Abstract:
We formulate the limits of applicability of the hydrodynamic equations and prove the necessity of introducing a correction to the potential energy transfer in the heat conductivity equation, which allows developing the hydrodynamic theory of the propagation of sound waves with small amplitudes. We show that this correction affects almost all predictions of the standard hydrodynamic theory. In particular, this correction allows extending the applicability domain of the hydrodynamic theory to the case of an arbitrarily viscous liquid. Moreover, in total accordance with the experimental data, the theory predicts that the sound speed and the damping rate remain finite at all frequencies up to frequencies of the order of 10−12sec−1, while the hydrodynamic equations make no sense at higher frequencies and sound wave propagation in the medium consequently becomes impossible. We show that the dimensionless dispersion equation contains only one material parameter. We predict the existence of the highly damped second sound.
Citation:
G. A. Martynov, “Hydrodynamic Theory of Sound Wave Propagation”, TMF, 129:1 (2001), 140–152; Theoret. and Math. Phys., 129:1 (2001), 1428–1438
This publication is cited in the following 7 articles:
Martynov G.A., “Fluctuation theory of critical phenomena in fluids”, Russ. J. Phys. Chem. A, 90:7 (2016), 1338–1349
Maximov G.A., “Generalized Variational Principle for Dissipative Continuum Mechanics”, Mechanics of Generalized Continua - One Hundred Years After the Cosserats, Advances in Mechanics and Mathematics, 21, 2010, 297–305
Maximov G.A., “A Generalized Variational Principle for Dissipative Hydrodynamics and its Application to Biot's Theory for the Description of a Fluid Shear Relaxation”, Acta Acustica united with Acustica, 96:2 (2010), 199–207
Kobryn, AE, “Statistical-mechanical theory of ultrasonic absorption in molecular liquids”, Journal of Chemical Physics, 126:4 (2007), 044504
G. A. Martynov, “General Theory of Acoustic Wave Propagation in Liquids and Gases”, Theoret. and Math. Phys., 146:2 (2006), 285–294
Maksimov G.A., “On the variational principle in dissipative hydrodynamics”, Proceedings of the International Conference Days on Diffraction 2006, 2006, 173–177
G. A. Martynov, “Thermodynamics and Hydrodynamics (Statistical Foundations): 3. Hydrodynamic Equations”, Theoret. and Math. Phys., 134:3 (2003), 427–438