A two‐dimensional continuum model of biofilm growth incorporating fluid flow and shear stress based detachment

Abstract

We present a two-dimensional biofilm growth model in a continuum framework using an Eulerian description. A computational technique based on the eXtended Finite Element Method (XFEM) and the level set method is used to simulate the growth of the biofilm. The model considers fluid flow around the biofilm surface, the advection-diffusion and reaction of substrate, variable biomass volume fraction and erosion due to the interfacial shear stress at the biofilm-fluid interface. The key assumptions of the model and the governing equations of transport, biofilm kinetics and biofilm mechanics are presented. Our 2D biofilm growth results are in good agreement with those obtained by Picioreanu et al. (Biotechnol Bioeng 69(5):504-515, 2000). Detachment due to erosion is modeled using two continuous speed functions based on: (a) interfacial shear stress and (b) biofilm height. A relation between the two detachment models in the case of a 1D biofilm is established and simulated biofilm results with detachment in 2D are presented. The stress in the biofilm due to fluid flow is evaluated and higher stresses are observed close to the substratum where the biofilm is attached.

Biomechanical Analysis of Infectious Biofilms

“…Lattice models with cellular automata-like rules for biofilm growth have predicted a wide range of biofilm morphologies [75], and also graphically demonstrated the advection of substrates around the fluid-biofilm interface [72]. Continuum representations of the biofilm as constitutively linear elastic [21,26,28,92], non-linear elastic [12,27], viscous [20], or viscoelastic [95] bodies is challenging as the interface must be tracked using stress and displacement matching; simplifications such as a one-way coupling or reduced dimensionality are sometimes employed. Interface tracking is not required for phase field models, which have been employed to argue that low matrix elasticity is required for streamers to form [94] and to investigate the role of cohesion on interface stabilisation [51].…”

“…To consider the effects of flow, some continuum fluid-structure coupling models have been extended to include detachment as reduced interfacial growth [21,26] or a critical stress threshold [12,72], and suggest erosion smoothens while sloughing roughens the biofilm surface. Note that not all of these include a two-way coupling between biofilm mechanics and fluid shear stress.…”

A 2D channel-clogging biofilm model

“…Substituting φ = 3λ(1 + νΦ) and rescaling s, x, v, E ∼ (3λ) −1/2 and r, g ∼ 3λ, we have 8) and thus for ν 1 this can be rearranged simply as…”

“…Kommedal and Bakke [12] fitted experimental data to a wide variety of functional forms for detachment, concluding that dependence on both shear stress and biofilm thickness/age are important. Duddu et al [8] made a detailed numerical study of biofilm microcolony growth with shear-dependent and thickness-dependent detachment rates. Recent theoretical studies [1,11] have examined the existence and stability of steady states in simple one-dimensional models of biofilm growth with loss terms due to decay or detachment.…”

A hybrid smoothed extended finite element/level set method for modeling equilibrium shapes of nano-inhomogeneities

“…The XFEM has been successfully used to solve many physical problems with arbitrary interfaces, such as holes and inclusions [20], phase solidification [21], multiphase flows [22], biofilm growth [23,24], etc. A comprehensive review of XFEM can be found in [25] and an open source C++ XFEM code is also available for use [26].…”