THE BULK VISCOSITY OF FLUIDS: THE MODERN PHYSICAL AND ANALYTICAL REPRESENTATIONS AND THEIR PROSPECTS OF THE DEVELOPMENT
DOI:
https://doi.org/10.15673/0453-8307.4/2015.38333Keywords:
bulk viscosity, stress tensor, relaxation, sound waves, molecular simulation, acoustic spectroscopy, optical methodsAbstract
Taking note of bulk viscosity is especially important at the description of high-intensity processes, such as explosion, a flow with high speeds, the acoustic phenomena, and also in characteristic points of a condition of substance. Bulk viscosity characterizes ability of substance to transformation of mechanical energy in thermal at nonequilibrium volume deformation. In the work the main theoretical directions of bulk viscosity influence studying are considered: physical acoustics, hydrodynamics, molecular and kinetic theory of gases and liquids. It is established that the molecular mechanism of the bulk viscosity emergence described in Landau's Enskog, Kramer works allows understanding more deeply the physical processes which are taking place at change of volume in the compressed liquid. Special interest submit the theory of a relaxation constructed by Mandelstam and Leontovich where the equation of a state included the parameter defining internal structure of liquid that allows to consider effects of acoustic waves distribution. Expediency of Green-Kubo formula application which connects bulk viscosity with autocorrelation function of pressure microscopic fluctuations is noted. The existing methods of bulk viscosity coefficient experimental determination such as acoustic spectroscopy and Brillouin-Mandelstam scattering are analyzed. Problems of bulk viscosity near a critical point liquid-gas determination are considered.
References
Vallander S. V. 1978. Lectures on hydroaeromechanics: the manual for high schools. – L.: Izd-vo Leningr. un-ta, – 296. (in Russian)
.Kopishev V. P. Medvedev V. P. Hrustalev V. V. 2004. Modelling estimation of viscosity of products of explosion of the condensed explosives. Phyzika goreniya i vzriva. – V. 40. – No. 2. – 82-88. (in Russian)
Krasilnikov V.A. Krilov V.V. 1984. Introduction in physical acoustics. – M.: Nauka. – P. 403. (in Russian)
Landaw L.D. Livshic E.M. 1988. The theoretical physics. – T.6. Hydromechanics. – M.: Nauka. – 736. (in Russian)
Malcev I. V. Mirzoev A.A. 2010. Design procedure of shift viscosity of liquid iron Green-Kubo method. Vestnic SUSU, series «Matematika. Mehanika. Fisika». [Mathematics. Mechanics. Physics] – V. 2. – No. 9. – 76-78. (in Russian)
Mirzadjanzade A. H., Bahtizin R. N. 2004. Modelling of processes oil production. Nonlinearity, nonequilibrium, uncertainty. – Moskva-Izhevsk: Institut komputernih issledovaniy. – 368. (in Russian)
Mihailov A. G., Solovyov V.A. 1953. Attenuation of ultrasonic waves in liquids and the molecular mechanism of volume viscosity. Uspehi phyzicheskih nauk. – V. L. – No. 1. – 50. (in Russian)
Petrov S. V. Saakov A.G. 2000. Plasma of products of combustion in surface engineering. – Kiev. Topas. – 220. (in Russian)
. Polezhaev V. I., Soboleva E. B. 2003. Hydrodynamics near critical liquids. Priroda. [Nature] – V. 10. – 17-26.
Resibua P., De Lener M. 1980. The classical kinetic theory of liquids and gases. – Moskva. Mir. – 424. (in Russian)
Surnichev V.V. Kovalenko V.I., Lagunov A.S. 2005. Relaxation of bulk and shift viscosity in diethylsiloxane and ethyloctylsiloxane. Jurnal tehnicheskoy fiziki., [Technical Physics] – V.75. – No.10 – 131-134. (in Russian)
Alfe D. Gillan M. J. 1998 First-Principles Calculation of Transport Coefficients, Phys Rev Vol. 81. – No. 23. – 8248 – 8256.
Berg R.F., Moldover M.R., Zimmerli G.A. 1999. Frequency-dependent viscosity of xenon near the critical point. Phys. Rev. E. – V. 60 – 4079.
Brady J. F., Khair A. S., Swaroop M., 2006. On the bulk viscosity of suspensions J. Fluid Mech., – V. 554. – pp. 109-123
Cramer M. S. 2012. Numerical estimates for the bulk viscosity of ideal gases, Phys. Fluids – V. 24. – 066102
Dave K. 2012. Critical Behavior of Viscosity at the Liquid–Gas Critical Point of Xe – Physics V. 563 – 9.
17. Dukhin A. S. and Goetz P. J. 2009. Bulk viscosity and compressibility measurement using acoustic spectroscopy. Chem. Phys. – 2009. – V. 130. – 124519.
Gillis K.A., Shinder I.I., Moldover M.R. 2005. Bulk Viscosity of Stirred Xenon Near the Critical Point. Phys. Rev. E. – V. 72. – 051201. doi: 10.1103/PhysRevE.72.051201
Guang-Jun Guo and Yi-Gang Zhang 2001. Equilibrium molecular dynamics calculation of the bulk viscosity of liquid water. Molecular Physics. – V. 99, No. 4. – 283–289.
Heyes D.M. 1984. Thermal Conductivity and Bulk Viscosity of Simple Fluids. J. Chem. SOC., Faraday Trans. – V. 80. – 1363-1394.
Hoheisel C. 1987. Bulk viscosity of model fluids. A comparison of equilibrium and nonequilibrium molecular dynamics results – J. Chem. Phys. – V. 86. – No.4. – P. 2328-2333. doi: 10.1063/1.452131
Holmes M. J., Parker N.G., Povey M. W. 2011. Temperature dependence of bulk viscosity in water using acoustic spectroscopy. Journal of Physics: Conference Series. – V. 296. – 012011. doi: 10.1088/1742-6596/269/1/012011
Okumura H.,Yonezawa F. 2002. Approximate Formula for Bulk Viscosity. Journal of the Physical Society of Japan. – V. 71. – No. 3. – P. 685–688. doi: 10.1143/JPSJ.71.685
Ain A. Sonin. 2001. Equation of Motion for Viscous Fluids. Massachusetts. – Р. 29.
Wonsoo Kim and Tong-Seek Chair. 2002. A Calculation for the Viscosity of Fluid at the Critical Point – Bull. Korean Chem. Soc. – V. 23. – No. 11.
Yuan Ge , Jiulin Shi , Kaixing Zhu, and Xingdao He. 2013. Determination of bulk viscosity of liquid water via pulse duration measurements in stimulated Brillouin scattering. Chinese Optics Letters. – V.11. – 112902. doi: 10.3788/COL201311.112902
Zaheri A.H.M. 2009. Calculation of bulk viscosity of two-component fluids from sech (at) form of the time correlation function. Armenian Journal of Physics. – V. 2. – Is. 4. – 333-336.
