Dynamics of the Shear Banding Instability

A variety of complex fluids, such as liquid crystals, polymers, and surfactant solutions (lamellae or cylindrical micelles), are easily perturbed by shear flow and exhibit apparent ``phase transitions'' and complex nonlinear dynamics. ``Shear banding,'' or separation of material into bands of different apparent viscosities, has been reliably observed in wormlike micelles and many other systems. Despite a general one dimensional (1D) theory that predicts stable bands, recent experiments suggest that the generic situation is dynamic, rather than steady bands. After an overview I will discuss recent calculations that address the possibility of rheo-chaos, and two dimensional calculations to verify or refute the previously found 1D solutions. I will also discuss the possibility of shear banding in the closely related system of entangled polymer solutions.