  We compute the first order correction of the effective viscosity for a
suspension containing solid particles with arbitrary shapes. We rewrite the
computation as an homogenization problem for the Stokes equations in a
perforated domain. Then, we extend the method of reflections to approximate the
solution to the Stokes problem with a fixed number of particles. By obtaining
sharp estimates, we are able to prove that this method converges for small
volume fraction of the solid phase whatever the number of particles. This
allows to address the limit when the number of particles diverges while their
radius tends to 0. We obtain a system of PDEs similar to the Stokes system with
a supplementary term in the viscosity proportional to the volume fraction of
the solid phase in the mixture.
