Two-Fluid Model of Biofilm Disinfection

Abstract

We consider a dynamic model of biofilm disinfection in two dimensions. The biofilm is treated as a viscous fluid immersed in a fluid of less viscosity. The bulk fluid moves due to an imposed external parabolic flow. The motion of the fluid is coupled to the biofilm inducing motion of the biofilm. Both the biofilm and the bulk fluid are dominated by viscous forces, hence the Reynolds number is negligible and the appropriate equations are Stokes equations. The governing partial differential equations are recast as boundary integral equations using a version of the Lorenz reciprocal relationship. This allows for robust treatment of the simplified fluid/biofilm motion. The transport of nutrients and antimicrobials, which depends directly on the velocities of the fluid and biofilm, is also included. Disinfection of the bacteria is considered under the assumption that the biofilm growth is overwhelmed by disinfection.

Numerical simulation and experimental validation of biofilm in a multi-physics framework using an SPH based method

“…where μ f is the fluid dynamic viscosity and (20) in which Einstein's summation rule has been applied for index k and v is the velocity field.…”

“…Such constitutive laws are similar to Eqs. (18)- (20) with the modification that the stress rate is proportional to the strain rate and μ f is replaced by μ s representing the shear modulus of the solid. The important point is that the stress rate must be objective to fulfill frame indifference.…”

“…The most recent open source simulator for biofilms is called iDynoMiCS (Individual based Dynamics of Microbial communities Simulator) developed in Java Language [17]. When it comes to a continuum framework for biofilm growth, almost all researcher assume the biofilm to behave like a viscous fluid with a mass source term [18][19][20]. This assumption is favourable although the biofilm is apparently a solid-like material.…”

Mathematical Model for MRSA Nasal Carriage

“…This switch is controlled by one or more quorum-sensing signals, several of which are well understood and have been modeled mathematically (Frederick et al 2011;Dockery and Keener 2001;Chopp et al 2002). Biofilm dynamics have also been modeled mathematically (Zhang et al 2008;Cogan 2008;Eberl and Sudarsan 2008); however, most of the literature focuses on the interaction between the external fluid dynamics and the internal biofilm dynamics. Similarly, there have been several mathematical treatments for mucus dynamics (Blake 1973;Agnew et al 1986).…”

Multiphase flow models of biogels from crawling cells to bacterial biofilms

“…There was an important extension of continuum models to include multiple phenotypes (Alpkvist and Klapper, 2007). Finally, there have been several attempts at including the collected fluid/structure interaction between the biofilm and the bulk fluid (Cogan and Keener, 2004;Cogan, 2008;Eberl and Sudarsan, 2008).…”