Dynamics of Dissipative Fluids

In the first chapter we explored the microscopic origins of orientational order. We now turn to macroscopic continuum theories. These are phenomenological theories that attempt to model real materials. They do not attempt to explain material properties by resorting to the molecular structure of matter, but they can draw inspiration from molecular theories—and the best of modern theories actually do so, in the spirit of a true multiscale approach to materials science. The same continuum theory can describe different materials by means of specific constitutive laws, which being first formulated in accordance with general invariance and symmetry principles, are then corroborated by matching experimental evidence with theoretical predictions, a comparison that eventually determines the phenomenological coefficients of the continuum theory. Often, it is also possible to link microscopic and macroscopic theories by estimating directly on molecular grounds the values of the phenomenological coefficients—for example, through a mean field theory. Whenever this happens, we extract the best from both worlds.