A minimum principle for Stokes flows containing rigid particles and an upper bound on the sedimentation speed

A minimum principle for Stokes flows containing rigid particles is presented. This variational principle is the hydrodynamic analog of the minimum principle of electrostatics known as Thomson's theorem. In comparison with other variational principles for Stokes flow (such as the classical minimum principle due to Helmholtz), the construction of admissible flows for the Variational principle presented is quite simple owing to a representation as a single layer potential. An upper bound on the average sedimentation speed in a suspension follows immediately from the variational principle. Estimation of the sedimentation speed of a rectangular plate using admissible flows generated from a uniform stress distribution on the plate gives the sedimentation speed with a relative error of about 5%.