Abstract
Shear induced dispersion of active matter is qualitatively distinct from the well-studied Taylor dispersion of passive particles. The distinctions mainly stem from biased particle motility and complex boundary interactions. Aris’s method of moments has been hugely successful in predicting the effective drift and diffusion along channels under no-flux conditions, but struggles when the
flux is non-zero. Non-zero flux has practical relevance in terms of biofilm formation in bioreactors, which leads to a reduction in their efficiency. Tracked particles are not conserved in such systems, resulting in cumbersome calculations at higher orders. Here, we develop a Fourier approach
that can side-step some of the complexities in Aris’ method to tackle a non-trivial class of active media problems with taxes and boundary interactions. The method is efficient and accessible. We challenge the predictions asymptotically with known results for leaky pipes with cross-flows and numerically with Lagrangian simulations, providing very good agreement for long-time and transient solutions. We find that a strict ordering of eigenvalues is unnecessary to derive meaningful analytical results. Interestingly, for the case of two absorbing walls with biased motion towards one, analysis reveals an optimal taxis strength for axial dispersion that desensitizes dependence on absorption rates. The Fourier approach opens a path for improved qualitative interpretation of results for this wide class of systems.
flux is non-zero. Non-zero flux has practical relevance in terms of biofilm formation in bioreactors, which leads to a reduction in their efficiency. Tracked particles are not conserved in such systems, resulting in cumbersome calculations at higher orders. Here, we develop a Fourier approach
that can side-step some of the complexities in Aris’ method to tackle a non-trivial class of active media problems with taxes and boundary interactions. The method is efficient and accessible. We challenge the predictions asymptotically with known results for leaky pipes with cross-flows and numerically with Lagrangian simulations, providing very good agreement for long-time and transient solutions. We find that a strict ordering of eigenvalues is unnecessary to derive meaningful analytical results. Interestingly, for the case of two absorbing walls with biased motion towards one, analysis reveals an optimal taxis strength for axial dispersion that desensitizes dependence on absorption rates. The Fourier approach opens a path for improved qualitative interpretation of results for this wide class of systems.
| Original language | English |
|---|---|
| Publication status | Published - 2024 |
| Event | 65th British Applied Mathematics Colloquium - Newcastle University, Newcastle, United Kingdom Duration: 9 Apr 2024 → 11 Apr 2024 Conference number: 65 https://conferences.ncl.ac.uk/bamc2024/ |
Conference
| Conference | 65th British Applied Mathematics Colloquium |
|---|---|
| Abbreviated title | BAMC 2024 |
| Country/Territory | United Kingdom |
| City | Newcastle |
| Period | 9/04/24 → 11/04/24 |
| Internet address |