Dynamical rheology of a lyotropic lamellar phase near an out-of-equilibrium transition

Abstract

This work deals with sustained oscillations of a complex fluid near a shear-induced transition. Rheological measurements of the onion texture near a layering transition are performed in a Couette cell. This complex fluid exhibits different regimes of sustained oscillations of the shear rate on a large time scale (500 s) at controlled stress. Transient dynamics strongly suggest the presence of a doubling period transition to chaos and the presence of a Hopf bifurcation. Using dynamical system theory, we analyse the different asymptotic temporal series of the shear rate and show that the dynamics do not strictly correspond to classical three-dimensional chaos. This may due to spatial organization of the fluid in the gap of the Couette cell.