Model for Effective Diffusivities in Aerobic Biofilms

Hinson, Roger K.; Kocher, Walter

doi:10.1061/(asce)0733-9372(1996)122:11(1023)

Cited by 55 publications

(42 citation statements)

References 38 publications

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“…In this study, however, the volume fraction of cellular and EPS material was evidently sufficient to cause only limited diffusion attenuation. Compared to the cell volume fraction, the EPS volume fraction is considered to have a greater impact on diffusion rates (2,16). Staining of thin sections with 1% toluidine blue-1% borax revealed an abundance of EPS material filling the spaces between bacteria and forming the matrix of the biofilm.…”

Section: Discussionmentioning

confidence: 99%

Magnetic Resonance Imaging of Structure, Diffusivity, and Copper Immobilization in a Phototrophic Biofilm

Phoenix

Holmes

2008

Appl Environ Microbiol

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Magnetic resonance imaging (MRI) was used to spatially resolve the structure, water diffusion, and copper transport of a phototrophic biofilm and its fate. MRI was able to resolve considerable structural heterogeneity, ranging from classical laminations ϳ500 m thick to structures with no apparent ordering. Pulsed-field gradient (PFG) analysis spatially resolved water diffusion coefficients which exhibited relatively little or no attenuation (diffusion coefficients ranged from 1.7 ؋ 10 ؊9 m 2 s ؊1 to 2.2 ؋ 10 ؊9 m 2 s ؊1 ). The biofilm was then reacted with a 10-mg liter ؊1 Cu 2؉ solution, and transverse-parameter maps were used to spatially and temporally map copper immobilization within the biofilm. Significantly, a calibration protocol similar to that used in biomedical research successfully quantified copper concentrations throughout the biofilm. Variations in Cu concentrations were controlled by the biofilm structure. Copper immobilization was most rapid (ϳ5 mg Cu liter ؊1 h ؊1 ) over the first 20 to 30 h and then much slower for the remaining 60 h of the experiment. The transport of metal within the biofilm is controlled by both diffusion and immobilization. This was explored using a Bartlett and Gardner model which examined both diffusion and adsorption through a hypothetical film exhibiting properties similar to those of the phototrophic biofilm. Higher adsorption constants (K) resulted in longer lag times until the onset of immobilization at depth but higher actual adsorption rates. MRI and reaction transport models are versatile tools which can significantly improve our understanding of heavy metal immobilization in naturally occurring biofilms.The biofilm is an exceptionally common mode of life for bacteria in natural, clinical, and engineered environments. These microbial "cities" range in thickness from a few cells to several centimeters and display a complex three-dimensional architecture which exhibits both structural and compositional heterogeneity (10,22,23).Mass transfer rates within biofilms are controlled by diffusive and advective processes. Where interconnected pore spaces and channels exist within the biofilm, advection can play an important role in contaminant or nutrient mass transfer. In the cell clusters between channels or in biofilms where channels are absent, molecular diffusion becomes the dominant mass transfer mechanism (4, 21). Although the key transport medium within a biofilm is water, the molecular diffusion of a molecule through a biofilm is commonly slower than it is in free water due to the lower permeability of the biofilm and the tortuous nature of any pathways. Consequently, the diffusion of nutrients (or indeed contaminants) can be the rate-limiting step in biofilm performance and can lead to steep chemical and redox gradients through the community (4, 6, 9, 17, 23). For that reason, direct measurements of biofilm diffusion properties are highly desirable when modeling biofilm function (3,40). Biofilms, however, are complex structures which exhibit a high degree of stru...

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Section: Discussionmentioning

confidence: 99%

Magnetic Resonance Imaging of Structure, Diffusivity, and Copper Immobilization in a Phototrophic Biofilm

Phoenix

Holmes

2008

Appl Environ Microbiol

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“…Comparison of Figure 5 with Figure 4 reveals, however, that the oxygen profiles are less sensitive to twofold changes in the substrate diffusion coefficients than to twofold changes in the value and equally sensitive to twofold changes in the K s value. (Hinson and Kocher, 1996;Lawrence et al, 1994;Williamson and McCarty, 1976).…”

Section: Resultsmentioning

confidence: 99%

Respirometric assay for biofilm kinetics estimation: Parameter identifiability and retrievability

Riefler

Ahlfeld

Smets

1998

Biotechnol. Bioeng.

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Currently, no fast and accurate methods exist for measuring extant biokinetic parameters for biofilm systems. This article presents a new approach to measure extant biokinetic parameters of biofilms and examines the numerical feasibility of such a method. A completely mixed attached growth bioreactor is subjected to a pulse of substrate, and oxygen consumption is monitored by on-line measurement of dissolved oxygen concentration in the bulk liquid. The oxygen concentration profile is then fit with a mechanistic mathematical model for the biofilm to estimate biokinetic parameters. In this study a transient biofilm model is developed and solved to generate dissolved oxygen profiles in the bulk liquid. Sensitivity analysis of the model reveals that the dissolved oxygen profiles are sufficiently sensitive to the biokinetic parameters-the maximum specific growth rate coefficient (µ ˆ) and the half-saturation coefficient (K s )-to support parameter estimation if accurate estimates of other model parameters can be obtained. Monte Carlo simulations are conducted with the model to add typical measurement error to the generated dissolved oxygen profiles. Even with measurement error in the dissolved oxygen profile, a pair of biokinetic parameters is always retrievable. The geometric mean of the parameter estimates from the Monte Carlo simulations prove to be an accurate estimator for the true biokinetic values. Higher precision is obtained for µ êstimates than for K s estimates. In summary, this theoretical analysis reveals that an on-line respirometric assay holds promise for measuring extant biofilm kinetic parameters.

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“…The density of microbial cells containing water is around 1,000 kg/m 3 , whereas the density of dry cells may vary between 200 and 670 kg/m 3 (Hinson and Kocher, 1996). On the other hand, the density of EPS material is always higher than 1,000 kg/m contain a significant fraction of EPS versus cell mass.…”

Section: Introductionmentioning

confidence: 98%

Biofilm physical structure, internal diffusivity and tortuosity

Melo

2005

Water Science and Technology

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The paper proposes tortuosity as a physical concept particularly useful to interpret internal diffusivities in terms of biofilm structure. Results from different authors are presented showing how average effective diffusivities in biofilms (measured with inert tracers) vary with the fluid velocity: in the case of biofilms formed under turbulent flow conditions, an increase in fluid velocity corresponds to a decrease in the diffusivity, although sometimes this decrease is very slight; however, in laminar flow situations, no common trend is found from research group to research group.

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Model for Effective Diffusivities in Aerobic Biofilms

Cited by 55 publications

References 38 publications

Magnetic Resonance Imaging of Structure, Diffusivity, and Copper Immobilization in a Phototrophic Biofilm

Magnetic Resonance Imaging of Structure, Diffusivity, and Copper Immobilization in a Phototrophic Biofilm

Respirometric assay for biofilm kinetics estimation: Parameter identifiability and retrievability

Biofilm physical structure, internal diffusivity and tortuosity

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