A fluid dynamics multidimensional model of biofilm growth: stability, influence of environment and sensitivity

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.

A time-space model for the growth of microalgae biofilms for biofuel production

“…Mixture theory was introduced in the 1960s by a series of articles by Trusdell and provides continuous models based on PDEs for multi-component fluids by assuming that several components may be present locally; for more details about mixture theory, see [34,26]. Mixture models have been successfully used later on for the description of several biological systems and, in particular, for modelling biofilms [12,13,1,16,38,39].…”

“…To do so, we improve and adapt the previous mixture model for biofilms of cyanobacteria in a fountain, proposed by Clarelli et al in [12,13]. Note that, from the analytical perspective, the existence of solutions for such mixture models has been established very recently and only for some simplified models [9].…”

“…This constraint is expressed on the mean hydrodynamic velocity and leads to an hydrostatic pressure term in the force balance equations of the model. As in [12,13], we keep the inertial terms in momentum equations to guarantee the hyperbolicity of the system and the finite speed of propagation of the front.…”

A discrete in continuous mathematical model of cardiac progenitor cells formation and growth as spheroid clusters (Cardiospheres)

“…In this section we present the calibration procedure in order to obtain as reliable results as possible. To achieve this goal, we studied the influence of the parameters on the model dynamics through a local sensitivity analysis (Saltelli et al, 2008;Clarelli et al, 2015). This approach determines a degree of dependency between input parameters (one at a time) and the results of simulations.…”

On the Modelling of Algal Biofouling Growth on Nano-TiO2 Coated and Uncoated Limestones and Sandstones

“…The modeling of biofouling involves a complex non-linear treatment because of the unpredictable behavior of microorganisms and their relationship with building materials and environment conditions. Biofouling on solid substrata was recently proposed to predict the growth of microorganisms on the surface of monuments, and a nonlinear hyperbolic-elliptic partial differential equation was used [32][33][34]. The dynamic biofilm growth in porous media at a microscopic scale was developed by implementing a growth of the biofilm in irregular domains by considering the thickness of the substrates as an independent variable [35].…”