Kinetic and thermodynamic aspects of the second coefficient of viscosity

Abstract

There are two macroscopic theories of bulk viscosity in fluids. The first is contained in the classical theory of hydrodynamics in which the instantaneous state of an element in the fluid is determined by two thermodynamic variables. This theory fails to account for sound absorption in a number of fluids (such as carbon disulphide). To do this, more than two thermodynamic variables must be introduced into a relaxation theory. This can be combined with hydrodynamics. In the acoustic approximation a wave equation can be formed and the resulting propagation of plane waves can be investigated. Under certain restrictions it is shown that ( a ) the presence of relaxation involves a correction to the ‘classically’ determined part of the absorption coefficient, ( b ) at frequencies much lower than the inverse relaxation time there is no way of distinguishing contributions to absorption due to bulk viscosity (p' + sp) and those due to relaxation. In a review of the kinetic calculations of bulk viscosity it is pointed out that the approximation used in Kirkwood’s work automatically excludes relaxation behaviour.