FLUIDS OF DIFFERENTIAL TYPE - CRITICAL-REVIEW AND THERMODYNAMIC ANALYSIS

Thermodynamics, in the form of a dissipation inequality and the common ly accepted idea that the stored energy should have an extremum in equ ilibrium, is used to find restrictions on the response functions for t he stress and the stored energy in incompressible fluids of differenti al type. For those special fluids of differential type known as grade n fluids these thermodynamic restrictions have been a source of some c ontroversy and much confusion not withstanding the fact that they are in complete harmony with results achieved by either linear or nonlinea r stability analysis. In order to clarify the issues that seem to unde rlie this controversy, we provide an extended analysis of the genesis and development of fluids of differential type. As part of our analysi s, we will show that certain ideas of flow retardation and model appro ximation have been consistently misinterpreted. Additionally, we estab lish several new results concerning the thermodynamics of these materi als. A special application of our results reveals that work of Joseph [1, 2] and Renardy [3] on the instability of the rest state for certai n, very special grade n fluids is in fact inapplicable to all those gr ade n fluids that are consistent with thermodynamics.