Collaborative Research: The Analysis and Simulation of Biologically Active Suspensions

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This award is funded under the American Recovery and Reinvestment Act of 2009 (Public Law 111-5).Biologically active suspensions, of which a bath of swimming bacteria is a paradigmatic example, are fluid systems whose microstructure is alive and motile. As the system's "active particles" propel themselves through the surrounding fluid, they produce disturbance flows that communicate their motions to other swimmers, thereby altering their swimming direction and speed. This reciprocal interaction can result in correlated, large-scale, and complex fluid flows that move on length- and time-scales much larger than those of any single swimmer. These swimmer-driven flows have important implications for the evolution and survival of micro-organismal colonies, as they impact nutrient delivery through both particle transport and fluid mixing, and may also play a role in other important phenomena such as quorum sensing and biofilm formation. They are also fundamental examples of non-equilibrium pattern-forming systems. In this project, we propose to further deepen our understanding of biologically active suspensions using a combination of analytical models and numerical simulations. The research will focus on the modeling and analysis of the coherent structures that arise in these systems and on their relation to fluid mixing. Specifically the effect of boundaries and boundary conditions, confinement, and system scale will be examined. New multiscale approaches allowing hundreds of thousands of interacting swimmers to be simulated will also be developed, thus approaching biological realism.As a result of this study, an improved theoretical understanding of active suspensions will be achieved and will reveal the core biophysical mechanisms underlying nutrient transport and mixing in colonies of motile microorganisms. It may also shed light on the evolution of locomotory strategies, particularly for microorganisms that live and thrive cooperatively, as in biofilms. The broader impacts of this research lie in the importance of active suspensions to several key areas of science, including biology, human health and medicine, soft-condensed matter physics, and engineering. An understanding of active suspensions and what drives (or stops) their large-scale mixing could lead to new ways of controlling infection. It provides to physics a well-characterized example of nonequilibrium pattern formation arising in biology, and in engineering this understanding could lead to new devices that exploit biological materials for tasks such as mixing and pumping. This project's impact also lies in the development of new and important areas of inquiry for applied and computational mathematics, and in its adding to the theoretical and computational tool-kit that applied mathematicians and theoretical engineers can bring to problems in biological and complex fluid dynamics.