  We study the convergence of the method of reflections for the Stokes
equations in domains perforated by countably many spherical particles with
boundary conditions typical for the suspension of rigid particles. We prove
that a relaxed version of the method is always convergent in $\dot H^1$ under a
mild separation condition on the particles. Moreover, we prove optimal
convergence rates of the method in $\dot W^{1,q}$, $1 < q < \infty$ and in
$L^\infty$ in terms of the particle volume fraction under a stronger separation
condition of the particles.
