Development of the Kinetic Theory of Gases. VI. Viscosity

This article reviews the development of theories of transport phenomena by Maxwell, Boltzmann, Chapman, and Enskog, and their application to the calculation of the viscosity coefficient. Maxwell's original mean-free-path theory for hard spheres (1860) was refined by Tait, Sutherland, Rayleigh, and Jeans, but suffered from inherent limitations because the velocity-distribution function in a nonuniform gas was unknown. Maxwell (1866) and Boltzmann (1872) proposed more general methods for dealing with transport processes in gases; these methods form the basis of the modern theory. However, Maxwell and Boltzmann did not manage to solve their equations except in a few special cases. It was not until half a century later that Chapman (1916) and Enskog (1917) independently succeeded in determining the velocity-distribution function to an accuracy sufficient for the calculation of transport coefficients for any assumed force law. The extension of the theory to dense gases of hard spheres was accomplished by Enskog (1922), who obtained an expression for the viscosity coefficient similar to one proposed by Jäger (1900).