Scientia Sinica

ON VOLUME VISCO-ELASTIC THEORY OF FLUIDS AND ITS APPLICATON TO SOUND DISPERSION PHENOMENA*

Lu Ho-Fu (Horr Lu, mesa )**

(Department of Physics, Futan University, Shanghai)

ABSTRACT

In this paper is shown that our volume visco-elastic theory of fluids is not merely applicable to the case of structural relaxation (as is liable to be regarded), but equally applicable to all three kinds of relaxations—thermal, structural and chemical, From our equation of. irreversibility of volume change is inferred the equation of thermal irreversibility as originally assumed by Herzfeld and Rice for the ‘case of thermal relaxation, Also, in the case of chemical relaxation, our equation of irreversibility of volume change is shown to imply the equation of chemical irreversibility as obtained from kinetic considerations by Liebermann.

Regarding the application of this theory to sound absorption and dispersion phenomena, BourginKneser equations for the case of thermal relaxation and Liebermann equation for the case of chemical relaxation are shown to follow directly from the results of our theory of compressibilities when appropriate thermodynamic considerations have been made. This derivation reveals that Liebermann equation of sound absorption can be a good approximation only for the case of liquids.

In the case of gases, illustrations are given in which the existing sound absorption and dispersion Measurements are already accurate enough as to make it possible to determine from them the static and instantaneous compressibilities- By and §B. and hence the two ratios of heat capacities Y) and ¥., as well as the external and internal heat capacities C(¢) and C(), thus subsequently enabling us to draw directly from them certain conclusions regarding the structure of the molecule and! the processes of energy exchanges upon collision,

Finally, the appropriateness of our definition of volume viscosity is discussed.

I. On tHE Votume Visco-ELastic EQUATION

The volume visco-elastic theory of fluids formulated phenomenologically by the author!» ***! started out with the assumption that the relative compressions=—AV/V of a fluid element ultimately produced by a suddenly applied constant pressure is composed of two parts, one instantaneous and the other relaxational, viz.,

Sol Senceisee (1) The instantaneous part s, is the usual elastic strain and, when present alone,

*First published in Chinese in Acta Physica Sinica, Vol. XII, No. 1, pp. 5—19, 1956. **Now at Peking University.