CBE Graduate Seminar
“Blood, bacteria and boundary integrals: dynamics of cells in flow”
Michael D. Graham, University of Wisconsin- Madison, Department of Chemical and Biological Engineering
In this talk we use simulations and theory to address two problems in the dynamics of cells in flow: the cross-stream distribution of blood cells and other particles during flow in small blood vessels and the interplay between cell geometry and mechanics in bacterial swimming.
Blood, the first system we consider, is a suspension of objects of various shapes, sizes and mechanical properties, whose distribution during flow is important in many contexts. Red blood cells migrate toward the center of a blood vessel, leaving a cell-free layer at the vessel wall, while white blood cells and platelets are preferentially found near the walls, a phenomenon called margination. We have developed a mechanistic theory to describe segregation in blood and other confined multicomponent suspensions.
The theory predicts, in good agreement with direct simulations and experiments, that the cell-free layer thickness follows a master curve with confinement ratio and volume fraction. It also predicts several regimes of segregation, depending on the value of a ``margination parameter'' M. Experiments performed in the laboratory of Wilbur Lam indicate the physiological and clinical importance of these observations.
Turning from blood to bacteria, we use a coarse-grained micromechanical model of a motile bacterium to characterize trajectories, conformations and velocities of swimming uni- and multiflagellar bacteria. For a uniflagellar cell that is pushed from behind by its flagellum, buckling of the flagellum or the hook protein that connects it to the cell body occurs above a critical flexibility relative to the torque exerted by the flagellar motor. Addition of flagella greatly expands the parameter regime of stable locomotion, because soft hooks that would lead to buckling instability in the uniflagellar case provide the flexibility required for flagellar bundling in the multiflagellar case. Swimming speed is also examined: it increases very weakly with number of flagella and a simple theory is developed that explains this observation.