Reaction diffusion, in biofilms

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... 

Diffusivities in biofilms have been estimated by measuring transient or steady-state fluxes through biofilms in diffusion chambers or in uptake experiments (Libicki et al. 1988). If the experiments are performed with a nonreacting compound or with killed biofilms, Deff can be calculated by fitting the measured fluxes with a diffusion model. In the case of a reacting compound, a reaction-diffusion model is necessary. 

Although reaction-diffusion limitation and the presence of nutritionally restricted phenotypes are obviously important determinants of biofilm drug resistance, neither, either separately or in combination, provides a complete explanation of the phenomena. Cells on the periphery of the biofilm, subject to nutrient fluxes similar to planktonic organisms would succumb to antibacterial concentrations that are effective against the planktonic cells. Cell-death at the periphery would lead to increased nutrient availability for deeper-lying cells. These would, in turn, grow faster and adopt a more susceptible... 

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. 

Wood B.D. and Whitaker S. 2000. Multi-species diffusion and reaction in biofilms and cellular media, Chem. Eng. Sci., 55, 3397-3418. 

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... 

Many different mechanisms of biofilm resistance are discussed in the literature, reflecting the different ways of biofilm organisms to withstand biocides. These mechanisms include physical and chemical diffusion-reaction barriers in the biofilm restricting biocide penetration of the biofilm, slow growth rate of biofilm cells due to nutrient limitation, activation of general stress response genes, the emergence of a biofilm-specific phenotype, and the presence of persister cells. 

Another explanation for reduced biocide penetration into biofilms is the interaction between biocide and biofilm constituents, including cells and EPS a result would be depletion of the antimicrobial compound in the biofilm interior. The underlying mechanisms may be chemical reactions of the biocide with, or sorption to, the biofilm components or the enzymatic degradation of the biocide, resulting in a restricted penetration of the biocide into the biofilms (reaction-diffusion interaction mechanism). 

Diffusion rate limited (first-order kinetics). In this case, the reaction rate is controlled by the rate of diffusion of the pollutant species into the biofilm. 

SRB, a diverse group of anaerobic bacteria isolated from a variety of environments, use sulfate in the absence of oxygen as the terminal electron acceptor in respiration. During biofilm formation, if the aerobic respiration rate within a biofilm is greater than the oxygen diffusion rate, the metal/biofilm interface can become anaerobic and provide a niche for sulfide production by SRB. The critical thickness of the biofilm required to produce anaerobie conditions depends on the availability of oxygen and the rate of respiration. The corrosion rate of iron and copper alloys in the presence of hydrogen sulfide is accelerated by the formation of iron sulfide minerals that stimulate the cathodic reaction. 

Chen et al. [54] have reported a model for the assessment of the combined effects of the intrinsic reaction kinetics and dye diffusion into phosphorylated polyvinyl alcohol (PVA) gel beads. The analysis of the experimental data in terms of biofilm effectiveness factor highlighted the relevance of intraparticle diffusion to the effective azo-dye conversion rate. On the basis of these results, they have identified the optimal conditions for the gel bead diameter and PVA composition to limit diffusion resistance. 

The biofilm thickness (Lf) and density (X = 50 g/L) were assumed uniform and the biofilm treated as a continuum. A substrate diffusion-reaction model assuming spherical particle was used. Diffusion coefficient of phenol and oxygen in the biofilm were assessed according to Fan et al. [64] ... 

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 redox reactions taking place in a sewer biofilm require that diffusion of both electron donor and electron acceptor be considered. The steady state mass balance for these two components is [cf. Equation (2.20)] ... 

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. 

Depending on the velocity of fluid flow, the thickness varies from 10 to 100 pm, and it may cover from less than 20% to more than 90% of the metal surface. Biofilms or macrofouling in seawater can cause redox reactions that initiate or accelerate corrosion. Biofilms accumulate ions, manganese and iron, in concentrations far above those in the surrounding bulk water. They can also act as a diffusion barrier. Finally, some bacteria are capable of being directly involved in the oxidation or reduction of metal ions, particularly iron and manganese. Such bacteria can shift the chemical equilibrium between Fe, Fe2+, and Fe3+, which often influences the corrosion rate. (Dexter)5... 

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... 

Biofilms that become too thick, however, may prevent full penetration of substrates the reaction rates become more dependent on the diffusion of substrates inside the film. Therefore, procedures for controlHng the biofilm thickness may be necessary in some reactor systems [53]. Oxygen may also become limited within such biofilms, reducing transformation rates of MTBE. It is possible to estimate whether oxygen or MTBE is Hmited inside a biofilm by the following expression [49] ... 

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