Dynamics of a rigid body in a Stokes fluid

Abstract

We demonstrate that the dynamics of a rigid body falling in an infinite viscous fluid can, in the Stokes limit, be reduced to the study of a three-dimensional system of ordinary differential equations can be approximated using the Rotne–Prager theory, and we present various examples corresponding to certain ideal shapes of knots which illustrate the various possible multiplicities of steady states. Our simulations of rigid ideal knots in a Stokes fluid predict an approximate linear relation between sedimentation speed and average crossing number, as has been observed experimentally for the much more complicated system of real DNA knots in gel electrophoresis.