Mathematics Colloquia and Seminars

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Fluid flows in micro-scale biological systems are inherently complex, with unique dynamics that arise due to geometry, interactions with cellular components, and the non-Newtonian nature of the fluid itself. I will outline some my efforts in recent years to tease apart and analyze some of these effects in two broad classes of problems: first, I will illustrate the physical features and mathematical analysis of flow around structures that form the backbones of cells: biopolymers. I will describe how these long slender filaments undergo instabilities to buckle and/or aggregate when placed in flow. Second, I will describe attempts at modeling the non-Newtonian nature of fluid membranes that encapsulate cells, and outline some of the consequences when a protein or membrane motor or an experimental probe moves within these membranes.