Flagella: Corkscrew Escape
Physics of Life & Earth arc, page 193 of 193. Back to The Pixelated Physics Universe
Who they are
Flagella swims where water feels like honey, and she gets there with a corkscrew.
Flagella is a character of the Physics of Life & Earth arc: drawn in pixels, ruled by one piece of real physics, and never allowed to break it.
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. 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).
$$ \begin{gathered} F = A v + B\Omega, \qquad N = B v + D\Omega \\ Re:\ \text{human swimmer} \sim 10^{4}, \quad E.\ coli \sim 10^{-5} \end{gathered} $$
| Symbol | Meaning | SI unit |
|---|---|---|
| $F$ | axial force on the helix | N |
| $N$ | axial torque | N·m |
| $v$ | axial velocity | m/s |
| $\Omega$ | angular velocity | rad/s |
| $A$ | propulsion-matrix coefficient | N·s/m |
| $B$ | propulsion-matrix coupling coefficient | N·s |
| $D$ | propulsion-matrix coefficient | N·m·s |
| $Re$ | Reynolds number | 1 |
Sources
- Purcell (1977) Life at low Reynolds number, Am. J. Phys. 45, 3
- Berg & Anderson (1973) Bacteria Swim by Rotating their Flagellar Filaments, Nature 245, 380
Crossovers
Flagella meets Sprinkla (Reverse Sprinkler). Sprinkla's sprinkler lives at high Reynolds number, where inertia and jets matter. Flagella lives at a Reynolds number of about 10⁻⁵, where inertia is negligible and only a non-reciprocal stroke like a corkscrew can swim.
Flagella meets Sensora (Berg–Purcell Limit). Flagella swims toward food, and Sensora decides which way is better. A bacterium's chemotaxis needs both the corkscrew and the counting.
Flagella meets Kayella (Kaye Effect). Flagella swims at a low Reynolds number, where viscosity wins completely. Kayella's shampoo has a viscosity that depends on shear. Both live where the fluid's stickiness rules.
Wear the lore
Concept keywords: Corkscrew Escape, Flagella, Physics of Life & Earth, physics lore, Pixelated Physics