The Four Basic Principles

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:

1. the conservation of mass;
2. the conservation of momentum;
3. the conservation of energy; and
4. the availability of energy.

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.