Past exam of the mathematics course of the University of Cambridge / 2014 / iii / Paper 77 / 3 / e / Solution

The rotlet is the point-torque fundamental solution of Stokes flow. Its torque strength $\mathbf{R}$ is an axial vector, and its circulating velocity decays as $r^{-2}$. A freely swimming cell with no external torque is torque-free. The motor applies opposite internal torques to its body and flagellar apparatus, so the net torque monopole satisfiesIndividual body and flagellar torques need not vanish. A spatially separated pair can therefore leave a rotlet dipole even though there is no far-field rotlet monopole.