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# Applied Mathematics Seminar

Date/Time/Room: Friday (11/04/2005) at 2:00pm in 304 Pickard Hall

Speaker: Dr. Nick G. Cogan, Visiting Assistant Professor
Department of Computational and Applied Mathematics, Rice University

### "Fluid Flow and Biofilm Disinfection"

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 interface motion is determined using the boundary integral method which transforms the equations governing the coupled fluid and biofilm dynamics to an integral equation whose domain is the interface. The method of regularized Stokeslets is used to determine the material velocities away from the interface. This couples 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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