3 - Binary collisions

Summary

So far our discussion of the kinetic theory of gases has been limited to kinematic equilibrium properties. We shall see later that molecular collisions are responsible for establishing the equilibrium condition (see Chapter 5). In the absence of equilibrium, intermolecular interactions result in transport of macroscopic gas quantities, such as mass, momentum and energy. Under equilibrium conditions the distribution of molecular velocities is the same Maxwell–Boltzmann distribution at every configuration space location. In other words the effects of molecular collisions cancel each other (the distribution function is constant in time and configuration space) and therefore the details of individual collisions do not play a role in determining the distribution of molecular velocities.

The situation is entirely different if we allow even the slightest deviation from equilibrium. In this case molecular collisions result in the transport of macroscopic quantities (such as mass, momentum and energy) accompanied by a gradual approach to the equilibrium velocity distribution. The details of the macroscopic transport and change of the distribution function are controlled by the specific nature of the molecular collision process. Molecular collisions represent the microscopic process governing all macroscopic transport phenomena.

This chapter lays part of the necessary groundwork for the dynamical description of transport phenomena in gases by examining the details of the most fundamental physical process in the gas: molecular collisions. We begin the discussion of collisional effects by considering in detail the process of two particle (or binary) collisions.