  We analyze experimentally the behavior of a non-Brownian, iso-dense
suspension of spheres submitted to periodic square wave oscillations of the
flow in a Hele-Shaw cell of gap $H$. We do observe an instability of the
initially homogeneous concentration in form of concentration variation stripes
transverse to the flow. The wavelength of these regular spatial structures
scales roughly as the gap of the cell and is independent of the particle
concentration and of the period of oscillation. This instability requires large
enough particle volume fractions $\phi\geq 0.25$, a gap large enough compared
to the spheres diameter ($H/d \geq 8$) and is observed in a rather broad range
of periods of the square waves and amplitudes of the fluid displacement. We map
the domain of existence of this instability in the space of the control
parameters. The analysis of the concentration distribution across the gap shows
that the instability is likely to be associated to the migration of the
particles from the center towards the cell walls. In order to account for the
main features of this stripes instability, we use the theory of longitudinal
instability due to normal stresses difference and recent measurements of the
first normal stresses difference dependence with particles concentration.
