(347a) Stokeslet Model of Swimming Multi-Flagellated Bacteria

To study the effect of the number of flagella and their geometric arrangement on the swimming of multi-flagellated bacteria, such as Escherichia coli, we develop a simulation method using a bead-spring model to account for the hydrodynamic and the mechanical interactions between multiple flagella and the cell body. The beads are bonded by 1) a spring potential, 2) a bending potential, and 3) a torsional potential to adjacent beads, and the flagella are driven to rotate by application of constant torques at their bases, along with a counter-torque applied to the body. This model allows us to derive the far- and mid-field flows around the bacterium as a function of the number and arrangement of flagellae.  We find that the the number and arrangement of flagellae strongly affects the coefficients of the far-field dipolar flow relative to that of the quadripolar flow and the rotlet dipolar flow. Thus, the hydrodynamic interactions of swimming bacteria, and their collective swimming behavior, is expected to be sensitive to flagellar arrangement.  We develop a low order multipole expansion of the flow field generated a single swimmer, which we couple to a Jeffreys equation for the orientation dynamics of a neighboring swimmer.  This model allows us to model the collective swimming dynamics of bacterial swimmers at low order in bacteria concentration.