  We consider the two-dimensional motion of the coupled system of a viscous
incompressible fluid and a rigid disc moving with the fluid, in the whole
plane. The fluid motion is described by the Navier-Stokes equations and the
motion of the rigid body by conservation laws of linear and angular momentum.
We show that, assuming that the rigid disc is not allowed to rotate, as the
radius of the disc goes to zero, the solution of this system converges, in an
appropriate sense, to the solution of the Navier-Stokes equations describing
the motion of only fluid in the whole plane. We also prove that the trajectory
of the centre of the disc, at the zero limit of its radius, coincides with a
fluid particle trajectory.
