Abstract
Convection and fluidization phenomena in vibrated granular beds have attracted a strong interest from the physics community since the last decade of the past century. As early reported by Faraday, the convective flow of large inertia particles in vibrated beds exhibits enigmatic features such as frictional weakening and the unexpected influence of the interstitial gas. At sufficiently intense vibration intensities surface patterns appear bearing a stunning resemblance with the surface ripples (Faraday waves) observed for low-viscosity liquids, which suggests that the granular bed transits into a liquid-like fluidization regime despite the large inertia of the particles. In his 1831 seminal paper, Faraday described also the development of circulation air currents in the vicinity of vibrating plates. This phenomenon (acoustic streaming) is well known in acoustics and hydrodynamics and occurs whenever energy is dissipated by viscous losses at any oscillating boundary. The main argument of the present paper is that acoustic streaming might develop on the surface of the large inertia particles in the vibrated granular bed. As a consequence, the drag force on the particles subjected to an oscillatory viscous flow is notably enhanced. Thus, acoustic streaming could play an important role in enhancing convection and fluidization of vibrated granular beds, which has been overlooked in previous studies. The same mechanism might be relevant to geological events such as fluidization of landslides and soil liquefaction by earthquakes and sound waves.
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M. Faraday, Philos. Trans. R. Soc. London 52, 299 (1831).
Sedley Taylor, Proc. R. Soc. London 27, 71 (1878).
V. Dvorak, Ann. Phys. 227, 634 (1874).
E.N. da C. Andrade, Proc. R. Soc. London, Ser A 134, 445 (1931).
B.A. Al-Zaitone, C. Tropea, Chem. Engin. Sci. 66, 3914 (2011).
Lord Rayleigh, Philos. Trans. R. Soc. London 175, 1 (1884).
Henk Jan van Gerner, Ko van der Weele, Martin A. van der Hoef, Devaraj van der Meer, J. Fluid Mech. 689, 203 (2011).
H. Schlichting, Phys. Z. 33, 327 (1932).
Peter J. Westervelt, J. Acous. Soc. Am. 25, 60 (1953).
J. Holtsmark, I. Johnsen, T. Sikkeland, S. Skavlem, J. Acous. Soc. Am. 26, 26 (1954).
N. Riley, Q. J. Mech. Appl. Math. 19, 461 (1966).
B.J. Davidson, N. Riley, J. Fluid Mech. 53, 287 (1972).
A. Gopinath, A.F. Mills, ASME: J. Heat Transf. 115, 332 (1993).
Chun P. Lee, Taylor G. Wang, J. Acoust. Soc. Am. 88, 2367 (1990).
E.H. Trinh, J.L. Robey, Phys. Fluids 6, 3567 (1994).
S.V. Komarov, Advanced Topics in Mass Transfer, chapter Application of Airborne Sound Waves for Mass Transfer Enhancement (InTech, 2011) pp. 61--86.
J.M. Valverde, J.M.P. Ebri, M.A.S. Quintanilla, Environ. Sci. Technol. 47, 9538 (2013).
Steven L. Garrett, Am. J. Phys. 72, 11 (2004).
F.H. Reynst, Pulsating combustion: the collected works of F.H. Reynst (Pergamom Press, 1961).
J.O. Gagnon, M.P. Paidoussis, J. Fluids Struct. 8, 293 (1994).
A.L. Yarin, G. Brenn, O. Kastner, D. Rensink, C. Tropea, J. Fluid Mech. 399, 151 (1999).
Frieder Mugele, Adrian Staicu, Rina Bakker, Dirk van den Ende, Lab Chip 11, 2011 (2011).
Martin Wiklund, Roy Green, Mathias Ohlin, Lab Chip 12, 2438 (2012).
Po-Chuan Huang, Chih-Cheng Chen, Hsiu-Ying Hwang, Int. J. Heat Mass Transfer 61, 696 (2013).
N. Riley, Annu. Rev. Fluid Mech. 33, 43 (2001).
Greg W. Swift, Thermoacoustics: A Unifying Perspective for Some Engines and Refrigerators (Acoustical Society of America through the American Institute of Physics, 2002).
S. Yavuzkurt, M.Y. Ha, G. Reethof, G. Koopmann, A.W. Scaroni, J. Energy Res. Technol. 113, 286 (1991).
A. Gopinath, H.R. Harder, Int. J. Heat Mass Transt. 43, 505 (2000).
Yonglin Ju, Yan Jiang, Yuan Zhou, Cryogenics 38, 649 (1998).
B.P.M. Helvensteijn, A. Kashani, A.L. Spivak, P.R. Roach, J.M. Lee, and P. Kittel, in Advances in Cryogenic Engineering, Vol. 43 edited by P. Kittel (Springer US, 1998) pp. 1619--1626.
Melda Ödinç Çarpinlioglu, Mehmet Yasar Gündogdu, Flow Meas. Instrum. 12, 163 (2001).
Li wen Jin, KaiChoong Leong, Transport Porous Media 72, 37 (2008).
J.M. Valverde, F.J. Duran-Olivencia, Riv. Nuovo Cimento 37, 591 (2014).
L.D. Landau, E.M. Lifshitz, Course of Theoretical Physics, chapter Fluid Mechanics (Pergamon Press, New York, 1995).
Jose Manuel Valverde, Contemp. Phys. DOI: 10.1080/00107514.2015.1008742(0):1--210.
Sungryel Choi, Kwanwoo Nam, Sangkwon Jeong, Cryogenics 44, 203 (2004).
D. Klotsa, Michael R. Swift, R.M. Bowley, P.J. King, Phys. Rev. E 79, 021302 (2009).
R. Wunenburger, V. Carrier, Y. Garrabos, Phys. Fluids 14, 2350 (2002).
C. Laroche, S. Douady, S. Fauve, J. Phys. (Paris) 50, 699 (1989).
R. Evesque, J. Phys. (Paris) 51, 697 (1990).
P. Evesque, Contemp. Phys. 33, 245 (1992).
D.-W. Wang, Y.-C. Chou, T.-M. Hong, Europhys. Lett. 35, 333 (1996).
Igor S. Aranson, Lev S. Tsimring, Rev. Mod. Phys. 78, 641 (2006).
H. Pak, E. Van Doorn, R.P. Behringer, Phys. Rev. Lett. 74, 4643 (1995).
M.H.I. Baird, M.G. Senior, R.J. Thompson, Chem. Engin. Sci. 22, 551 (1967).
E.B. Tunstall, G. Houghton, Chem. Engin. Sci. 23, 1067 (1968).
Yong Deng, Mooson Kwauk, Chem. Engin. Sci. 45, 483 (1990).
T.S. Zhao, P. Cheng, Cryogenics 36, 333 (1996).
J.A.C. Gallas, H.J. Herrmann, S. Sokołowski, Phys. Rev. Lett. 69, 1371 (1992).
Y.-h. Taguchi, Phys. Rev. Lett. 69, 1367 (1992).
J.J. Moreau, in Powders Grains 93, edited by C. Thornton (Balkema, Rotterdam, 1993) p. 227.
S. Luding, E. Clément, A. Blumen, J. Rajchenbach, J. Duran, Phys. Rev. E 50, R1762 (1994).
Henk Jan van Gerner, Martin A. van der Hoef, Devaraj van der Meer, Ko van der Weele, Phys. Rev. E 76, 051305 (2007).
Henk Jan van Gerner, Gabriel A. Caballero-Robledo, Devaraj van der Meer, Ko van der Weele, Martin A. van der Hoef, Phys. Rev. Lett. 103, 028001 (2009).
J. Li, I.S. Aranson, W.-K. Kwok, L.S. Tsimring, Phys. Rev. Lett. 90, 134301 (2003).
Stuart B. Savage, J. Fluid Mech. 194, 457 (1988).
P. Evesque, E. Szmatula, J.-P. Denis, Europhys. Lett. 12, 623 (1990).
Jose Manuel Valverde, Fluidization of Fine Powders: Cohesive versus Dynamical Aggregation, Vol. 18 Particle Technology Series (Springer, 2013).
R.D. Wildman, J.M. Huntley, D.J. Parker, Phys. Rev. E 63, 061311 (2001).
G. D'Anna, P. Mayor, A. Barrat, V. Loreto, Franco Nori, Nature 424, 909 (2003).
Heinrich M. Jaeger, Sidney R. Nagel, Robert P. Behringer, Rev. Mod. Phys. 68, 1259 (1996).
M. Nakagawa, S.A. Altobelli, A. Caprihan, E. Fukushima, E.K. Jeong, Exp. Fluids 16, 54 (1993).
A. Castellanos, J.M. Valverde, A.T. Perez, A. Ramos, P.K. Watson, Phys. Rev. Lett. 82, 1156 (1999).
J.M. Valverde, A. Castellanos, M.A.S. Quintanilla, Contemp. Phys. 44, 389 (2003).
R.P. Behringer, E. van Doorn, R.R. Hartley, H.K. Pak, Granular Matter 4, 9 (2002).
E. Falcon, K. Kumar, K. Bajaj, J.K. Bhattacharjee, Phys. Rev. E 59, 5716 (1999).
H. Pak, R.P. Behringer, Phys. Rev. Lett. 71, 1832 (1993).
F. Melo, P. Umbanhowar, H.L. Swinney, Phys. Rev. Lett. 72, 172 (1994).
Benku Thomas, Arthur M. Squires, Phys. Rev. Lett. 81, 574 (1998).
J. Duran, Phys. Rev. Lett. 84, 5126 (2000).
R.J. Milburn, M.A. Naylor, A.J. Smith, M.C. Leaper, K. Good, Michael R. Swift, P.J. King, Phys. Rev. E 71, 011308 (2005).
P. Evesque, J. Rajchenbach, Phys. Rev. Lett. 62, 44 (1989).
Eric van Doorn, R.P. Behringer, Phys. Lett. A 235, 469 (1997).
Francisco Melo, Paul B. Umbanhowar, Harry L. Swinney, Phys. Rev. Lett. 75, 3838 (1995).
Sui Lei, Miao Guo-Qing, Wei Rong-Jue, Chin. Phys. Lett. 18, 614 (2001).
P.C. Carman, Chem. Engin. Res. Design 75, S32 (1997).
K. Rietema, The Dynamics of Fine Powders (Elsevier, London, 1991).
M.L. Hunt, C.R. Wassgren, C.E. Brennen, J. Appl. Mech. 63, 712 (1996).
J.M. Valverde, A. Castellanos, Europhys. Lett. 75, 985 (2006).
R.L. Brown, J.C. Richards, P.V. Danckwerts, Principles of Powder Mechanics: Essays on the Packing and Flow of Powders and Bulk Solids (Elsevier Science, 2013).
W.C. Yang, Handbook of Fluidization and Fluid-Particle Systems (Taylor & Francis, 2003).
A.C. Hoffmann, H.J. Finkers, Powder Technol. 82, 197 (1995).
E.R. Nowak, J.B. Knight, E. Ben-Naim, H.M. Jaeger, S.R. Nagel, Phys. Rev. E 57, 1971 (1998).
Osborne Reynolds, Philos. Mag. Ser. 5 20, 469 (1885).
Sandra Wegner, Ralf Stannarius, Axel Boese, Georg Rose, Balazs Szabo, Ellak Somfai, Tamas Borzsonyi, Soft Matter 10, 5157 (2014).
E. van Doorn, R.P. Behringer, Europhys. Lett. 40, 387 (1997).
Jose Manuel Valverde, Soft Matter 9, 8792 (2013).
P.B. Umbanhowar, F. Melo, H.L. Swinney, Nature 382, 793 (1996).
P.B. Umbanhowar, F. Melo, H.L. Swinney, Physica A 249, 1 (1998).
S. Douady, S. Fauve, C. Laroche, Europhys. Lett. 8, 621 (1989).
John R. de Bruyn, B.C. Lewis, M.D. Shattuck, Harry L. Swinney, Phys. Rev. E 63, 041305 (2001).
Osamu Sano, Ataka Takei, AIP Conf. Proc. 1145, 729 (2009).
H.J. Melosh, Nature 379, 601 (1996).
Kaiwen Xia, Sheng Huang, Chris Marone, Geochem. Geophys. Geosyst. 14, 1012 (2013).
Antoine Lucas, Anne Mangeney, Jean Paul Ampuero, Nat. Commun. 5, 3417 (2014).
Alexander Wong, Chi-Yuen Wang, J. Geophys. Res. B: Solid Earth 112, B10305 (2007).
R. Chirone, L. Massimilla, S. Russo, Chem. Engin. Sci. 48, 41 (1993).
A. Ajbar, Y. Bakhbakhi, S. Ali, M. Asif, Powder Technol. 206, 327 (2011).
P. Ammendola, R. Chirone, F. Raganati, Chem. Engin. Proc.: Proc. Intensif. 50, 885 (2011).
J.M. Valverde, F. Raganati, M.A.S. Quintanilla, J.M.P. Ebri, P. Ammendola, R. Chirone, Appl. Energy 111, 538 (2013).
F. Raganati, P. Ammendola, R. Chirone, Appl. Energy 113, 1269 (2014).
C. Soria-Hoyo, J.M. Valverde, A. Castellanos, Powder Technol. 196, 257 (2009).
H. Schubert, Powder Technol. 37, 105 (1984).
M. Campbell, J.A. Cosgrove, C.A. Greated, S. Jack, D. Rockliff, Optics Laser Technol. 32, 629 (2000).
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Prof. José Manuel Valverde Millán obtained a Batchelor Science degree in Physics at the University of Seville in Spain in 1993, and a Ph.D. in Physics from the same University in 1997. He is currently Professor and Researcher at the University of Seville. His research activity has been focused on the study of fluidization and mechanical properties of granular materials and can be considered as highly interor multi-disciplinary, lying between the areas of engineering and fundamental physics. A main subject of current interest is the development of novel techniques to enhance the CO2 capture and thermochemical energy storage efficiencies of CaO-based materials by means of the Ca-looping technology based on carbonation/calcination of natural limestone and dolomite in fluidized beds.
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Valverde, J.M. Convection and fluidization in oscillatory granular flows: The role of acoustic streaming. Eur. Phys. J. E 38, 66 (2015). https://doi.org/10.1140/epje/i2015-15066-7
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DOI: https://doi.org/10.1140/epje/i2015-15066-7