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Mechanics of collisional motion of granular materials. Part 2. Wave propagation through vibrofluidized granular layers

Published online by Cambridge University Press:  26 April 2006

Alexander Goldshtein ,
Michael Shapiro ,
Leonid Moldavsky  and
Mati Fichman
Alexander Goldshtein
Affiliation:
Faculty of Mechanical Engineering, Technion – Israel Institute of Technology, Haifa 32000, Israel
Michael Shapiro
Affiliation:
Faculty of Mechanical Engineering, Technion – Israel Institute of Technology, Haifa 32000, Israel
Leonid Moldavsky
Affiliation:
Faculty of Mechanical Engineering, Technion – Israel Institute of Technology, Haifa 32000, Israel
Mati Fichman
Affiliation:
Faculty of Mechanical Engineering, Technion – Israel Institute of Technology, Haifa 32000, Israel
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Abstract

According to numerous experimental observations and theoretical models vibrated layers composed of large granules behave like a solid plastic body. In contrast, in this study experimental data are presented that reveal that, for constant vibration amplitudes A ≥ 1 cm with the frequency ω increasing from zero, all layers pass through three vibrational states, with the respective behaviours being as of (i) a solid plastic body, (ii) a liquid, (iii) a gas. In the liquid-like vibrational state transverse waves propagating along the layer width were observed. These waves were shown to be gravitational resonance waves, with the corresponding frequencies well correlated by the known formula for incompressible liquids. In the gas-like vibrational state compression (shock) and expansion waves propagating across the layer height, were observed.

A theoretical model for time-periodic collisional vibrational regimes was developed on the basis of the Euler-like equations of a granular gas composed of inelastic spheres. The model shows that the vibrational granular state (bed porosity, shock wave speed, granular pressure and kinetic energy) is inter alia governed by the dimensionless parameter V = (Aω)/(hmg)1/2, with g, hm being the gravitational acceleration and the height of the resting layer, respectively. This is in contrast with the previous studies, where the behaviour of vibrated granular layers was interpreted in terms of the dimensionless acceleration Δ = (Aω2)/g. The proposed model was tested by processing the data obtained from photographs of the particle distribution within vibrated layers. Theoretical predictions of the particle average concentration compared favourably with the experimental data.

Other phenomena observed in vibrated granular layers include the formation of caverns, circulatory motion of granules and synchronized periodic motion of two adjacent vibrated layers of different widths. The importance of the observed phenomena in relation to various technological processes involving bulk materials (vibromixing, vibroseparation, etc.) is discussed.

Information

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 287 , 25 March 1995 , pp. 349 - 382
Copyright
© 1995 Cambridge University Press

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References

Ahmad, K. & Smalley, I. J. 1973 Observation of particle segregation in a vibrated granular system. Powder Technol. 8, 69–75.Google Scholar
Alder, B. J. & Hoover, W. G. 1968 Numerical statistical mechanics. In Physics of Simple Liquids, pp. 79–114. North-Holland.
Bachmann, D. 1940 Verfahrensttechnik Z.V.D.I. Beiheft 2, 43, cited in the paper by Thomas et al. (1989).
Blekhman, I.I. & Dzhanelidze, D. G. 1964 Vibrational Transport. Moscow: Nauka (in Russian).
Buevich, Yu. A., Sutkin, S. V. & Tetukhin, V. V. 1984 To the theory of magneto-fluidized bed. Sov. Mag. Gidrod. 4, 3–11.Google Scholar
Campbell, C. S. 1990 Rapid granular flows. Ann. Rev. Fluid Mech. 22, 57–92.Google Scholar
Chapman, S. & Cowling, T. G. 1970 The Mathematical Theory of Non-Uniform Gases, 3rd edn. Cambridge University Press.
Chlenov, V. A. & Mikhailov, N. D. 1972 Vibrofluidized Beds. Moscow: Nauka (in Russian).
Clement, E. & Rajchenbach, J. 1991 Fluidization of a bidimensional powder Europhys. Lett. 16, 133–138.Google Scholar
Courant, R. & Friedrichs, K. O. 1948 Supersonic Flow and Shock Waves. Interscience.
Drake, T. G. 1990 Granular flow: physical experiments and their implication for microstructural theories. J. Fluid Mech. 225, 121–152.Google Scholar
Erdèsz, K. & Mujumdar, A. S. 1989 Numerical investigation of a phenomenological model for vibrated fluidized beds. Drying Technol. 7, 487–502.Google Scholar
Erdèsz, K. & Nèmeth, J. 1988 Methods of calculation of vibrational transport rate of granular material. Powder Technol. 55, 161–170.Google Scholar
Fauve, A., Douady, S. & Laroshe, C. 1989 Collective behaviors of granular masses under vertical vibrations. J. Physique Colloque C3, 50 (3), 187–191.Google Scholar
Goldshtein, A. & Shapiro, M. 1995 Mechanics of collisional motion of granular materials. Part 1. General hydrodynamic equations. J. Fluid Mech. 282, 75–114.Google Scholar
Goldshtein, A., Shapiro, M. & Gutfinger, C. 1995 Mechanics of collisional motion of granular materials. Part 3. Self-similar shock-wave propagation. J. Fluid Mech. (submitted).Google Scholar
Gray, W. A. & Rhodes, G. T. 1972 Energy transfer during vibratory compaction of powders. Powder Techn. 6, 271–281.Google Scholar
Gutman, I. 1968 Industrial Uses of Mechanical Vibrations. London: Business Books.
Gutman, R. G. 1976 Vibrated beds of powders. Part I: A theoretical model for the vibrated bed. Trans. Inst. Chem. Engrs 54, 174–183.Google Scholar
Haff, P. K. 1983 Grain flow as a fluid-mechanical phenomenon. J. Fluid Mech. 134, 401–430.Google Scholar
Homsy, G. M., Jackson, R. & Grace, J. R. 1992 Report of a symposium on mechanics of fluidized beds. J. Fluid Mech. 236, 447–495.Google Scholar
Jenkins, J. T. & Savage, S. B. 1983 A theory for rapid flow of identical, smooth, nearly elastic, spherical particles. J. Fluid Mech. 130, 187–202.Google Scholar
Kroll, W. 1954 Über das Verhalten von Schüttgut in Lotrecht Schwingenden Gefäben. Forshung 20, 2–15.Google Scholar
Landau, L. & Lifshitz, E. 1987 Fluid Mechanics. Pergamon.
Meakin, P. & Skjeltorp, A. T. 1993 Application of experimental and numerical models to the physics of multiparticle systems. Adv. Phys. 42, 1–127.Google Scholar
Moody, D. M. 1990 Unsteady expansion of an ideal gas into a vacuum. J. Fluid Mech. 214, 455–468.Google Scholar
Nigmatullin, R. I. 1978 Fundamentals of the Mechanics of Heterogeneous Media. Moscow: Nauka (in Russian).
Raskin, Kh. I. 1975 Application of the methods of physical kinetics to problems of vibrated granular media. Dokl. Acad. Nauk SSSR 220, 54–57.Google Scholar
Roberts, A. W. 1984 Handbook of Powder Science and Technology. Van Nostrand Reinhold.
Savage, S. B. 1984 The mechanics of rapid granular flows. Adv. Appl. Mech. 24, 289–366.Google Scholar
Savage, S. B. 1988 Streaming motions in a bed of vibrationally fluidized dry materials. J. Fluid Mech. 194, 457–478.Google Scholar
Thomas, B., Liu, Y. A., Chan, R. & Squires, A. M. 1987 A method of observing phase dependent phenomena in cyclic systems: Application to study of dynamic of vibrated bed of granular solids. Powder Technol. 52, 77–92.Google Scholar
Thomas, B., Mason, M. O., Liu, Y. A. & Squires, A. M. 1989 Identifying states in shallow vibrated beds. Powder Technol. 57, 267–280.Google Scholar
Thomas, B. & Squires, A. M. 1989 Vibrated bed microreactors simulating catalytic fluid beds: A feasibility bed. In Fluidization IV (ed. J. R. Grace, L. W. Shemilt & M. A. Bergoughou) Alberta, Canada: Benif.