Abstract
Acoustic streaming created by sharp-edged structures in micromixers can achieve a homogeneous and quick mixing. This study is performed numerically on the mixing performance of an acoustic sharp-edge-based micromixer using the convection–diffusion equation and the generalized Lagrangian mean theory. The perturbation theory is employed to solve the zeroth-, first-, and second-order equations. The impact of parameters such as displacement amplitude, background flow velocity, channel width, frequency, and sharp edge characteristics (height, angle, number, distance, asymmetry, and shape) on the mixing performance is evaluated to obtain the optimal model. It is demonstrated that the mixing performance is improved by increasing driving frequency, displacement amplitude, and sharp edge height. The mixing efficiency is enhanced by decreasing background flow velocity, tip angle, and channel width.
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References
Bahrami D, Ahmadi Nadooshan A, Bayareh M (2020) Numerical study on the effect of planar normal and halbach magnet arrays on micromixing. Int J Chem React Eng 18:20200080. https://doi.org/10.1515/ijcre-2020-0080
Bayareh M (2020) Artificial diffusion in the simulation of micromixers: a review. Proc Inst Mech Eng C J Mech Eng Sci. https://doi.org/10.1177/0954406220982028
Bayareh M, Nazemi Ashani M, Usefian A (2020) Active and passive micromixers: a comprehensive review. Chem Eng Process 147:107771. https://doi.org/10.1016/j.cep.2019.107771
Buhler O (2009) Waves and mean flows, 2nd edn. Cambridge Monographs on Mechanics, Cambridge
Chono K, Shimizu N, Matsu Y, Kondoh J, Shiokawa S (2004) Development of novel atomization system based on SAW streaming. Jpn J Appl Phys 43:2987–2991. https://doi.org/10.1143/JJAP.43.2987
DeMello AJ (2006) Control and detection of chemical reactions in microfluidic systems. Nature 442:394–402. https://doi.org/10.1038/nature05062
Doinikov AA, Gerlt MS, Pavlic A, Dual J (2020a) Acoustic streaming produced by sharp-edge structures in microfluidic devices. Microfluid Nanofluid 24:32. https://doi.org/10.1007/s10404-020-02335-5
Doinikov AA, Gerlt MS, Pavlic A, Dual J (2020b) Acoustic radiation forces produced by sharp-edge structures in microfluidic systems. Phys Rev Lett 124:154501. https://doi.org/10.1103/PhysRevLett.124.154501
Eckart C (1948) Vortices and streams caused by sound waves. Phys Rev 73:68–76. https://doi.org/10.1103/PhysRev.73.68
Faraday M (1831) XVII. On a peculiar class of acoustical figures; and on certain forms assumed by groups of particles upon vibrating elastic surfaces. Philos Trans R Soc Lond, B, Biol Sci 121:299–340. https://doi.org/10.1098/rstl.1831.0018
Friend J, Yeo LY (2011) Microscale acoustofluidics: Microfluidics driven via acoustics and ultrasonics. Rev Mod Phys 83:647–704. https://doi.org/10.1103/RevModPhys.83.647
Ghorbani Kharaji Z, Bayareh M, Kalantar V (2021) A review on acoustic field-driven micromixers. Int J Chem React Eng 19:553–569. https://doi.org/10.1515/ijcre-2020-0188
Hamilton MF, Ilinskii YA, Zabolotskaya E (2002) Acoustic streaming generated by standing waves in two-dimensional channels of arbitrary width. J Acoust Soc Am 113:153–160. https://doi.org/10.1121/1.1528928
Hsieh SS, Huang YC (2008) Passive mixing in micro-channels with geometric variations through µPIV and µLIF measurements. J Micromech Microeng 18:065017. https://doi.org/10.1088/0960-1317/18/6/065017
Huang P-H, Xie Y, Ahmed D, Rufo J, Nama N, Chen Y, Chan CY, Huang TJ (2013a) An acoustofluidic micromixer based on oscillating sidewall sharp-edges. Lab Chip 13(19):3847. https://doi.org/10.1039/c3lc50568e
Huang PH, Xie Y, Ahmed D, Rufo J, Nama N, Chen Y, Chan CY, Huang TJ (2013b) An acoustofluidic micromixer based on oscillating sidewall sharp-edges. Lab Chip 13:3847–3852. https://doi.org/10.1039/C3LC50568E
Huang P-H, Nama N, Mao Z, Li P, Rufo J, Chen Y, Xie Y, Wei C-H, Wang L, Huang TJ (2014) A reliable and programmable acoustofluidic pump powered by oscillating sharp-edge structures. Lab Chip 14(22):4319–4323. https://doi.org/10.1039/c4lc00806e
Huang PH, Zhao S, Bachman H, Nama N, Li Z, Chen C, Yang S, Wu M, Zhang SP, Huang TJ (2019) Acoustofluidic synthesis of particulate nanomaterials. Adv Sci 6:1900913. https://doi.org/10.1002/advs.201900913
Legay M, Simony B, Boldo P, Gondrexon N, Le Person S, Bontemps A (2012) Improvement of heat transfer by means of ultrasound: application to a double-tube heat exchanger. Ultrason Sonochem 19:1194–1200. https://doi.org/10.1016/j.ultsonch.2012.04.001
Muller PB, Barnkob R, Jensen MJH, Bruus H (2012) A numerical study of microparticle acoustophoresis driven by acoustic radiation forces and streaming-induced drag forces. Lab Chip 12:4617–4627. https://doi.org/10.1039/C2LC40612H
Murochi N, Sugimoto M, Matui Y, Kondoh J (2007) Deposition of thin film using a surface acoustic wave device. Jpn J Appl Phys 46:4754–4759. https://doi.org/10.1143/JJAP.46.4754
Nam J, Jang WS, Lim CS (2018) Micromixing using a conductive liquid-based focused surface acoustic wave (CL-FSAW). Sens Actuators B Chem 258:991–997. https://doi.org/10.1016/j.snb.2017.11.188
Nama N, Huang P-H, Huang TJ, Costanzo F (2014) Investigation of acoustic streaming patterns around oscillating sharp edges. Lab Chip 14(15):2824–2836. https://doi.org/10.1039/c4lc00191e
Nama N, Huang PH, Huang TJ, Costanzo F (2016) Investigation of micromixing by acoustically oscillated sharp-edges. Biomicrofluidics 10:024124. https://doi.org/10.1063/1.4946875
Nyborg WL (1998) Nonlinear acoustics. In: Blackstock DT (ed) Hamilton MF. Academic Press, San Diego, pp 207–231
Ovchinnikov M, Zhou J, Yalamanchili S (2014) Acoustic streaming of a sharp edge. J Acoust Soc Am 136:22. https://doi.org/10.1121/1.4881919
Qiu W, Karlsen JT, Bruus H, Augustsson P (2019) Experimental characterization of acoustic streaming in gradients of density and compressibility. Phys Rev Appl 11:024018. https://doi.org/10.1103/PhysRevApplied.11.024018
Rasouli MR, Tabrizian M (2019) An ultra-rapid acoustic micromixer for synthesis of organic nanoparticles. Lab Chip 19:3316–3325. https://doi.org/10.1039/C9LC00637K
Rayleigh L (1884) On the circulation of air observed in Kundt’s tubes, and on some allied acoustical problems. Philos Trans R Soc Lond 175:1–21
Rotter M, Kalameitsev AV, Govorov AO, Ruile W, Wixforth A (1999) Charge conveyance and nonlinear acoustoelectric phenomena for intense surface acoustic waves on a semiconductor quantum well. Phys Rev Lett 82:2171–2174. https://doi.org/10.1103/PhysRevLett.82.2171
Ruby R (2007) 11E–2 Review and comparison of bulk acoustic wave FBAR, SMR technology. IEEE Ultrasonics Symposium Proceedings 2007:1029–1040. https://doi.org/10.1109/ULTSYM.2007.262
Sadd MH (2009) Elasticity: theory, applications, and numerics, 2nd edn. Elsevier Academic Press Inc, Amsterdam
Sankaranarayanan SK, Cular S, Bhethanabotla VR, Joseph B (2008) Flow induced by acoustic streaming on surface-acoustic-wave devices and its application in biofouling removal: a computational study and comparisons to experiment. Phys Rev E 77:066308. https://doi.org/10.1103/PhysRevE.77.066308
Schlichting H, Gersten K (2017) Boundary-layer theory, 9th edn. Springer Nature, New York
Sritharan K, Strobl CJ, Schneider MF, Wixforth A (2006) Acoustic mixing at low Reynold’s numbers. Appl Phys Lett 88:054102. https://doi.org/10.1063/1.2171482
Strobl CJ, Guttenberg Z, Wixforth A (2004) Nano- and pico dispensing of fluids on planar substrates using SAW. IEEE Trans Ultrason Ferroelectr Freq Control 51:1432–1436. https://doi.org/10.1109/TUFFC.2004.1367483
Tian C, Liu W, Zhao R, Li T, Xu J, Chen SW, Wang J (2018) Acoustofluidics-based enzymatic constant determination by rapid and stable in situ mixing. Sens Actuators B Chem 272:494–501. https://doi.org/10.1016/j.snb.2018.05.149
Usefian A, Bayareh M (2019) Numerical and experimental study on mixing performance of a novel electro-osmotic micro-mixer. Meccanica 54:1149–1162. https://doi.org/10.1007/s11012-019-01018-y
Usefian A, Bayareh M (2020) Numerical and experimental investigation of an efficient convergent-divergent micromixer. Meccanica 55:1025–1035. https://doi.org/10.1007/s11012-020-01142-0
Usefian A, Bayareh M, Nadooshan AA (2019) Rapid mixing of Newtonian and non-Newtonian fluids in a three-dimensional micro-mixer using non-uniform magnetic field. J Heat Mass Trans Res 6:55–61
Valverde JM (2015) Pattern-formation under acoustic driving forces. Contemp Phys 56:338–358. https://doi.org/10.1080/00107514.2015.1008742
Vuillermet G, Gires PY, Casset F, Poulain C (2016) Chladni patterns in a liquid at microscale. Phys Rev Appl 116:184501. https://doi.org/10.1103/PhysRevLett.116.184501
Wixforth A, Strobl C, Gauer C, Toegl A, Sciba J, Guttenberg ZV (2004) Acoustic manipulation of small droplets. Anal Bioanal Chem 379:982–991. https://doi.org/10.1007/s00216-004-2693-z
Zhang C, Brunet P, Royon L, Guo X (2021) Mixing intensification using sound-driven micromixer with sharp edges. Chem Eng J 410:128252. https://doi.org/10.1016/j.cej.2020.128252
Zhang C, Guo X, Brunet P, Costalonga M, Royon L (2019) Acoustic streaming near a sharp structure and its mixing performance characterization. Microfluid Nanofluid 23:104. https://doi.org/10.1007/s10404-019-2271-5
Zhang C, Guo X, Brunet P, Royon L (2020a) The effect of sharp-edge acoustic streaming on mixing in a microchannel. Ann De Congrès SFT. https://doi.org/10.25855/SFT2020-041
Zhang C, Guo X, Royon L, Brunet P (2020b) Acoustic streaming generated by sharp edges: the coupled influences of liquid viscosity and acoustic frequency. Micromachines 11:607. https://doi.org/10.3390/mi11060607
Zhang C, Guo X, Royon L, Brunet P (2020) Unveiling of the mechanisms of acoustic streaming induced by sharp edges. Phys Rev E. https://doi.org/10.1103/physreve.102.04311
Zhao S, He W, Ma Z, Liu P, Huang PH, Bachman H, Wang L, Yang S, Tian Z, Wang Z, Gu Y, Xiea Z, Huang TJ (2019) On-chip stool liquefaction via acoustofluidics. Lab Chip 19:941–947. https://doi.org/10.1039/C8LC01310A
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Ghorbani Kharaji, Z., Kalantar, V. & Bayareh, M. Acoustic sharp-edge-based micromixer: a numerical study. Chem. Pap. 76, 1721–1738 (2022). https://doi.org/10.1007/s11696-021-01994-0
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DOI: https://doi.org/10.1007/s11696-021-01994-0