Compressional Relaxation in Liquids

A set of phenomenological equations, valid at all frequencies, is proposed for the rates of change of internal relaxation parameters describing molecular excitations and structural changes in liquid. An Onsager coupling is found to exist between the rate equations for the parameters and the pressure tensor, so that the diagonal terms of the pressure contain a linear sum of thermodynamic affinities governing the internal irreversible processes. These affinities can be eliminated from the pressure, using the rate equations, to give a complex compressional modulus, reducing to a bulk viscosity term at low frequencies and a contribution to the bulk modulus at very high frequencies. The bulk viscosity is calculated at 20°C for two nonassociated liquids, on the assumption of a single thermal and single structural relaxation time, with use of a “hole” model of structural relaxation based on a shear viscosity theory of Mooney. The acoustic absorption coefficient is computed from the bulk viscosity, yielding fair order-of-magnitude agreement with experiment in both cases.