Force and torque on a cylinder rotating in a narrow gap at low Reynolds number: Scaling and lubrication analyses

The hydrodynamic forces and torques on a rotating cylinder in a narrow channel are investigated in this paper using lubrication analysis and scaling analysis. To explore the effect of the shape of the gap, three different geometries are considered. The force and torque expressions from lubrication analysis agree well with numerical solutions when the gap between cylinder and wall is small. The solutions from scaling analysis can be applied over a broader range, but only if the scaling coefficients are properly deduced from numerical solution or lubrication analysis. Self-similarity in the solutions is discussed as well.

Bistable helices

We extend elasticity theory of filaments to encompass systems, such as bacterial flagella, that display competition between two helical structures of opposite chirality. A general, fully intrinsic formulation of the dynamics of bend and twist degrees of freedom is developed using the natural frame of space curves, spanning from the inviscid limit to the viscously overdamped regime applicable to cellular biology. Aspects of front propagation found in flagella are discussed.

Chiral self-propulsion of growing bacterial macrofibers on a solid surface

Supercoiling motions that accompany the growth of bacterial macrofibers (multicellular filamentous structures formed in B. subtilis by cell division without separation) are responsible for rolling, pivoting, and walking of fibers on a surface. Fibers possess a fulcrum about which they pivot and step in a chiral manner; forces and torques associated with cell growth, when blocked by friction, result in self-propulsion. The elastic engine that drives macrofiber motions generates torques estimated as microdyn cm and femtowatts of power; optical trapping studies yield a first direct measurement of the Young's modulus of the bacterial cell wall, the engine's "working fluid," of ca. 0.05 GPa.

Twirling and whirling: viscous dynamics of rotating elastic filaments

Motivated by diverse phenomena in cellular biophysics, including bacterial flagellar motion and DNA transcription and replication, we study the overdamped nonlinear dynamics of a rotationally forced filament with twist and bend elasticity. Competition between twist injection, twist diffusion, and writhing instabilities is described by coupled PDEs for twist and bend evolution. Analytical and numerical methods elucidate the twist/bend coupling and reveal two regimes separated by a Hopf bifurcation: (i) diffusion-dominated axial rotation, or twirling, and (ii) steady-state crankshafting motion, or whirling. The consequences of these phenomena for self-propulsion are investigated, and experimental tests proposed.