Abstract

Shear induced dispersion of active matter is qualitatively distinct from the well-studied Taylor dispersion of passive particles. In applications from bioreactors to biofilms, active media involving biased swimming particles is typically confined with complex boundary interactions. Aris’s method of moments has been hugely successful in predicting the effective drift and diffusion along channels when no-flux conditions apply, but struggles in cases with non-zero flux at boundaries for which active components are not conserved, requiring cumbersome calculations at higher orders. Here, we develop a Fourier approach that can side-step some of these complexities 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 system.