Longtime behavior of one-dimensional biofilm models with shear dependent detachment rates

Fazal Abbas; Rangarajan Sudarsan; Hermann J. Eberl; Fazal Abbas; Rangarajan Sudarsan; Hermann J. Eberl

doi:10.3934/mbe.2012.9.215

Mathematical Biosciences and Engineering

2012, Volume 9, Issue 2: 215-239. doi: 10.3934/mbe.2012.9.215

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Longtime behavior of one-dimensional biofilm models with shear dependent detachment rates

1.
Dept. Mathematics and Statistics, University of Guelph, 50 Stone Rd E, Guelph, ON, N1G 2W1

Received: 01 May 2011 Accepted: 29 June 2018 Published: 01 March 2012
MSC : Primary: 92D25; Secondary: 34C60.

We investigate the role of non shear stress and shear stressed based detachment rate functions for the longterm behavior of one-dimensional biofilm models. We find that the particular choice of a detachment rate function can affect the model prediction of persistence or washout of the biofilm. Moreover, by comparing biofilms in three settings: (i) Couette flow reactors, (ii) Poiseuille flow with fixed flow rate and (iii) Poiseuille flow with fixed pressure drop, we find that not only the bulk flow Reynolds number but also the particular mechanism driving the flow can play a crucial role for longterm behavior. We treat primarily the single species-case that can be analyzed with elementary ODE techniques. But we show also how the results, to some extent, can be carried over to multi-species biofilm models, and to biofilm models that are embedded in reactor mass balances.
- Mathematical model,
- detachment.,
- biofilm
Citation: Fazal Abbas, Rangarajan Sudarsan, Hermann J. Eberl. Longtime behavior of one-dimensional biofilm models with shear dependent detachment rates[J]. Mathematical Biosciences and Engineering, 2012, 9(2): 215-239. doi: 10.3934/mbe.2012.9.215

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Abstract

We investigate the role of non shear stress and shear stressed based detachment rate functions for the longterm behavior of one-dimensional biofilm models. We find that the particular choice of a detachment rate function can affect the model prediction of persistence or washout of the biofilm. Moreover, by comparing biofilms in three settings: (i) Couette flow reactors, (ii) Poiseuille flow with fixed flow rate and (iii) Poiseuille flow with fixed pressure drop, we find that not only the bulk flow Reynolds number but also the particular mechanism driving the flow can play a crucial role for longterm behavior. We treat primarily the single species-case that can be analyzed with elementary ODE techniques. But we show also how the results, to some extent, can be carried over to multi-species biofilm models, and to biofilm models that are embedded in reactor mass balances.
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