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Updated: May 16, 2026

An Analog Macroscopic Technique for Studying Molecular Hydrodynamic Processes in Dense Gases and Liquids
Published on: December 4, 2017
Thermal and viscous effects on sound waves: revised classical theory
Anthony M J Davis1, Howard Brenner
1Mechanical and Aerospace Engineering Department, University of California, San Diego, La Jolla, California 92093-0411, USA. amdavis@ucsd.edu
Abstract:
In this paper the recently developed, bi-velocity model of fluid mechanics based on the principles of linear irreversible thermodynamics (LIT) is applied to sound propagation in gases taking account of first-order thermal and viscous dissipation effects. The results are compared and contrasted with the classical Navier-Stokes-Fourier results of Pierce for this same situation cited in his textbook. Comparisons are also made with the recent analyses of Dadzie and Reese, whose molecularly based sound propagation calculations furnish results virtually identical with the purely macroscopic LIT-based bi-velocity results below, as well as being well-supported by experimental data. Illustrative dissipative sound propagation examples involving application of the bi-velocity model to several elementary situations are also provided, showing the disjoint entropy mode and the additional, evanescent viscous mode.
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