[Paper Review] A fluid dynamics multidimensional model of biofilm growth: stability, influence of environment and sensitivity

Fabrizio Clarelli, Cristiana Di Russo+2 more|arXiv (Cornell University)|Aug 9, 2014

Particle Dynamics in Fluid Flows37 references22 citations

TL;DR

This paper presents a multidimensional fluid dynamics model for phototrophic cyanobacteria biofilm growth, incorporating light and temperature dependencies, stability analysis, and parameter sensitivity. The model accurately simulates 2D and 3D biofilm development over 30 days, showing good agreement with experimental thickness (0.11–0.12 cm) and light attenuation patterns.

ABSTRACT

In this article, we study in details the fluid dynamics system proposed in Clarelli et al (2013) to model the formation of cyanobacteria biofilms. After analyzing the linear stability of the unique non trivial equilibrium of the system, we introduce in the model the influence of light and temperature, which are two important factors for the development of cyanobacteria biofilm. Since the values of the coefficients we use for our simulations are estimated through information found in the literature, some sensitivity and robustness analyses on these parameters are performed. All these elements enable us to control and to validate the model we have already derived and to present some numerical simulations in the 2D and the 3D cases.

Motivation & Objective

• To develop a physically grounded fluid dynamics model for biofilm formation on stone substrates under water layers.
• To analyze the linear stability of the model’s non-trivial equilibrium in one dimension, establishing theoretical robustness.
• To incorporate the influence of light and temperature as key environmental drivers in the biofilm growth process.
• To perform sensitivity and robustness analysis on model parameters using literature-based estimates.
• To validate the calibrated model through 2D and 3D numerical simulations matching experimental biofilm thickness and light distribution.

Proposed method

• Formulates a multiphase mixture model using balance laws for mass and momentum, with four components: cyanobacteria (B), dead cells (D), EPS (E), and liquid (L).
• Applies mixture theory with incompressible, Newtonian assumptions and distinct velocities for solid (B, D, E) and liquid (L) phases.
• Introduces reaction terms (Γ_B, Γ_D, Γ_E, Γ_L) in mass balance equations, constrained by total volume fraction (B+D+E+L=1) and total mass conservation (ΣΓ_φ=0).
• Incorporates light-dependent growth via a phototrophic term in the cyanobacteria equation, with light attenuation modeled using Beer-Lambert law.
• Uses parameter calibration based on literature values for growth rates, density, and stress tensor coefficients.
• Performs sensitivity analysis on key parameters (e.g., growth rate, stress tensor coefficient) and validates results via 2D and 3D simulations.

Experimental results

Research questions

• RQ1 How does the fluid dynamics model behave under linear stability analysis around its non-trivial equilibrium in one dimension?
• RQ2 How do light intensity and temperature influence the growth dynamics of cyanobacteria biofilms in the model?
• RQ3 Which model parameters are most sensitive to variations, and how robust is the model under parameter uncertainty?
• RQ4 Can the model reproduce experimentally observed biofilm thickness and light attenuation patterns in 2D and 3D geometries?
• RQ5 What is the quantitative evolution of biofilm volume and structure over 30 days under realistic environmental conditions?

Key findings

• The model exhibits linear stability around the unique non-trivial equilibrium in one dimension, confirming theoretical consistency.
• Incorporating light and temperature dependence significantly improves the model’s biological relevance and predictive power.
• Sensitivity analysis reveals that the cyanobacteria growth rate and stress tensor coefficient are the most critical parameters.
• 2D simulations over 30 days produce a final biofilm volume of 0.5980 cm² with an average thickness of 0.1196 cm, matching experimental observations.
• 3D simulations show a final biofilm volume of 0.0227 cm³ and maximum thickness of 2–3 mm, with average thickness of 0.1135 cm under aligned initial conditions.
• Light distribution maps confirm strong attenuation within the biofilm, with a clear boundary between liquid and biofilm layers, consistent with experimental data.