Supersonic Absorption and Stokes' Viscosity Relation

It is pointed out that the reduction of the two viscosity coefficients to one according to the Stokes' relation $2\mu +3\mathrm{}\lambda =0\mathrm{}$ is not justified except in the special case of a monatomic gas. The generalization of this relation by the re-introduction of the second independent viscosity coefficient $\kappa =\frac{2}{3}\mu +\lambda$ makes it possible to develop the phenomenological theory of the absorption and dispersion of sound, in agreement with experiment in complete analogy to the corresponding optical phenomena. The connection of the well-known relaxation theory with classical hydrodynamics can be established and in the case of polyatomic gases $\kappa$ is expressed by the characteristic constants of this theory. The case of liquids is discussed. In polyatomic gases and liquids one has generally $\kappa \gg \mu$. Other hydrodynamical consequences of the introduction of $\kappa$ are discussed.