Coupled flow and biomass-nutrient growth at pore-scale with permeable biofilm, adaptive singularity and multiple species

Abstract

<abstract><p>In this paper we describe a coupled model for flow and microbial growth as well as nutrient utilization. These processes occur within and outside the biofilm phase formed by the microbes. The primary challenge is to address the volume constraint of maximum cell density but also to allow some microbial presence outside the contiguous biofilm phase. Our model derives from the continuum analogues of the mechanism of cell shoving introduced in discrete biomass models, and in particular from the models exploiting singular diffusivity as well as from models of variational inequality type which impose explicit constraints. We blend these approaches and propose a new idea to adapt the magnitude of the diffusivity automatically so as to ensure the volume constraint without affecting the reactions; this construction can be implemented in many variants without deteriorating the overall efficiency. The second challenge is to account for the flow and transport in the bulk fluid phase adjacent to the biofilm phase. We use the Brinkman flow model with a spatially variable permeability depending on biomass amount. The fluid flow allows some advection of the nutrient within the biofilm phase as well as for the flow even when the pores are close to being plugged up. Our entire model is monolithic and computationally robust even in complex pore-scale geometries, and extends to multiple species. We provide illustrations of our model and of related approaches. The results of the model can be easily post—processed to provide Darcy scale properties of the porous medium, e.g., one can predict how the permeability changes depending on the biomass growth in many realistic scenarios.</p></abstract>

Numerical Analysis of A Mixed Finite Element Approximation of a Coupled System Modeling Biofilm Growth in Porous Media with Simulations

“…The particular Biofilm-Nutrient model considered in this paper is proposed in [35] as an enhancement of model in [32] consistent with the ideas which is proposed in [15]. The model is a coupled system of two nonlinear parabolic advection-diffusionreaction PDEs in a biomass density u 1 (x, t), and a nutrient concentration u 2 (x, t) required for the microbes to grow [15,35].…”

“…After this density is close to maximal, the majority of the growth occurs through the interface between the biofilm and the ambient fluid [3], which is the free boundary to be modeled. The bulk fluid may penetrate the biofilm region in the permeable and partially permeable zones to transport the substrate so that microbes continue growing in its domain [38,35].…”

“…It is also subject to a volume constraint. In this paper we consider a model proposed in [35] which is a coupled system involving a nonlinear parabolic variational inequality (PVI) equipped with a new nonlinear diffusivity term and subject to Neumann boundary conditions assuming the system is isolated. The model of the biofilm growth is discussed in detail in Sec.…”

Unification of cell-scale metabolic activity with biofilm behavior by integration of advanced flow and reactive-transport modeling and microfluidic experiments

“…This is accomplished by introducing a permeability, k which is used by the Navier-Stokes-Brinkman equation to represent the ability of the biofilm to support advective mass transport while decreasing D to approximately 0.05 mm 2 h -1 . 32 In the absence of reported k values for GS biofilms, we used the maximum and minimum k values found for general biofilms as the upper and lower bounds (see ESI). The red shaded areas in Figure 2 show the I biofilm solution space that was obtained using k values within these limits.…”

Microscale advection governs microbial growth and oxygen consumption in macroporous aggregates

“…Discontinuities within this gel matrix (such as large pores or channels) permit advective flow through the matrix if pressure gradients across the discontinuities imposed by the surrounding fluids are sufficient to overcome the frictional resistance. This is an important distinction to microbial growth in porous media (such as soils, sediments, aquifers, or engineered systems like packed bed reactors or trickling filter systems in wastewater treatment) where numerical studies of the interaction between the biofilm surface roughness and mass transport ( 27 ) and simulations of coupled microbial growth and flow in porous media ( 28 – 32 ) have provided key insights on how flow can shape localized growth conditions. However, in contrast to the microenvironments we focus on in this study, microbial communities in porous media attach to the solid structures and create streamers that can clog macropores ( 33 , 34 ) and alter preferential flow paths within the porous media with consequences for nutrient supply ( 35 , 36 ).…”