Mohit P. Dalwadi
A Systematic Upscaling of Nonlinear Chemical Uptake Within a Biofilm
Dalwadi, Mohit P.; King, John R.
Abstract
When modelling transport of a chemical species to a colony of bacteria in a biofilm, it is computationally expensive 4 to treat each bacterium even as a point sink, let alone to capture the finite nature of each bacterium. Instead, models tend to 5 treat the bacterial and extracellular matrix domains as a single phase, over which an effective bulk uptake is imposed. In this 6 paper, we systematically derive the effective equations that should govern such a system, starting from the microscale problem of a 7 chemical diffusing through a colony of finite-sized bacteria, within which the chemical species can also diffuse. The uptake within 8 each bacterium is a nonlinear function of the concentration; across the bacterial membrane the concentration flux is conserved and 9 the concentration ratio is constant. We upscale this system using homogenization via the method of multiple scales, investigating 10 the two distinguished limits for the effective uptake and the effective diffusivity, respectively. This work is a natural sequel to 11 Dalwadi et al. 2018 (SIAM J Appl Math, 78(3), 1300-1329), the main difference in this current work being nonlinear uptake within 12 the bacteria and a general partition coefficient across the bacterial membrane. The former results in a significantly more involved 13 general asymptotic analysis, and the latter results in the merging of two previous distinguished limits. We catalogue the different 14 types of microscale behaviour that can occur in this system and the effect they have on the observable macroscale uptake. In 15 particular, we show how the nonlinearities in microscale uptake should be modified when upscaled to an effective uptake and how 16 different microscale uptake properties and behaviours, such as chemically depleted regions within the bacteria, can lead to the same 17 observed uptake. 18
Citation
Dalwadi, M. P., & King, J. R. (2020). A Systematic Upscaling of Nonlinear Chemical Uptake Within a Biofilm. SIAM Journal on Applied Mathematics, 80(4), 1723-1750. https://doi.org/10.1137/19m130220x
Journal Article Type | Article |
---|---|
Acceptance Date | Apr 8, 2020 |
Online Publication Date | Jul 23, 2020 |
Publication Date | Jul 23, 2020 |
Deposit Date | Jun 21, 2020 |
Publicly Available Date | Jul 23, 2020 |
Journal | SIAM Journal on Applied Mathematics |
Print ISSN | 0036-1399 |
Electronic ISSN | 1095-712X |
Publisher | Society for Industrial and Applied Mathematics |
Peer Reviewed | Peer Reviewed |
Volume | 80 |
Issue | 4 |
Pages | 1723-1750 |
DOI | https://doi.org/10.1137/19m130220x |
Keywords | homogenization; multiscale; distinguished limits; effective uptake; quiescent core; depleted core 19 AMS subject classifications 35B25; 35B27; 35B40; 92C45 20 |
Public URL | https://nottingham-repository.worktribe.com/output/4696759 |
Publisher URL | https://epubs.siam.org/doi/10.1137/19M130220X |
Files
Nonlinear Homogenization
(722 Kb)
PDF
You might also like
Multicellular mathematical modelling of mesendoderm formation in amphibians
(2016)
Journal Article
The Hele-Shaw injection problem for an extremely shear-thinning fluid
(2015)
Journal Article
Vertex-element models for anisotropic growth of elongated plant organs
(2013)
Journal Article
Systems Analysis of Auxin Transport in the Arabidopsis Root Apex
(2014)
Journal Article
Downloadable Citations
About Repository@Nottingham
Administrator e-mail: discovery-access-systems@nottingham.ac.uk
This application uses the following open-source libraries:
SheetJS Community Edition
Apache License Version 2.0 (http://www.apache.org/licenses/)
PDF.js
Apache License Version 2.0 (http://www.apache.org/licenses/)
Font Awesome
SIL OFL 1.1 (http://scripts.sil.org/OFL)
MIT License (http://opensource.org/licenses/mit-license.html)
CC BY 3.0 ( http://creativecommons.org/licenses/by/3.0/)
Powered by Worktribe © 2024
Advanced Search