Hyperbolic model for bacterial movement through an orthotropic two-dimensional porous medium

Abstract

In this paper an alternative hyperbolic model for bacterial movement is used to represent the migration of a bacterial population through an anisotropic porous medium filled with a nutrient. It is shown how this model can effectively reproduce bacterial wave fronts, which are observed in bacterial migration through porous media experiments. Time and length scales are defined where hyperbolic model preserves its physical validity and predicts very different bacterial concentration profiles in comparison with the classical Keller–Segel model for chemosensitive movement. Representative values of the hyperbolic model parameters are taken from experimental systems reported in literature and it is found that characteristic diffusion time is much smaller than characteristic growth time; in this way, the practical usefulness of the proposed model is limited to time scales when bacterial growth is negligible for the studied system. An analytical solution is presented and discussed for the two-dimensional diffusion of bacterial population within a square orthotropic porous medium, and it is shown that anisotropic properties of the medium lead to preferential bacterial flows.