Variational upper bound on the renormalized mean sedimentation speed in concentrated suspensions of identical randomly arranged spheres

An upper bound on the renormalized mean sedimentation speed in a concentrated suspension of identical randomly arranged spheres is derived. A random-periodic model, which interpolates between random suspensions and periodic suspensions, is the basis of the renormalization method. A variational principle, the hydrodynamic analogue of Thomson's theorem of electrostatics, is the basis for the bound on the sedimentation speed. Advantages of the methodology presented include (i) the definite sign of the error in the upper bound viewed as an estimate of the sedimentation speed, (ii) a clear separation of modeling and computational issues, and (iii) a path for systematic improvement of the bound.