms as in pure electrochemical systems. Beyond reproducibility of the biofilm electrode surface, simply characterizing biofilm structure itself has historically been difficult [114-116]. Furthermore, the result of biofilm heterogeneity is local variation of not only diffusion coefficients, but also flow velocities [117-120]. The unknown mass transfer conditions suggest that not all cells in the EAB contribute equally to current production. Several chapters in this book are dedicated to the use of CV to characterize electron transfer processes in EABs. 

Before discussing electron-transfer processes in biofilms, it is necessary to compare the easily identified one-step ferri/ferrocyanide electrochemical reaction based on diffusion to the unknown oxidation and reduction processes occurring in a biofilm with a finite thickness, Z (Fig. 5.11) [26]. In the former case, mass transfer is handled analytically through simple Fickian boundary conditions in the boundary value problem [4]. Electrochemical reactions are also confined to the electrode surface any self-exchange reactions in the bulk are ignored. In the latter, biofilm, case, mass... 

Just as in the case of synthetic catalysts, the process can be reaction limited (i.e., tire reaction is the rate-deterrniriing step) or diffusion limited. Concentration profiles for these two cases within the biofilm are shown in Figure 4.12b... 

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