Self-buckling and self-writhing of semi-flexible swimmers

Multi-flagellated microorganisms can buckle and writhe under their own activity as they swim through a viscous fluid. New equilibrium configurations and steady-state dynamics emerge which depend both on the organism's mechanical properties and the oriented distribution of flagella along its surface. Modeling the cell body as a semi-flexible Kirchhoff rod driven from equilibrium by a dynamically evolving flagellar orientation field, we derive the Euler-Poincaré equations governing the evolution of the system, and rationalize experimental observations of buckling and writhing of elongated P. mirabilis cells. We identify, through numerical simulation, a sequence of pitchfork and Hopf bifurcations as the body is made more compliant. The results suggest a maximum speed that can be achieved by swimming microorganisms for a given body stiffness.