Low-Reynolds-number flagellar locomotion and the scallop theorem
At Re≪1 (Stokes flow), inertia is negligible and the Navier-Stokes equation is linear and time-reversible. The Scallop Theorem (Purcell 1977): any swimmer with a single degree of freedom executes a time-reversible stroke and achieves zero net displacement. Bacteria escape this by using rotating helical flagella — a non-reciprocal, chiral mechanism that converts rotation to translation via the helix geometry.