Homogenization approximations for unidirectional transport past randomly distributed sinks

Research output: Contribution to journalArticle

Abstract

Transport in biological systems often occurs in complex spatial environments involving random structures. Motivated by such applications, we investigate an idealised model for solute transport past an array of point sinks, randomly distributed along a line, which remove solute via first-order kinetics. Random sink locations give rise to long-range spatial correlations in the solute field and influence the mean concentration. We present a non-standard approach to evaluating these features based on rationally approximating integrals of a suitable Green’s function, which accommodates contributions varying on short and long lengthscales and has deterministic and stochastic components. We refine the results of classical two-scale methods for a periodic sink array (giving more accurate higher-order corrections with non-local contributions) and find explicit predictions for the fluctuations in concentration and disorderinduced corrections to the mean for both weakly and strongly disordered sink locations Our predictions are validated across a large region of parameter space.

Bibliographical metadata

Original languageEnglish
JournalIMA Journal of Applied Mathematics
Early online date18 Feb 2019
DOIs
Publication statusPublished - 2019