  We study the Saffman-Taylor instability in a non-Brownian suspension by
injection of air. We find that flow structuration in the Hele-Shaw cell can be
described by an effective viscosity depending on the volume fraction. When this
viscosity is used to define the control parameter of the instability, the
classical finger selection for Newtonian fluids is recovered. However, this
picture breaks down when the cell thickness is decreased below approximatively
10 grain sizes. The discrete nature of the grains plays also a determinant role
in the the early destabilization of the fingers observed. The grains produce a
perturbation at the interface proportional to the grain size and can thus be
considered as a "controlled noise". The finite amplitude instability mechanism
proposed earlier by Bensimon et al. allows to link this perturbation to the
actual values of the destabilization threshold.
