Beyond Fluid Mechanics: An Introduction to the Statistical Foundations of Gas Dynamics

Abstract

While introducing Fluid Mechanics, we had to introduce also the idea of continuous media, which is the mathematical idealization of real fluids (or solids). In many circumstances, the limits of this approach arose: for instance the rheological laws, which relate strain and stress, are not given by Fluid Mechanics, they need another model. Fluid Mechanics considers these laws as given. In the first chapter we observed that in the limit of small perturbations of the basic thermodynamic equilibrium by the flow, we could derive the functional form of the rheological laws, namely that of Newtonian fluids, but the specificity of the fluid was then condensed in its viscosity or, more generally, in its transport coefficients.