Hydrodynamic dispersion within porous biofilms

Abstract

OATAO is an open access repository that collects the work of Toulouse researchers and makes it freely available over the web where possible. Many microorganisms live within surface-associated consortia, termed biofilms, that can form intricate porous structures interspersed with a network of fluid channels. In such systems, transport phenomena, including flow and advection, regulate various aspects of cell behavior by controlling nutrient supply, evacuation of waste products, and permeation of antimicrobial agents. This study presents multiscale analysis of solute transport in these porous biofilms. We start our analysis with a channel-scale description of mass transport and use the method of volume averaging to derive a set of homogenized equations at the biofilm-scale in the case where the width of the channels is significantly smaller than the thickness of the biofilm. We show that solute transport may be described via two coupled partial differential equations or telegrapher's equations for the averaged concentrations. These models are particularly relevant for chemicals, such as some antimicrobial agents, that penetrate cell clusters very slowly. In most cases, especially for nutrients, solute penetration is faster, and transport can be described via an advection-dispersion equation. In this simpler case, the effective diffusion is characterized by a second-order tensor whose components depend on (1) the topology of the channels' network; (2) the solute's diffusion coefficients in the fluid and the cell clusters; (3) hydrodynamic dispersion effects; and (4) an additional dispersion term intrinsic to the two-phase configuration. Although solute transport in biofilms is commonly thought to be diffusion dominated, this analysis shows that hydrodynamic dispersion effects may significantly contribute to transport.

Time-dependent Taylor–Aris dispersion of an initial point concentration

“…injected drugs could occur over unexpectedly long distances of the arteries. Furthermore, recent findings of Taylor-Aris dispersion for solutes acting as signals and nutrition within biofilms (Davit et al 2013) suggests that our results may also be useful in the growing community of biofilm control, for which both the promotion of desirable biofilms (for e.g. wastewater treatment) as well as the inhibition of undesirable biofilms (e.g.…”

Motility ofEscherichia coliin a quasi-two-dimensional porous medium

“…Concerning the quantitative differences observed between the experimental and the simulated turn-angle PDFs and mean squared displacement curves, or analyses suggest that they may be due to bacterium-obstacle interactions not accounted for by our model. For instance, these extra interactions may be of hydro-dynamic nature, or due to physical contact between the bacterium flagella and the spherical beads [11,12,29,39]. Answering this questions demands future experimental and mathematicalmodeling work…”

“…However, bacterial motility in micron and sub-micron constricted spaces has only been studied with ideal geometries [3,28,[36][37][38]. In order to study bacterial motility in a more realistic environment, we have generated a device that simulates a quasi-two-dimensional porous media [39], and studied how E. coli motility is affected by varying porosity conditions. Our aim is to retrieve information that could help us find answers for problems in biology, medicine, and ecology, that involve microbial motility [2,17,37,40].…”

Diffusion in Spatially Varying Porous Media

“…This idea of upscaling is ubiquitous in many sciences. In particular, diffusive transport in heterogeneous media occurs in hydrogeology (aquifers, groundwater [13,14]), contaminant transport (water filtration with membranes), lithium-ion batteries [7], and biological applications such as porous biofilms [12] and intracellular transport [22].…”