Structural steady states and relaxation oscillations in a two-phase fluid under shear flow: experiments and phenomenological model.

By means of several rheophysics techniques, we report on an extensive study of the couplings between flow and microstructures in a two-phase fluid made of lamellar (L(alpha)) and sponge (L(3)) phases. Depending on the nature of the imposed dynamical parameter (stress or shear rate) and on the experimental conditions (brine salinity or temperature), we observe several different structural steady states consisting of either multilamellar droplets (with or without a long range order) or elongated (L(3)) phase domains. Two different astonishing phenomena, shear-induced phase inversion and relaxation oscillations, are observed. We show that (i) phase inversion is related to a shear-induced topological change between monodisperse multilamellar droplets and elongated structures and (ii) droplet size relaxation oscillations result from a shear-induced change of the surface tension between both coexisting (L(alpha)) and (L(3)) phases. To explain these relaxation oscillations, we present a phenomenological model and compare its numerical predictions to our experimental results.