Applying a condition of observability to constitutive equations of laminar motion

Abstract

The constitutive law of the material element, be it a fluid in laminar motion or a solid, is subject to two sets of fundamental requirements. The first set pertains to the Thermodynamics of Irreversible Processes, the second to stability. Stability considerations concerning the fluid generally confine, via Gibbs' postulate, to the case of the equilibrium, to the effect of specifying the signs of the specific heat and compressibility coefficient. Do such observability conditions somehow extend to the out -of - equilibrium motion of the fluid element? The question is given hereafter a positive answer by reducing it to the point of deciding whether the step-by-step determination of the motion in the vicinity of the element constitutes a well-posed problem. This approach ends up in two distinct necessary observability conditions, one for motion, one for equilibrium, the expressions of which involve the same dispersion function systematically built upon the constitutive law. Applications are made to the three most common models of fluid behaviour.