1. Thermodynamics and Evolution

This is an introductory, yet fundamental chapter, where all the relevant concepts that are encountered in transport phenomena are defined. After a brief introduction (Sect. 1.1) on what transport phenomena consist of, in Sect. 1.2 we describe the relation between thermodynamics and transport phenomena, by defining the condition of local equilibrium. We explain that, under very general conditions, although far from thermal and mechanical equilibrium, we can speak of thermodynamic quantities such as temperature and pressure. This idea is further explored in Sect. 1.3, where the basic concepts of continuum mechanics are briefly sketched. Then, in Sect. 1.4, we show that mass, momentum, and energy can be transported through two fundamentally different modalities, namely convection and diffusion. The former is a time reversible process due to a net movement of the fluid, and the related convective fluxes admit exact analytical expressions. On the other hand, diffusion is intrinsically irreversible, and diffusive fluxes are expressed through so called constitutive relations, that characterize the fluid at the molecular level. In the case of ideal gases, as shown in Sects. 1.5–1.7, diffusion of momentum, energy and mass can be modeled rigorously, leading to Newton’s, Fourier’s and Fick’s constitutive relations, respectively. The analogy between different transport phenomena is further explored in Sect. 1.8, showing that diffusion can be modeled through a random walk process, so that the mean square displacement of the appropriate tracer of momentum, energy or mass grows linearly with time. Finally, in Sect. 1.9, a few examples of diffusion are presented.