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Center for Nonlinear Studies |
When sheared out of equilibrium, a variety of complex fluids such as worm-like micells, liquid crystals, and colloidal suspensions exhibit a nonlinear response of the measured bulk stress to an applied, non-inertial strain rate. In many materials this phenomenon results from the formation of two bands, whose appearnce is typically attributed to nonlinear material rheology. Natural questions emerge: Is there universal mechanism underlying shear banding in complex fluids? What sets the band width - a kinetic rate balance, such as in classical pattern formation instabilities, or some generalized, out-of-equilibrium chemical potential? In this talk I will describe an experiment in which dense collidal crystal under oscilatory shear is shown to yield and develop bands for a range of applied strains and frequencies. I will show how the experimental data enable us to conclude that shear banding in this system results from linear, rather than nonlinear material rheology. Following this observation, I will introduce a new theory for shear banding, as a nonequilbiurm coexistence between linearly responding phases of a complex fluid. Some consequences will be discussed, such as the singular role played by near-wall pure solvent layers and possible nonequilibrium generalizations of Clausius-Clapeyron's equilibrium formula.