Hidden Invariants in Rheology: The Persistent Granular Nature of Liquids

This article will use arguments derived from the deformation driven component of mixing, especially important for microfluidics, to show that the standard invariant based approaches to rheology are lacking. It is shown that the deviator, $D_{ij}$, after the process of symmetrization, loses microscopically determined information that distinguish rotation from shear and extension in a unique fashion. We recover this information through an analysis of the discrete processes that must underlie deformation driven mixing in highly correlated fluids. Without this we show there is no hope of ever deriving adequate general material parameters for rheology from microscopic dynamics. There is an unambiguous microscopic notion of the rotation rate for every parcel and we derive a general class of invariant rheological theories from it. We discuss some implications of higher order flows on solutions and suspensions including possibilities for driving and stabilization of nonuniform distributions using hydrodynamic forces alone.