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Numerical Analysis of Droplet Motion over a Flat Plate Due to Surface Acoustic Waves

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Abstract

Micro-scale systems have gained considerable attention in recent years and a large amount of researches have been done in this field. In this study, the hydrodynamic interference of a droplet is comprehensively investigated under surface acoustic waves. This paper reveals the effects of some control parameters such as wave amplitude and wave frequency on the dynamical behavior of droplet. For these purposes, a two-dimensional multiple-relaxation-time color-gradient model lattice Boltzmann method is developed. This model is first validated by dynamical behaviors of a droplet subjected to shear flow. Moreover, displacement of a droplet affected by surface acoustic waves is comprehensively investigated. Our obtained simulations agree well with observations. According to our finding, the increase of frequency leads to the increment of required power to change the modes of the system from streaming to pumping or jetting states. Obtained results clearly show that hydrophobicity, reduction of viscosity, and increase of surface tension coefficient significantly influence on the flow control system and grow its sensitivity. Our results demonstrate that the minimum wave amplitude required to initiate pumping mode changes from 0.8 nm to about 1 nm when the frequency ranges are within 20 MHz to 200 MHz. The variations in jetting mode are also observed. Our findings clearly show that the minimum wave amplitude varies from about 2 nm to 4 nm when the frequency is changed from 20 MHz to 200 MHz. According to numerical analysis using lattice Boltzmann method, this work tried to capture the deformations of the fluid/fluid interface affected by surface acoustic waves and simulated the moving contact line in the high density ratio. These two main phenomena are recognized as significant parameter in our problem.

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References

  • Alghane, M., Chen, B.X., Fu, Y.Q., Li, Y., Luo, J.K., Walton: Experimental and Numerical Investigation of Acoustic Streaming Excited by Using a Surface Acoustic Wave Device on a 128 YX-LiNbO3 Substrate. J. Mic. Mech. Mic. Eng. 21(10), 1–11 (2011)

    Google Scholar 

  • Antil, H., Glowinski, R., Hoppe, R.H.W., Linsenmann, C., Pan, T.W., Wixforth, A.: Modeling, Simulation, and Optimization of Surface Acoustic Wave Driven Microfluidic Biochips. J. Comput. Math. 28(2), 1–22 (2009)

    MathSciNet  MATH  Google Scholar 

  • Ba, Y., Liu, H., Sun, J., Zheng, R.: Color-Gradient Lattice Boltzmann Model for Simulating Droplet Motion with Contact-Angle Hysteresis. Phys. Rev. E. 88(10), 1–13 (2013)

    Google Scholar 

  • Ba, Y., Liu, H., Li, Q., Kang, Q., Sun, J.: Multiple-Relaxation-Time Color-Gradient Lattice Boltzmann Model for Simulating Two-Phase Flows with High Density Ratio. Phys. Rev. E. 94(8), 1–15 (2016)

    MathSciNet  Google Scholar 

  • Beyssen, D., Le Brizoual, L., Elmazria, O., Alnot, P.: Microfluidic Device Based on Surface Acoustic Wave. Sensors Actuators B. 118(5), 380–385 (2006)

    Google Scholar 

  • Brunet, P., Baudoin, M., Bou Matar, O., Zoueshtiagh, F.: Droplets Displacement and Oscillation Induced by Ultrasonic Surface Acoustic Waves: A Quantitative Study. APS. 123(2), 1–9 (2010)

    Google Scholar 

  • Ding, X., Li, P., Lin, S., Stratton, Z.S., Nama, N., Guo, F., Slotcavage, D., Mao, X., Shi, J., Costanzo, F.: Surface Acoustic Wave Microfluidics. Lab Chip. 13(6), 3626–3649 (2013)

    Google Scholar 

  • Eral, H.B., Oh, J.M.: Contact angle hysteresis: a review of fundamentals and applications. Colloid Polym. Sci. 291(2), 247–260 (2013)

    Google Scholar 

  • Franke, T., Hoppe, R.H.W., Linsenmann, C., Zeleke, K.: Numerical Simulation of Surface Acoustic Wave Actuated Cell Sorting. Cent. Eur. J. Math. 11(4), 760–778 (2013)

    MathSciNet  MATH  Google Scholar 

  • Frommelt, T., Gogel, D., Kostur, M., Talkner, P., Hӓnggi, P., Wixforth, A.: Flow Patterns and Transport in Rayleigh Surface Acoustic Waves Streaming: Combined Finite Element Method and Raytracing Numerics Versus Experiments. Tran. Ult. Son. Con. 55(10), 2298–2305 (2008a)

    Google Scholar 

  • Frommelt, T., Kostur, M., Wenzel-Schӓfer, M., Talkner, P., Hӓnggi, P., Wixforth, A.: Microfluidic Mixing via Acoustically Driven Chaotic Advection. Phys. Rev. Lett. 100(1), 1–4 (2008b)

    Google Scholar 

  • Grunau, D., Chen, S., Eggert, K.: A Lattice Boltzmann Model for Multi-Phase Fluid Flows. Phys. Fluids. 43(4320), 1–15 (1993)

    MATH  Google Scholar 

  • Gubaidullin, A.A., Yakovenko, A.V.: Effects of Heat Exchange and Nonlinearity on Acoustic Streaming in a Vibrating Cylindrical Cavity. J. Acoust. Soc. Am. 137(6), 3281–3287 (2015)

    Google Scholar 

  • Gunstensen, A.K., Rothman, D.H., Zaleski, S., Zanetti, G.: Lattice Boltzmann Model of Immiscible Fluids. Phys. Rev. 43(8), 4320–4327 (1991)

    Google Scholar 

  • Guo, Y.J., Lv, H.B., Li, Y.F., He, X.L., Zhou, J., Luo, J.K., Zu, X.T., Walton, A.J., Fu, Y.Q.: High Frequency Microfluidic Performance of LiNbO3 and ZnO Surface Acoustic Wave Devices. J. Appl. Phys. 116(7), 1–8 (2014)

    Google Scholar 

  • Haydock, D., Yeomans, J.M.: Lattice Boltzmann Simulations of Attenuation-Driven Acoustic Streaming. J. Phys. A Math. Gen. 36(5), 5683–8694 (2003)

    MathSciNet  MATH  Google Scholar 

  • He, X., Luo, L.S.: Theory of the Lattice Boltzmann Method: from the Boltzmann Equation to the Lattice Boltzmann Equation. Phys. Rev. 56, 11 (1997)

    Google Scholar 

  • Huang, H., Huang, J.J., Lu, X.Y.: On Simulations of High-Density Ratio Flows Using Color-Gradient Multiphase Lattice Boltzmann Models. Int. J. Modern Phys. C. 24(4), 1–19 (2013)

    Google Scholar 

  • Huang, H., Sukop, M., and Lu, X: "Multiphase Lattice Boltzmann Methods". Wiley Blackwell, 1st Edition, (2015)

  • Jang, L.S., Chao, S.H., Holl, M.R., Meldrum, D.R.: Resonant Mode-hoping Micromixing. Sensors Actuators. 138(1), 179–186 (2007)

    Google Scholar 

  • Kawasaki, A., Onishi, J., Chen, Y., Ohashi, H.: A Lattice Boltzmann Model for Contact-Line Motions. Comput. Math. Appl. 55(8), 1492–1502 (2008)

    MathSciNet  MATH  Google Scholar 

  • Korshak BA, Mozhaev VG, Zyryanova AV: "Observation and interpretation of SAW-induced regular and chaotic dynamics of droplet shape". InIEEE Ultrasonics Symposium, 2005. 2005 Sep 18 (Vol. 2, pp. 1019–1022). IEEE

  • Kӧster, D.: Numerical Simulation of Acoustic Streaming on Surface Acoustic Wave-Driven Biochips. Soc. Ind. App. Math. 29(6), 2352–2380 (2007)

    MathSciNet  MATH  Google Scholar 

  • Lallemand, P., Luo, L.S.: Theory of the Lattice Boltzmann Method: Dispersion, Dissipation, Isotropy, Galilean Invariance, and Stability. Phys. Rev. 61, 11 (2000a)

    MathSciNet  Google Scholar 

  • Lallemand, P., Luo, L.S.: Theory of the lattice Boltzmann method: Dispersion, dissipation, isotropy, Galilean invariance, and stability. Phys. Rev. E. 61(6), 6546 (2000b)

    MathSciNet  Google Scholar 

  • Latva-Kokko, M., Rothman, D.H.: Diffusion Properties of Gradient-Based Lattice Boltzmann Models of Immiscible Fluids. Phys. Rev. 71(5), 1–7 (2005)

    Google Scholar 

  • Latva-Kokko, M., Rothman, D.H.: Scaling of dynamic contact angles in a lattice-Boltzmann model. Phys. Rev. Lett. 98(25), 254503 (2007)

    Google Scholar 

  • Leclaire, S., Pellerin, N., Reggio, M., Trepanier, J.Y.: A Multiphase Lattice Boltzmann Method for Simulating Immiscible Liquid-Liquid Interface Dynamics. Appl. Math. Model. 40(13), 6376–6394 (2016)

    MathSciNet  MATH  Google Scholar 

  • Leclaire, S., Parmigiani, A., Chopard, B., Latt, J.: Three-Dimensional Lattice Boltzmann Method Benchmarks Between Color-Gradient and Pseudo-Potential Immiscible Multi-Component Models. Int. J. Modern Phys. C. 28(6), 1–30 (2017a)

    Google Scholar 

  • Leclaire, S., Parmigiani, A., Chopard, B., Latt, J.: Generalized Three-Dimensional Lattice Boltzmann Color-Gradient Method for Immiscible Two-Phase Pore-Scale Imbibition and Drainage in Porous Media. Phys. Rev. E. 95(3), 1–31 (2017b)

    Google Scholar 

  • Lighthill, S.J.: Acoustic Streaming. J. Sound Vib. 61(3), 391–418 (1978)

    MATH  Google Scholar 

  • Liu, H., Ju, Y., Wang, N., Xi, G.: Lattice Boltzmann Modeling of Contact Angle and Its Hysteresis in Two-Phase Flow with Large Viscosity Difference. Phys. Rev. E. 92(9), 1–9 (2015)

    MathSciNet  Google Scholar 

  • Luong, T.D., Nguyen, N.T.: Surface Acoustic Wave Driven-A Review. Micro. Nano Sys. 2(3), 1–9 (2010)

    MathSciNet  Google Scholar 

  • Marmur, A., Della Volpe, C., Siboni, S., Amirfazli, A., Drelich, J.W.: Contact angles and wettability: Towards common and accurate terminology. Surf. Innov. 5(1), 3–8 (2017)

    Google Scholar 

  • Mohamad, A.A.: Lattice Boltzmann Method, 1st edn. Springer, London (2011)

    MATH  Google Scholar 

  • Montessori, A., Lauricella, M., La Rocca, M., Succi, S., Stolovicki, E., Ziblat, R., Weitz, D.: Regularized Lattice Boltzmann Multicomponent Models for Low Capillary and Reynolds Microfluidics Flows. Comput. Fluids. 167(15), 33–39 (2018)

    MathSciNet  MATH  Google Scholar 

  • Moudjed, B., Botton, V., Henry, D., Millet, S., Garandet, J.P., Hadid, H.B.: Near-Field Acoustic Streamin Jet. Physiol. Rev. 91(3), 1–10 (2015)

    Google Scholar 

  • Muller, P.B.: “Acoustofluidics in microsystems: investigation of acoustic streaming”, Master Thesis, DTU Nanotech, Denmark, (2012)

  • Nguyen, N.T., Wereley, S.T.: Fundamentals and Applications of Microfluidics, 2nd edn. Artech House, Boston (2006)

    MATH  Google Scholar 

  • Nyborg, W.L.: Acoustic Streaming due to Attenuated Plane Waves. J. A. S. A. 25(1), 68–75 (1953)

    MathSciNet  Google Scholar 

  • Ovchinnikov, M., Zhou, J., Yalamanchili, S.: Acoustic Streaming of a Sharp Edge. J. Acoust. Soc. Am. 136(1), 22–29 (2014)

    Google Scholar 

  • Pedersen, P.S.: “Acoustic Forces on Particles and Liquids in Microfluidic Systems”, Master Thesis, DTU Nanotech, Denmark, (2008)

  • Petersson, F., Nilsson, A., Holm, C., Jonsson, H., Laurell, T.: Continuous Separation of Lipid Particles from Erythrocytes by Means of Laminar Flow and Acoustic Standing Wave Forces. Lab Chip. 5(1), 20–22 (2005)

    Google Scholar 

  • Reis, T., Phillips, T.N.: Lattice Boltzmann Model for Simulating Immiscible Two-Phase Flows. J. Phys. A: Math. Theory. 40(3), 4033–4053 (2007)

    MathSciNet  MATH  Google Scholar 

  • Riaud, A., Baudoin, M., Matar, O.B., Thomas, J.L., Brunet, P.: On the influence of viscosity and caustics on acoustic streaming in sessile droplets: an experimental and a numerical study with a cost-effective method. J. Fluid Mech. 821, 384–420 (2017)

    MathSciNet  MATH  Google Scholar 

  • Rothman, D.H., Keller, J.M.: Immiscible Cellular-Automaton Fluids. J. Stat. Phys. 52(3), 1119–1127 (1988)

    MathSciNet  MATH  Google Scholar 

  • Sajjadi, B., Abdul Raman, A.A., Ibrahim, S.: Influence of Ultrasound Power on Acoustic Streaming and Micro-Bubbles Formations in a Low Frequency Sono-Reactor: Mathematical and 3D Computational Simulation. Ultransonics Sonochem. 24(11), 193–203 (2015)

    Google Scholar 

  • Sankaranarayanan, S.K.R.S., Cular, S., Bhethanabotla, V.R., Joseph, B.: Flow Induced by Acoustic Streaming on Surface-Acoustic-Wave Devices and Its Application in Biofouling Removal: A Computational Study and Comparisons to Experiment. Physiol. Rev. 77(6), 1–19 (2008)

    Google Scholar 

  • Satoh, A.: Introduction to Practice of Molecular Simulation, 1st edn. Elsevier, London (2011)

    Google Scholar 

  • Shan, X.: Analysis and Reduction of the Spurious Current in a Class of Multiphase Lattice Boltzmann Models. Phys. Rev. 73(4), 1–4 (2006)

    Google Scholar 

  • Shan, X., Chen, H.: Simulation of Non-Ideal Gases and Liquid-Gas Phase Transitions by Lattice Boltzmann Equation. Phys. Rev. 49(4), 1–24 (1994)

    Google Scholar 

  • Sheikholeslam Noori, S.M., Taeibi, M., Shams Taleghani, S.A.: Multiple Relaxation Time Color Gradient Lattice Boltzmann Model for Simulating Contact Angle in Two-Phase Flows with High Density Ratio. Euro. Phys. J. Plus. 134(399), 1–15 (2019)

    Google Scholar 

  • Shilton, R.J., Travagliati, M., Beltram, F., Cecchini, M.: Nanoliter-Droplet Acoustic Streaming via Ultra High Frequency Surface Acoustic Waves. Adv. Mater. 26(1), 4941–4946 (2014)

    Google Scholar 

  • Shiokawa, S., Matsui, Y., and Ueda, T.: “Liquid Streaming and Droplet Formation Caused by Leaky Rayleigh Waves”. Ultrasonic Symposium, Johoku, Hamamatsu, 432, Japan, (1989)

  • Snoeijer JH, Andreotti B: "Moving contact lines: scales, regimes, and dynamical transitions". Annual review of fluid mechanics. 45, (2013)

  • Sritharan, K., Strobl, C.J., Schneider, M.F., Wixforth, A.: Acoustic Mixing at Low Reynold’s Numbers. Appl. Phys. Lett. 88(2), 1–3 (2006)

    Google Scholar 

  • Sukop, M.C., Throne, D.T.: Lattice Boltzmann Modeling, 1st edn. Springer, Florida (2006)

    Google Scholar 

  • Swift, M.R., Orlandini, E., Osborn, W.R., Yeomans, J.M.: Lattice Boltzmann Simulations of Liquid-Gas and Binary Fluid Systems. Phys. Rev. 54(5), 5041–5052 (1996)

    Google Scholar 

  • Taeibi-Rahni, M., Karbaschi, M., Miller, R.: Computational Methods for Complex Liquid-Fluid Interfaces. CRC Press, U.S.A. (2015)

    Google Scholar 

  • Tan, M.K., Yeo, L.Y., Friend, J.R.: Rapid Fluid Flow and Mixing Induced in Microchannels Using Surface Acoustic Waves. EPL. 87(9), 1–6 (2009a)

    Google Scholar 

  • Tan, M.K., Friend, J.R., Yeo, L.Y.: Interfacial jetting phenomena induced by focused surface vibrations. Phys. Rev. Lett. 103(2), 024501 (2009b)

    Google Scholar 

  • Tang, Q., Hu, J.: Diversity of Acoustic Streaming in a Rectangular Acoustofluidic Field. Ultrasonics. 58(12), 27–34 (2015)

    Google Scholar 

  • Tsutahara, M.: The Finite-Difference Lattice Boltzmann Method and its Application in Computational Aero-Acoustics. Fluid Dyn. Res. 44(4), 1–19 (2012)

    MathSciNet  MATH  Google Scholar 

  • Uemura, Y., Sasaki, K., Minami, K., Sato, T., Choi, P.K., Takeuchi, S.: Observation of Cavitation Bubbles and Acoustic Streaming in High Intensity Ultrasound Fields. Jpn. J. Appl. Phys. 54(6), 1–7 (2015)

    Google Scholar 

  • Valverde, J.M.: Convection and Fluidization in Oscillatory Granular Flows: The Role of Acoustic Streaming. Eur. Phy. J. 38(66), 1–13 (2015)

    Google Scholar 

  • Vanneste, J., Buhler, O.: Streaming by Leaky Surface Acoustic Waves. Roy. Soc. 467(2130), 1–26 (2011)

    MathSciNet  MATH  Google Scholar 

  • Westervelt, P.J.: The Theory of Steady Rotational Flow Generated by a Sound Field. J. A. S. A. 25(1), 60–67 (1953)

    MathSciNet  Google Scholar 

  • Wixforth, A.: Acoustically Driven Planar Microfluidics. Superlattice. Microst. 33(5–6), 389–396 (2004)

    Google Scholar 

  • Wixforth, A., Strobl, C., Gauer, C., Toegl, A., Scriba, J., Guttenberg, Z.V.: Acoustic Manipulation of Small Droplets. Anal. Bioanal. Chem. 379(7), 982–991 (2004)

    Google Scholar 

  • Wu, L., Tsutahara, M., Kim, L.S., Ha, M.Y.: Three-Dimensional Lattice Boltzmann Simulations of Droplet Formation in a Cross-Junction Microchannel. Int. J. Multiphase Flow. 34(3), 852–864 (2008)

    MATH  Google Scholar 

  • Yeo, L.Y., Friend, J.R.: Surface Acoustic Wave Microfluidics. Annu. Rev. Fluid Mech. 46(9), 379–406 (2014)

    MathSciNet  MATH  Google Scholar 

  • Yu, H., Kim, E.S.: “Noninvasive Acoustic-wave Microfluidic Driver”, 15th IEEE International Conference on Micro Electro Mechanical Systems, Los Angeles, USA. (2002)

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Authors and Affiliations

  1. Department of Aerospace Engineering, Sharif University of Technology, Tehran, Iran

    S. M. Sheikholeslam Noori & M. Taeibi Rahni

  2. Aerospace Research Institute Ministry of Science, Research and Technology, Tehran, Iran

    M. Taeibi Rahni & S. A. Shams Taleghani

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  1. S. M. Sheikholeslam Noori
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Sheikholeslam Noori, S.M., Taeibi Rahni, M. & Shams Taleghani, S.A. Numerical Analysis of Droplet Motion over a Flat Plate Due to Surface Acoustic Waves. Microgravity Sci. Technol. 32, 647–660 (2020). https://doi.org/10.1007/s12217-020-09784-1

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