The objective of this chapter is to present a systematic formulation of the fundamental equations governing the joint hydrodynamic and thermodynamic behavior of a fluid mixture. These equations are merely the mathematical statements of four basic principles of physics regarding:
The first three principles lead to four important equations governing fluid mixtures. The fourth principle concerns changes in the entropy of the fluid and is not a conservation law. It represents an inequality which imposes certain restrictions on such processes as diffusion, heat conduction, dissipation of energy by viscous processes, chemical reactions, etc.
Before embarking on a detailed discussion of these principles it is necessary to set forth a suitable definition of velocity as pertains to the ensemble of microscopic particles of which a real fluid mixture is composed.