Material instability in complex fluids

A review is given of the stability of complex fluids subject to homogeneous states of shearing, a research field that is scarcely two decades old. For the benefit of fluid mechanicians, a brief, somewhat historical overview is presented of material instability in elastoplastic solids, where one finds a considerable body of experiment and a rich source of theoretical concepts including Hadamard instability, strain localization, and nonlocal constitutive models. A survey is then given of recent theoretical and experimental studies of instability with shear banding in various complex fluids, including micellar solutions, particulate suspensions, and rapidly sheared granular media. Various stability analyses are encapsulated in a mathematical dynamical-systems model for constitutive equations of the rate-type, and a general linear-stability theory is given for viscoelastic fluids in unbounded homogeneous shear flows. A general form of (Kelvin) wave-vector stretching is shown to play a key role in the growth of Fourier modes, as illustrated by recent computations for granular shear flow. The Fourier description also provides an explicit representation of higher-gradient (nonlocal) effects as higher-order powers of wave number.