So far we have considered gases which were in kinematic equilibrium. It was always assumed that the molecules did not have any organized motion (bulk motion), and that the gas temperature and the number density of the molecules were constant everywhere. Under such conditions there is no net particle transport from one place to another.

In this chapter we relax our earlier assumptions and let the macroscopic quantities (gas bulk velocity, temperature, pressure, concentration, etc.) have slow spatial variations. These configuration space gradients result in macroscopic transport phenomena, such as diffusion or heat flow. Fluid dynamics describes these transport phenomena using empirical transport coefficients, such as viscosity, diffusion coefficient or heat conductivity.

In this chapter we shall use the elementary mean free path method to describe macroscopic transport phenomena and to calculate approximate values for the transport coefficients. This simple and remarkably successful method is quite general because it does not depend on the form of the distribution function and, therefore, does not assume equilibrium.

The mean free path method is based on the assumption that the gas is not in equilibrium, but the deviation from equilibrium is so small that locally the distribution of molecular velocities can be approximated by Maxwellians. However, the macroscopic parameters of the local Maxwellians slowly vary with configuration space location. Mathematically this assumption can be translated into two basic conditions.

The first condition is that the variation of all macroscopic quantities is small within a mean free path.