Propulsion by a Helical Flagellum in a Capillary Tube

Abstract

We study the microscale propulsion of a rotating helical filament confined by a cylindrical tube, using a boundary-element method for Stokes flow that accounts for helical symmetry. We determine the effect of confinement on swimming speed and power consumption. Except for a small range of tube radii at the tightest confinements, the swimming speed at fixed rotation rate increases monotonically as the confinement becomes tighter. At fixed torque, the swimming speed and power consumption depend only on the geometry of the filament centerline, except at the smallest pitch angles for which the filament thickness plays a role. We find that the `normal' geometry of \textit{Escherichia coli} flagella is optimized for swimming efficiency, independent of the degree of confinement. The efficiency peaks when the arc length of the helix within a pitch matches the circumference of the cylindrical wall. We also show that a swimming helix in a tube induces a net flow of fluid along the tube.

13 pages, 5 figures

References in corpus (3)

• The hydrodynamics of swimming microorganisms
• Low-Reynolds number swimming in a capillary tube
• Helical swimming in Stokes flow using a novel boundary-element method

Cited by in corpus (12)

• Bacterial hydrodynamics
• Helical propulsion in shear-thinning fluids
• Swimming in Complex Fluids
• Amoeboid motion in confined geometry
• Encapsulated bacteria deform lipid vesicles into flagellated swimmers
• Amoeboid swimming in a channel
• Swimming droplet in 1D geometries, an active Bretherton problem
• Bacteria-inspired robotic propulsion from bundling of soft helical filaments at low Reynolds number
• Elastohydrodynamics of swimming helices: effects of flexibility and confinement
• Shapes and dynamic regimes of a polar active fluid droplet under confinement
• The effect of axisymmetric confinement on propulsion of a three-sphere microswimmer
• Motion of microswimmers in cylindrical microchannels