  In this paper we study the evolution of a small rigid body in a viscous
incompressible fluid, in particular we show that a small particle is not
accelerated by the fluid in the limit when its size converges to zero under a
lower bound on its mass. This result is based on a new a priori estimate on the
velocities of the centers of mass of rigid bodies that holds in the case when
their masses are also allowed to decrease to zero.
