Hostname: page-component-6bb9c88b65-lm65w Total loading time: 0.006 Render date: 2025-07-22T06:34:15.309Z Has data issue: false hasContentIssue false
  • English
  • Français

Vortex modes in acoustofluidic cylindrical resonators

Published online by Cambridge University Press:  17 July 2025

Alisson da Silva Marques  and
Glauber Tomaz da Silva Open the ORCID record for Glauber Tomaz da Silva [Opens in a new window]
Alisson da Silva Marques
Affiliation:
Group of Physical Acoustics & Microfluidics, Institute of Physics, Federal University of Alagoas, Maceió 57072-970, Brazil
Glauber Tomaz da Silva*
Affiliation:
Group of Physical Acoustics & Microfluidics, Institute of Physics, Federal University of Alagoas, Maceió 57072-970, Brazil
*
Corresponding author: Glauber Tomaz da Silva, gtomaz@fis.ufal.br
Get access Rights & Permissions [Opens in a new window]

Abstract

This paper presents a theoretical investigation of vortex modes in acoustofluidic cylindrical resonators with rigid boundaries and viscous fluids. By solving the Helmholtz equation for linear pressure, incorporating boundary conditions that account for no-slip surfaces and vortex and non-vortex excitation at the base, we analyse both single- and dual-eigenfunction modes near system resonance. The results demonstrate that single-vortex modes generate spin angular momentum exclusively along the axial direction, while dual modes introduce a transverse spin component due to the nonlinear interaction between axial and transverse ultrasonic waves, even in the absence of vortex excitation. We find that nonlinear acoustic fields, including energy density, radiation force potential and spin, scale with the square of the shear wave number, defined as the ratio of the cavity radius to the thickness of the viscous boundary layer. Theoretical predictions align closely with finite element simulations based on a model for an acoustofluidic cavity with adiabatic and rigid walls. These findings hold particular significance for acoustofluidic systems, offering potential applications in the precise control of cells and microparticles.

JFM classification

Micro-/Nano-fluid dynamics: Microfluidics Vortex Flows: Vortex dynamics Acoustics: Acoustics

Information

Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 1015 , 25 July 2025 , A34
Check for updates
Copyright
© The Author(s), 2025. Published by Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Article purchase

Temporarily unavailable

References

Baasch, T., Pavlic, A. & Dual, J. 2019 Acoustic radiation force acting on a heavy particle in a standing wave can be dominated by the acoustic microstreaming. Phys. Rev. E 100 (6), 061102.10.1103/PhysRevE.100.061102CrossRefGoogle Scholar
Baasch, T., Qiu, W. & Laurell, T. 2024 Whole-channel acoustic energy and acoustophoretic efficiency frequency spectrum by the in-flow focusing method. Phys. Rev. Appl. 22 (4), 044049.10.1103/PhysRevApplied.22.044049CrossRefGoogle Scholar
Bach, J.S. & Bruus, H. 2018 Theory of pressure acoustics with viscous boundary layers and streaming in curved elastic cavities. J. Acoust. Soc. Am. 144 (2), 766–784.10.1121/1.5049579CrossRefGoogle ScholarPubMed
Balk, A.L., Mair, L.O., Mathai, P.P., Patrone, P.N., Wang, W., Ahmed, S., Mallouk, T.E., Liddle, J.A. & Stavis, S.M. 2014 Kilohertz rotation of nanorods propelled by ultrasound, traced by microvortex advection of nanoparticles. ACS Nano 8 (8), 8300–8309.10.1021/nn502753xCrossRefGoogle ScholarPubMed
Barmatz, M. & Collas, P. 1985 Acoustic radiation potential on a sphere in plane, cylindrical, and spherical standing wave fields. J. Acoust. Soc. Am. 77 (3), 928–945.10.1121/1.392061CrossRefGoogle Scholar
Barnkob, R., Augustsson, P., Laurell, T. & Bruus, H. 2012 Acoustic radiation- and streaming-induced microparticle velocities determined by microparticle image velocimetry in an ultrasound symmetry plane. Phys. Rev. E 86 (5), 056307.10.1103/PhysRevE.86.056307CrossRefGoogle Scholar
Baudoin, M. & Thomas, J.-L. 2019 Acoustic tweezers for particle and fluid micromanipulation. Annu. Rev. Fluid Mech. 52 (1), 205–234.CrossRefGoogle Scholar
Berggren, M., Bernland, A. & Noreland, D. 2018 Acoustic boundary layers as boundary conditions. J. Comput. Phys. 371, 633–650.10.1016/j.jcp.2018.06.005CrossRefGoogle Scholar
Bliokh, K.Y. & Nori, F. 2019 Spin and orbital angular momenta of acoustic beams. Phys. Rev. B 99 (17), 174310.10.1103/PhysRevB.99.174310CrossRefGoogle Scholar
Coakley, W.T. 1997 Ultrasonic separations in analytical biotechnology. Trends Biotechnol. 15 (12), 506–511.10.1016/S0167-7799(97)01122-0CrossRefGoogle ScholarPubMed
Doinikov, A.A. 2003 Acoustic radiation forces: classical theory and recent advances. In Recent Research Developments in Acoustics, chap. 3, pp. 39–67. Transworld Research Network.Google Scholar
Fuchsluger, A., Pastina, A., Ecker, R., Mitteramskogler, T., Voglhuber-Brunnmaier, T., Andrianov, N., Cselyuszka, N. & Jakoby, B. 2024 Acoustofluidic particle trapping in a structured microchannel using lateral transducer modes. IEEE Sensors J. 24 (24), 40274–40285.10.1109/JSEN.2024.3443418CrossRefGoogle Scholar
Goddard, G. & Kaduchak, G. 2005 Ultrasonic particle concentration in a line-driven cylindrical tube. J. Acoust. Soc. Am. 117 (6), 3440–3447.10.1121/1.1904405CrossRefGoogle Scholar
Gong, Z., Marston, P.L. & Li, W. 2019 Reversals of acoustic radiation torque in bessel beams using theoretical and numerical implementations in three dimensions. Phys. Rev. Appl. 11 (6), 064022.10.1103/PhysRevApplied.11.064022CrossRefGoogle Scholar
Gor’kov, L.P. 1962 On the forces acting on a small particle in an acoustic field in an ideal fluid. Sov. Phys.-Dokl. 6 (9), 773–775.Google Scholar
Gralinski, I., Raymond, S., Alan, T. & Neild, A. 2014 Continuous flow ultrasonic particle trapping in a glass capillary. J. Appl. Phys. 115 (5), 054505.10.1063/1.4863645CrossRefGoogle Scholar
Gutiérrez-Ramos, S., Hoyos, M. & Ruiz-Suárez, J.C. 2018 Induced clustering of Escherichia coli by acoustic fields. Sci. Rep. 8 (1), 4668.10.1038/s41598-018-22960-zCrossRefGoogle ScholarPubMed
Hahn, P. & Dual, J. 2015 A numerically efficient damping model for acoustic resonances in microfluidic cavities. Phys. Fluids 27 (6), 062005.10.1063/1.4922986CrossRefGoogle Scholar
Hahn, P., Leibacher, I., Baasch, T. & Dual, J. 2015 Numerical simulation of acoustofluidic manipulation by radiation forces and acoustic streaming for complex particles. Lab Chip 15 (22), 4302–4313.10.1039/C5LC00866BCrossRefGoogle ScholarPubMed
Hefner, B.T. & Marston, P.L. 1999 An acoustical helicoidal wave transducer with applications for the alignment of ultrasonic and underwater systems. J. Acoust. Soc. Am. 106 (6), 3313–3316.10.1121/1.428184CrossRefGoogle Scholar
Holmes, M.J., Parker, N.G. & Povey, M.J.W. 2011 Temperature dependence of bulk viscosity in water using acoustic spectroscopy. J. Phys.: Conf. Ser. 269, 012011.Google Scholar
Kundt, A. 1866 Ueber eine neue art akustischer staubfiguren und über die anwendung derselben zur bestimmung der schallgeschwindigkeit in festen körpern und gasen. Annalen der Physik 203, 497–523.10.1002/andp.18662030402CrossRefGoogle Scholar
Lenshof, A., Evander, M., Laurell, T. & Nilsson, J. 2012 Acoustofluidics 5: building microfluidic acoustic resonators. Lab Chip 12 (4), 684–695.10.1039/c1lc20996eCrossRefGoogle ScholarPubMed
Leão-Neto, J.P., Hoyos, M., Aider, J.-L. & Silva, G.T. 2021 Acoustic radiation force and torque on spheroidal particles in an ideal cylindrical chambera). J. Acoust. Soc. Am. 149 (1), 285–295.10.1121/10.0003046CrossRefGoogle Scholar
Lima, E.B., Leão-Neto, J.P., Marques, A.S., Silva, G.C., Lopes, J.H. & Silva, G.T. 2020 Nonlinear interaction of acoustic waves with a spheroidal particle: radiation force and torque effects. Phys. Rev. Applied 13 (6), 064048.10.1103/PhysRevApplied.13.064048CrossRefGoogle Scholar
Lopes, J.H., Lima, E.B., Leão Neto, J.P. & Silva, G.T. 2020 Acoustic spin transfer to a subwavelength spheroidal particle. Phys. Rev. E 101 (4), 043102.10.1103/PhysRevE.101.043102CrossRefGoogle ScholarPubMed
Maidanik, G. 1958 Torques due to acoustical radiation pressure. J. Acoust. Soc. Am. 30 (7), 620–623.10.1121/1.1909714CrossRefGoogle Scholar
Morse, P. 1948 Vibration and Sound. 2nd edn. McGraw-Hill.Google Scholar
Pavlic, A. & Dual, J. 2021 On the streaming in a microfluidic kundt’s tube. J. Fluid Mech. 911, A28.10.1017/jfm.2020.1046CrossRefGoogle Scholar
Qiu, W. 2024 High-performance and environmentally-friendly bulk-wave-acoustofluidic devices driven by lead-free piezoelectric materials. Small 21 (10), 2407453.10.1002/smll.202407453CrossRefGoogle ScholarPubMed
Qiu, W., Baasch, T. & Laurell, T. 2022 Enhancement of acoustic energy density in bulk-wave-acoustophoresis devices using side actuation. Phys. Rev. Appl. 17 (4), 044043.10.1103/PhysRevApplied.17.044043CrossRefGoogle Scholar
Rayleigh, J.W.S. 1945 Theory of Sound. vol. 2, 2nd edn. Dover Publications.Google Scholar
Rednikov, A.Y. & Sadhal, S.S. 2011 Acoustic/steady streaming from a motionless boundary and related phenomena: generalized treatment of the inner streaming and examples. J. Fluid. Mech. 667, 426–462.CrossRefGoogle Scholar
Rocha, U., Silva, G.C., Sales, M.V.S., D’Amato, F.O.S., Leite, A.C.R. & Silva, G.T. 2023 Advancing Raman spectroscopy of erythrocytes with 3D-printed acoustofluidic devices. Appl. Phys. Lett. 123 (3), 034105.10.1063/5.0145565CrossRefGoogle Scholar
Santos, H.D.A., 2021 3D-printed acoustofluidic devices for Raman spectroscopy of cells. Adv. Eng. Mater. 23 (10), 2100552.10.1002/adem.202100552CrossRefGoogle Scholar
Silva, G.T. 2014 Acoustic radiation force and torque on an absorbing compressible particle in an inviscid fluid. J. Acoust. Soc. Am. 136 (5), 2405–2413.10.1121/1.4895691CrossRefGoogle Scholar
Silva, G.T., Lobo, T.P. & Mitri, F.G. 2012 Radiation torque produced by an arbitrary acoustic wave. Europhys. Lett. 97 (5), 54003.10.1209/0295-5075/97/54003CrossRefGoogle Scholar
Spengler, J.F., Jekel, M., Christensen, K.T., Adrian, R.J., Hawkes, J.J. & Coakley, W.T. 2000 Observation of yeast cell movement and aggregation in a small-scale MHz-ultrasonic standing wave field. Bioseparation 9 (6), 329–341.10.1023/A:1011113826753CrossRefGoogle Scholar
Tijdeman, H. 1975 On the propagation of sound waves in cylindrical tubes. J. Sound Vib. 39 (1), 1–33.10.1016/S0022-460X(75)80206-9CrossRefGoogle Scholar
Toftul, I.D., Bliokh, K.Y., Petrov, M.I. & Nori, F. 2019 Acoustic radiation force and torque on small particles as measures of the canonical momentum and spin densities. Phys. Rev. Lett. 123 (18), 183901.10.1103/PhysRevLett.123.183901CrossRefGoogle ScholarPubMed
Tran-Huu-Hue, L.P., Levassort, F., Felix, N., Damjanovic, D., Wolny, W. & Lethiecq, M. 2000 Comparison of several methods to characterise the high frequency behaviour of piezoelectric ceramics for transducer applications. Ultrasonics 38 (1-8), 219–223.10.1016/S0041-624X(99)00059-1CrossRefGoogle ScholarPubMed
Wang, W., Castro, L.A., Hoyos, M. & Mallouk, T.E. 2012 Autonomous motion of metallic microrods propelled by ultrasound. ACS Nano 67 (7), 6122–6132.10.1021/nn301312zCrossRefGoogle Scholar
Xu, D., Cai, F., Chen, M., Li, F., Wang, C., Meng, L., Xu, D., Wang, W., Wu, J. & Zheng, H. 2019 Acoustic manipulation of particles in a cylindrical cavity: theoretical and experimental study on the effects of boundary conditions. Ultrasonics 93, 18–25.10.1016/j.ultras.2018.10.003CrossRefGoogle Scholar
Zhang, L. 2018 Reversals of orbital angular momentum transfer and radiation torque. Phys. Rev. Appl. 10 (3), 034039.10.1103/PhysRevApplied.10.034039CrossRefGoogle Scholar
Zhang, L. & Marston, P.L. 2011 a Acoustic radiation torque and the conservation of angular momentum (L). J. Acoust. Soc. Am. 129 (4), 1679–1680.10.1121/1.3560916CrossRefGoogle ScholarPubMed
Zhang, L. & Marston, P.L. 2011 b Angular momentum flux of nonparaxial acoustic vortex beams and torques on axisymmetric objects. Phys. Rev. E 84 (6), 065601.10.1103/PhysRevE.84.065601CrossRefGoogle ScholarPubMed
Zhang, L. & Marston, P.L. 2011 c Geometrical interpretation of negative radiation forces of acoustical Bessel beams on spheres. Phys. Rev. E 84 (3), 035601.10.1103/PhysRevE.84.035601CrossRefGoogle ScholarPubMed
Zhang, L. & Marston, P.L. 2014 Acoustic radiation torque on small objects in viscous fluids and connection with viscous dissipation. J. Acoust. Soc. Am. 136 (6), 2917–2921.10.1121/1.4900441CrossRefGoogle ScholarPubMed
Supplementary material: File

Marques and Tomaz da Silva supplementary material

Marques and Tomaz da Silva supplementary material
Download Marques and Tomaz da Silva supplementary material(File)
File 934.2 KB