  Experimental observations of droplet size sustained oscillations are reported
in a two-phase flow between a lamellar and a sponge phase. Under shear flow,
this system presents two different steady states made of monodisperse
multilamellar droplets, separated by a shear-thinning transition. At low and
high shear rates, the droplet size results from a balance between surface
tension and viscous stress whereas for intermediate shear rates, it becomes a
periodic function of time. A possible mechanism for such kind of oscillations
is discussed.
