Abstract
Chemotaxis, the microorganisms autonomous motility along or against the concentration gradients of a chemical species, is an important, yet often neglected factor controlling the transport of bacteria through saturated porous media. For example, chemotactic bacteria could enhance bioremediation by directing their own motion to residual contaminants trapped in low hydraulic conductive zones of contaminated aquifers. The aim of the present work is to develop an accurate numerical scheme to model chemotaxis in saturated porous media and other advective dominating flow systems. We propose to model chemotaxis by using a new class of meshless Lagrangian particle methods we recently developed for applications in fluid mechanics. The method is based on the Smooth Particle Hydrodynamics (SPH) formulation of (Ben Moussa et al., Int Ser Numer Math, 13(1):29–62, 2006), combined with a new Weighted Essentially Non-Oscillatory (WENO) reconstruction technique on moving point clouds in multiple space dimensions. The purpose of this new numerical scheme is to fully exploit the advantages of SPH among traditional mesh-based and mesh-free schemes and to overcome drawbacks related to the use of standard SPH for modeling chemotaxis in porous media. First, we test the new scheme against analytical reference solutions. Then, under the assumption of complete mixing at the Darcy scale, we perform two-dimensional conservative solute transport simulations under steady-state flow conditions, to show the capability of the proposed new scheme to model chemotaxis.
Highlights
Chemotaxis is the ability of biological cells and organisms to move along or against chemical concentration gradients [see for example Alt 1980; Erban and Othmer 2004; Hilpert 2005; Hillen and Painter 2009; Long and Ford 2009; Pedit et al 2002], and it can be observed in a wide range of biological processes occurring at a multiplicity of spatial scales
A number of numerical models for chemotaxis in porous media are based on Finite Elements (FE) and Finite Volume (FV) schemes, [see for example Blackburn et al 1997; Bosma et al 1988; Dillon and Fauci 2000; Nakaguchi and Yagi 2001; Tyson et al 2000; Zhu and Murray 1995; Ward et al 2011; Widman et al 1997]
The primary goal of this paper is to extend a new class of Smooth Particle Hydrodynamics schemes, hereafter referred as MWSPH, developed by Avesani et al (2014, 2015), to model chemotaxis
Summary
Chemotaxis is the ability of biological cells and organisms to move along or against chemical concentration gradients [see for example Alt 1980; Erban and Othmer 2004; Hilpert 2005; Hillen and Painter 2009; Long and Ford 2009; Pedit et al 2002], and it can be observed in a wide range of biological processes occurring at a multiplicity of spatial scales. A number of numerical models for chemotaxis in porous media are based on Finite Elements (FE) and Finite Volume (FV) schemes, [see for example Blackburn et al 1997; Bosma et al 1988; Dillon and Fauci 2000; Nakaguchi and Yagi 2001; Tyson et al 2000; Zhu and Murray 1995; Ward et al 2011; Widman et al 1997] These well established numerical schemes suffer of artificial numerical diffusion, leading to significant errors in the reproduction of solute gradients, thereby hampering their ability to correctly reproduce the movement of chemotactic bacteria.
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