Primary Bjerknes force in a three-dimensional nonlinear resonator: Numerical simulations

Eller, 1968, Force on a bubble in a standing acoustic wave, J. Acoust. Soc. Am., 43, 170, 10.1121/1.1910755 Leighton, 1990, Primary Bjerknes forces, European J. Phys., 11, 47, 10.1088/0143-0807/11/1/009 Yoshida, 2011, Experimental investigation on reversal of secondary Bjerknes force between two bubbles in ultrasonic standing wave, J. Acoust. Soc. Am., 130, 135, 10.1121/1.3592205 Jiao, 2015, Experimental and theoretical analysis of secondary Bjerknes forces between two bubbles in a standing wave, Ultrasonics, 58, 35, 10.1016/j.ultras.2014.11.016 Akhatov, 1997, Bjerknes force threshold for stable single bubble sonoluminescence, Phys. Rev. E, 55, 3747, 10.1103/PhysRevE.55.3747 Matula, 1997, Bjerknes force and bubble levitation under single-bubble sonoluminescence conditions, J. Acoust. Soc. Am., 102, 1522, 10.1121/1.420065 Naugolnykh, 1998, 16 Vanhille, 2014, Numerical simulations of the primary Bjerknes force experienced by bubbles in a standing ultrasonic field: Nonlinear vs. linear, Wave Motion, 51, 1127, 10.1016/j.wavemoti.2014.06.001 Ellenberger, 2005, Exploiting the Bjerknes force in bubble column reactors, Chem. Eng. Sci., 60, 5962, 10.1016/j.ces.2005.03.036 Fan, 2005, Effect of acoustic standing wave in a bubble column, Ind. Eng. Chem. Res., 44, 7010, 10.1021/ie050125i Servant, 2001, Spatio-temporal dynamics of cavitation bubble clouds in a low frequency reactor: comparison between theoretical and experimental results, Ultrason. Sonochem., 8, 163, 10.1016/S1350-4177(01)00074-8 Birkin, 2003, Experimental and theoretical characterisation of sonochemical cells. Part 1. Cylindrical reactors and their use to calculate the speed of sound in aqueous solutions, J. Phys. Chem. A, 107, 306, 10.1021/jp014532t Mettin, 2013, Acoustic bubbles: Control and interaction with particles adhered to a solid substrate, Solid State Phenom., 195, 161, 10.4028/www.scientific.net/SSP.195.161 Gotoh, 2015, Delicate laundering of textiles with application of 38 kHz ultrasonic waves, Text. Res. J., 85, 1565, 10.1177/0040517515569523 Offin, 2007, Electrodeposition of copper in the presence of an acoustically excited gas bubble, Electrochem. Commun., 9, 1062, 10.1016/j.elecom.2006.12.025 Rogers, 2011, Selective particle trapping using an oscillating microbubble, Lab Chip, 11, 3710, 10.1039/c1lc20459a Nilsson, 2004, Acoustic control of suspended particles in micro fluidic chips, Lab Chip, 4, 131, 10.1039/B313493H Shibata, 2008, Froth separation of ferrihydrite slurry using microbubbles with ultrasonic irradiation, Mater. Trans., 49, 1681, 10.2320/matertrans.M-MER2008815 Leighton, 1990, Search for sonoluminescence in vivo in the human cheek, Ultrasonics, 28, 181, 10.1016/0041-624X(90)90083-Z Leighton, 1988, Studies of the cavitational effects of clinical ultrasound by sonoluminescence: 1 correlation of sonoluminescence with the standing-wave pattern in an acoustic field produced by a therapeutic unit, Phys. Med. Biol., 33, 1239, 10.1088/0031-9155/33/11/002 Pickworth, 1989, Studies of the cavitational effects of clinical ultrasound by sonoluminescence: 4. The effect of therapeutic ultrasound on cells in monolayer culture in a standing wave field, Phys. Med. Biol., 34, 1553, 10.1088/0031-9155/34/11/004 Pickworth, 1988, Studies of the cavitational effects of clinical ultrasound by sonoluminescence: 2 Thresholds for sonoluminescence from a therapeutic ultrasound beam and the effect of temperature and duty cycle, Phys. Med. Biol., 33, 1249, 10.1088/0031-9155/33/11/003 Young, 1989 Galavani, 2010, On the dynamics of moving single bubble sonoluminescence, Phys. Lett. A, 374, 4531, 10.1016/j.physleta.2010.09.017 Xi, 2011, Study on the bubble transport mechanism in an acoustic standing wave field, Ultrasonics, 51, 1014, 10.1016/j.ultras.2011.05.018 Louisnard, 2012, A simple model of ultrasound propagation in a cavitating liquid. Part II: Primary Bjerknes force and bubble structures, Ultrason. Sonochem., 19, 66, 10.1016/j.ultsonch.2011.06.008 Lauterborn, 2002, Nonlinear acoustics and acoustic chaos, vol. 586, 265 Watanabe, 1993, Translational and radial motions of a bubble in an acoustic standing wave field, Phys. Fluids A, 5, 2682, 10.1063/1.858731 P. Koch, D. Krefting, T. Tervo, R. Mettin, W. Lauterborn, Bubble path simulations in standing and travelling acoustic waves, in: Proc. 18th Int. Cong. Acoust., ICA 2004, International Commission for Acoustics, Kyoto, 2004, pp. V-3571–V-3572. Holzfuss, 2002, Acoustical stability of a sonoluminescing bubble, Phys. Rev. E, 66, 10.1103/PhysRevE.66.046630 Holzfuss, 2004, Micromanipulation of sonoluminescing bubbles, Phys. Rev. E, 69, 10.1103/PhysRevE.69.056304 Zabolotskaya, 1973, Emission of harmonic and combination-frequency waves by air bubbles, Sov. Phys.-Acoust., 18, 396 Hamilton, 1998, Dispersion, 151 Vanhille, 2013, Numerical simulations of three-dimensional nonlinear acoustic waves in bubbly liquids, Ultrason. Sonochem., 20, 963, 10.1016/j.ultsonch.2012.11.009 Blackstock, 2000, 386 Magnaudet, 1998, The viscous drag force on a spherical bubble with a time-dependent radius, Phys. Fluids, 10, 550, 10.1063/1.869582