MATHEMATICS COLLOQUIUM
Speaker: Nick Cogan
Title: Mathematical Treatment of Biofilm/Fluid Interactions
and Disinfection
Affiliation: Rice University
Date: Friday, October 14, 2005.
Place and Time: Room 101 - Love Building, 3:35-4:30 pm.
Refreshments: Room 204 - Love Building, 3:00 pm.
Abstract.
Biofilms are aggregates of bacteria enmeshed in a polysaccharide matrix.
Found at essentially all solid/liquid interfaces, biofilms are sources
of impurities and corrosion in industrial settings and infections in
medical settings. Bacteria within the biofilm have multi-layered protective
mechanisms against antibiotics and antimicrobials and are therefore
extremely difficult to eliminate.
Protective mechanisms including
heterogeneous growth rates, diffusion limitation, quorum
sensing and persister cells all depend on spatial heterogeneities.
As the biofilms interacts with the external fluid, the fluid exerts
force on the biofilm deforming the biofilm. In turn, the presence of
the biofilm influences the fluid dynamics. This coupling
alters the dynamics of nutrients and biocides as they diffuse and
advect throughout the fluid/biofilm system. The motion of the biofilm
due to fluid forces and the advection/diffusion of chemicals both
introduce spatial heterogeneities. Mathematical models have been
introduced which address these two processes separately. The goal of
this investigation is to develop a more comprehensive framework to
investigate biofilm properties during disinfection.
In this talk I will outline the development of a dynamic model of
a biofilm that includes the motion of the biofilm due to fluid
interaction, the subsequent bulk fluid dynamics and how these
processes affect the disinfection of the biofilm. The fluid component
of the model is based on the boundary integral method which transforms
the equations governing the coupled fluid and biofilm dynamics to
an integral equation whose domain is the interface between the two
materials. The method of regularized Stokeslets is used to determine
the material velocities away from the interface. This couples to
the advection/diffusion of chemicals throughout the system to the
motion of the fluid/biofilm system. The strengths of the model
include robust treatment of the (viscous) fluid dynamics and
motion of the biofilm for a generic interface. The method can also
be extended to include more realistic physics of the biofilm including
gel properties of the biofilm such as viscoelastic motion and
osmotic swelling.
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