Flagella

Flagella swims where water feels like honey, and she gets there with a corkscrew.

The Physics

For a bacterium, viscosity wins completely: the Reynolds number is about 10⁻⁵, against about 10⁴ for a human swimmer. Purcell's scallop theorem says that a stroke that looks the same run backwards gets you nowhere. A rotating helix breaks that symmetry, because turning a corkscrew is linked to pushing it.

F = A v + B Ω, N = B v + D Ω

• F: thrust force (N)
• N: torque (N·m)
• v: swimming speed (m/s)
• Ω: rotation rate (rad/s)
• A, B, D: drag coefficients set by the helix shape and viscosity

E. M. Purcell set out the scallop theorem in 1977 (Am. J. Phys.); Berg and Anderson showed bacteria swim by rotating their flagellar bundles (Nature, 1973).

On the shirt

Front: Flagella, the pixel-art character, with the title. Back: Purcell's propulsion matrix, the Reynolds numbers, the scallop theorem and the 1973 and 1977 sources. Printed on a unisex tee.