Extending the Kinetic Theory to Denser Gases

By use of the typical numerical value for the mean free path given above for a gas at temperature iOOK and pressure 101325Pa, this condition indicates that the continuum assumption is valid provided that the characteristic dimension of the apparatus is L 0.001cm. Nevertheless, it is noted that at low gas pressures, say lOPa, the mean free path is increased and might be comparable with the characteristic dimensions of the apparatus. In particular, for low pressures and small characteristic dimensions we might enter a flow regime where the continuum assumption cannot be justifled. 

The preceding sections in this chapter deal with the kinetic theory of dilute gases summarizing the statistical modeling concepts, deriving the governing conservation equations and fairly accurate relations determining the transport coefficients from first principles. 

The starting point for the kinetic theory of dilute mono-atomic gases is the Boltzmann equation determining the evolution of the distribution function in time and space. The formulation of the collision term is restricted to gases that are sufficiently dilute so that only binary collisions need to be taken into account. It is also required that the molecular dimensions are small in comparison with the mean distance between the molecules, hence the transfer of molecular properties is solely regarded as a consequence of the free motion of molecules between collisions. 

Basically Enskog s kinetic theory extension consists in the introduction of corrections that account for the fact that for dense gases the molecular diameter is no longer small compared with the average intermolecular distance. 

The fundamental postulate is that as a dilute gas is compressed two novel effects become important because the molecules have finite volumes. First, it is expected that during a molecular collision momentum and energy are transferred over a distance equal to the separation of the molecules. In the particular case of rigid spherical molecules this collisional transfer of momentum and energy takes place instantaneously and results in a transfer over the distance between their centers. Second, the collision frequency may be altered. One possible mechanism is that the collision frequency is increased 

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