Morphogenesis of Biofilms in Porous Media and Control on Hydrodynamics

Abstract

The functioning of natural and engineered porous media, like soils and filters, depends in many cases on the interplay between biochemical processes and hydrodynamics. In such complex environments, microorganisms often form surface-attached communities known as biofilms. Biofilms can take the shape of clusters, which alter the distribution of fluid flow velocities within the porous medium, subsequently influencing biofilm growth. Despite numerous experimental and numerical efforts, the control of the biofilm clustering process and the resulting heterogeneity in biofilm permeability is not well understood, limiting our predictive abilities for biofilm-porous medium systems. Here, we use a quasi-2D experimental model of a porous medium to characterize biofilm growth dynamics for different pore sizes and flow rates. We present a method to obtain the time-resolved biofilm permeability field from experimental images and use the obtained permeability field to compute the flow field through a numerical model. We observe a biofilm cluster size distribution characterized by a spectrum slope evolving in time between −2 and −1, a fundamental measure that can be used to create spatio-temporal distributions of biofilm clusters for upscaled models. We find a previously undescribed biofilm permeability distribution, which can be used to stochastically generate permeability fields within biofilms. An increase in velocity variance for a decrease in physical heterogeneity shows that the bioclogged porous medium behaves differently than expected from studies on heterogeneity in abiotic porous media.

Internal Biofilm Heterogeneities Enhance Solute Mixing and Chemical Reactions in Porous Media

“…This is in agreement with previous findings for a permeable biofilm in 2D. 20,27 In the range of very low velocities, a similar scaling (i.e., p(v) ∼ v −1 ) is observed for all the cases. Most previous studies consider only either impermeable biofilms or biofilms having a single-homogeneous permeability value.…”

“…(a) Three-dimensional rendering of the biofilm (green color) and of the solid grains (gray color). (b) Underlying distribution of biofilm permeabilities (κ b ) from Kurz et al (c) 3D randomized realization of the internal biofilm permeability and the surface of the solid grains (gray color) for visual clarity.…”

“…The advantage of this method is that it generates the randomness in the permeabilities based on the spatial domain rather than the spectral domain, which allows us to relate the randomness to physical attributes of the biofilm such as the correlation length. A detailed discussion about this and other methods for generating random fields is out of the scope of this work, and the reader is referred to Räss et al The underlying distribution of permeabilities is obtained from the experiments of Kurz et al, which have an average pore-scale velocity of 0.96 mm/s and corresponds to the highest measured coverage of the porous medium by the biofilm. The biofilm permeability κ b has a mean μ κ normalb = 5.12 · 10 − 12 .25em normalm 2 and variance σ κ normalb 2 = 2.1716 .25em normalm 4 (i.e., a hydraulic heterogeneity of σ ln nobreak0em.25em⁡ κ normalb 2 = 0.75 ) (Figure b).…”

“…The advantage of this method is that it generates the randomness in the permeabilities based on the spatial domain rather than the spectral domain, which allows us to relate the randomness to physical attributes of the biofilm such as the correlation length. A detailed discussion about this and other methods for generating random fields is out of the scope of this work, and the reader is referred to Rass et al 38 The underlying distribution of permeabilities is obtained from the experiments of Kurz et al, 20 ) (Figure 2b). Because of the high computational cost of our numerical model (Section 2.3), we used 10 different realizations and verified that the average and fluctuation do not change significantly with an increasing number of realizations.…”

“…When biologically driven reactions are considered (e.g., chemical uptake), similar trends are observed regarding the significant impact of biofilm permeability heterogeneity on reactivity. The probability density function of permeabilities within the biofilm, together with the recent observation of a scaling law of biofilm cluster sizes, 20 can be a first step in our attempt to upscale these pore-scale observations. While in this manuscript we do not discuss scaling laws of biofilm cluster size distribution, we generally conclude that it is important to consider permeability heterogeneity within the biofilm and the uncertainty that their stochastic realization can introduce in predictions of bioaccumulation and bioremediation.…”