Longtime behavior of one-dimensional biofilm models with shear dependent detachment rates
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. More...
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| Format: | Article |
| Language: | English |
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AIMS Press
2012-02-01
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| Series: | Mathematical Biosciences and Engineering |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/mbe.2012.9.215 |
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| author | Fazal Abbas Rangarajan Sudarsan Hermann J. Eberl |
| author_facet | Fazal Abbas Rangarajan Sudarsan Hermann J. Eberl |
| author_sort | Fazal Abbas |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-78b804c445754ca7a7b1962a037609e4 |
| institution | Kabale University |
| issn | 1551-0018 |
| language | English |
| publishDate | 2012-02-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | Mathematical Biosciences and Engineering |
| spelling | doaj-art-78b804c445754ca7a7b1962a037609e42025-01-24T02:05:29ZengAIMS PressMathematical Biosciences and Engineering1551-00182012-02-019221523910.3934/mbe.2012.9.215Longtime behavior of one-dimensional biofilm models with shear dependent detachment ratesFazal Abbas0Rangarajan Sudarsan1Hermann J. Eberl2Dept. Mathematics and Statistics, University of Guelph, 50 Stone Rd E, Guelph, ON, N1G 2W1Dept. Mathematics and Statistics, University of Guelph, 50 Stone Rd E, Guelph, ON, N1G 2W1Dept. Mathematics and Statistics, University of Guelph, 50 Stone Rd E, Guelph, ON, N1G 2W1We 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.https://www.aimspress.com/article/doi/10.3934/mbe.2012.9.215mathematical modeldetachment.biofilm |
| spellingShingle | Fazal Abbas Rangarajan Sudarsan Hermann J. Eberl Longtime behavior of one-dimensional biofilm models with shear dependent detachment rates Mathematical Biosciences and Engineering mathematical model detachment. biofilm |
| title | Longtime behavior of one-dimensional biofilm models with shear dependent detachment rates |
| title_full | Longtime behavior of one-dimensional biofilm models with shear dependent detachment rates |
| title_fullStr | Longtime behavior of one-dimensional biofilm models with shear dependent detachment rates |
| title_full_unstemmed | Longtime behavior of one-dimensional biofilm models with shear dependent detachment rates |
| title_short | Longtime behavior of one-dimensional biofilm models with shear dependent detachment rates |
| title_sort | longtime behavior of one dimensional biofilm models with shear dependent detachment rates |
| topic | mathematical model detachment. biofilm |
| url | https://www.aimspress.com/article/doi/10.3934/mbe.2012.9.215 |
| work_keys_str_mv | AT fazalabbas longtimebehaviorofonedimensionalbiofilmmodelswithsheardependentdetachmentrates AT rangarajansudarsan longtimebehaviorofonedimensionalbiofilmmodelswithsheardependentdetachmentrates AT hermannjeberl longtimebehaviorofonedimensionalbiofilmmodelswithsheardependentdetachmentrates |