Related papers: Mathematical Modeling of Biofilm Development
In this report we formulate and analyse a mathematical model describing the evolution of a thin liquid film coating a wire via an extrusion process. We consider the Navier-Stokes equations for a 2D incompressible Newtonian fluid coupled to…
The focus of this paper is the numerical solution of a pore-scale model for the growth of a permeable biofilm. The model includes water flux inside the biofilm, different biofilm components, and shear stress on the biofilm-water interface.…
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…
This work presents the existence and uniqueness of solution to a free boundary value problem related to biofilm growth. The problem consists of a system of nonlinear hyperbolic partial differential equations governing the microbial species…
We derive a physiologically structured multiscale model for biofilm development. The model has components on two spatial scales, which induce different time scales into the problem. The macroscopic behavior of the system is modeled using…
In the present contribution we review basic mathematical results for three physical systems involving self-organising solid or liquid films at solid surfaces. The films may undergo a structuring process by dewetting,…
We propose and analyse numerical schemes for a system of quasilinear, degenerate evolution equations modelling biofilm growth as well as other processes such as flow through porous media and the spreading of wildfires. The first equation in…
Biofilms are bacterial aggregates encased in a self-produced polymeric matrix which attach to moist surfaces and are extremely resistant to chemicals and antibiotics. Recent experiments show that their structure is defined by the interplay…
A hydrodynamic model is proposed to describe one of the most critical problems in intensive medical care units: the formation of biofilms inside central venous catheters. The incorporation of approximate solutions for the flow-limited…
The sessile microbial communities known as biofilms exhibit varying architectures as environmental factors are varied, which for immersed biofilms includes the shear rate of the surrounding flow. Here we modify an established agent-based…
The paper considers a system of equations that models a lateral flow of a Boussinesq--Scriven fluid on a passively evolving surface embedded in $\mathbb{R}^3$. For the resulting Navier-Stokes type system, posed on a smooth closed…
We prove results on existence and uniqueness of solutions of a system of equations modeling the evolution of a generalized bioconvective flow. The mathematical model considered in the present work describes the convective motion generated…
The bacterium {\em Bacilus subtilis} frequently forms biofilms at the interface between the culture medium and the air. We develop a mathematical model that couples a description of bacteria as individual discrete objects to the standard…
For the water-air system, the bulk density ratio is as high as about 1000; no model can fully tackle such a high density ratio system. In the Navier-Stokes and Euler equations, the density $\rho$ within the water-air interface is assumed to…
Direct numerical simulations of a temporally-developing, low-speed, variable-density, turbulent, plane mixing layer are performed. The Navier-Stokes equations in the low-Mach number approximation are solved using a novel algorithm based on…
In this article, we consider the frame hydrodynamics of biaxial nematic phases, a coupled system between the evolution of the orthonormal frame and the Navier--Stokes equation, which is derived from a molecular-theory-based dynamical tensor…
We study a free-boundary fluid-structure interaction problem with growth, which arises from the plaque formation in blood vessels. The fluid is described by the incompressible Navier-Stokes equation, while the structure is considered as a…
Many technological processes include preparing some special materials adhering to a product surface. For example, this problem is important for the magnetic tape producing, wire adhering, etc. For a surface withdrawn from the molten metal…
An implicit Euler finite-volume scheme for a cross-diffusion system modeling biofilm growth is analyzed by exploiting its formal gradient-flow structure. The numerical scheme is based on a two-point flux approximation that preserves the…
We study the Navier-Stokes equations governing the motion of isentropic compressible fluid in three dimensions driven by a multiplicative stochastic forcing. In particular, we consider a stochastic perturbation of the system as a function…