In the preceding chapter a highly simplified discussion of molecular transport in non-equilibrium dilute gases was presented. Even though this discussion was highly simplified, it helped us to illuminate the basic physical processes resulting in the transport of macroscopic physical quantities.

In this chapter the theory of macroscopic transport will be treated in a more rigorous way. Our discussion will be based on the Boltzmann equation, a non-linear seven dimensional partial differential equation which describes the evolution of the phase space distribution function in non-equilibrium gases. Conservation equations for macroscopic physical quantities will be obtained in the next chapter as the velocity moments of the Boltzmann equation.

In this chapter our discussions will be based on the following fundamental assumptions:

1. (i) We assume that the gas density is low enough to ensure that the mean free path is large compared to the effective range of the intermolecular forces. This assumption makes it possible to apply the principle of molecular chaos in the treatment of binary encounters. Molecular chaos means that the velocities of the colliding particles are uncorrelated, i.e. particles which have already collided with each other will have many encounters with other molecules before they meet again. A direct consequence of this assumption is the time irreversibility of the Boltzmann equation.

2. (ii) The mean free path is short compared to the dimensions of the problem. This assumption eliminates consideration of wall effects and other edge-related problems.

3. […]