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Li Yikai, Zhu Ming, Xi Ru, Wang Dongfang, Yang Ziming, Wu Kun. Analysis of the surface wave instability of a semi-spherical droplet under vertical excitation. Chinese Journal of Theoretical and Applied Mechanics, 2023, 55(9): 1867-1879. DOI: 10.6052/0459-1879-23-238
Citation: Li Yikai, Zhu Ming, Xi Ru, Wang Dongfang, Yang Ziming, Wu Kun. Analysis of the surface wave instability of a semi-spherical droplet under vertical excitation. Chinese Journal of Theoretical and Applied Mechanics, 2023, 55(9): 1867-1879. DOI: 10.6052/0459-1879-23-238

ANALYSIS OF THE SURFACE WAVE INSTABILITY OF A SEMI-SPHERICAL DROPLET UNDER VERTICAL EXCITATION

  • Received Date: June 11, 2023
  • Accepted Date: August 01, 2023
  • Available Online: August 02, 2023
  • Surface destabilization of droplets under external excitation has always been a matter of interest in the field of fluid dynamics. Waveforms with different morphologies or secondary droplets would appear in the surface under different excitation conditions. In this paper, the analysis of the dynamic characteristics and generation mechanism of latitudinal and longitudinal waves was conducted. Firstly, an experimental system of droplet oscillation with controllable excitation amplitude and frequency was established. The experimental results show that different forcing amplitudes lead to different droplet interface instability modes. The longitudinal waves are generated only when the amplitude is large enough, and its evolution frequency is half of the driving frequency, while the latitudinal waves are always present whose frequency equals to the driving frequency. A change in driving frequency causes a shift in destabilization modes, and an increase in driving frequency increases the number of surface wave modes and decreases the wavelength of the surface waves. When the driving frequency exceeds a certain threshold, the waveform will shift from a latitudinal wave mode only to a latitudinal wave superimposed on a longitudinal wave mode. Meanwhile, three-dimensional numerical simulations were conducted. By studying the velocity and pressure fields of droplets, combined with the phase relationship between droplet vertex displacement and inertial force, the mechanism of droplet formation of latitudinal waves is elucidated: under the combined action of inertial force and surface tension, the droplet surface wave completes periodic energy conversion and transition. The surface wave characteristics dominated by the Faraday instability are analyzed comparatively for vertical versus radial acceleration direction. It is found that the geometrical characteristics of the droplet generate radial forces normal to the contact line, and when the vertical inertial force increases so that the radial force reaches a certain threshold, the droplet undergoes longitudinal instability, and the corresponding longitudinal wave frequency is half of the driving frequency.
  • [1]
    Samantha AM, Susmita D, Sami K, et al. Evaporative crystallization of spirals. Langmui, 2019, 35: 10484-10490
    [2]
    侯晓松, 刘晨星, 任爱玲等. 超声雾化/表面活性剂强化吸收耦合生物洗涤净化甲苯废气. 化工学报, 2022, 73(10): 4692-4706 (Hou Xiaosong, Liu Chenxing, Ren Ailing, et al. Study on purification of toluene waste gas by ultrasonic atomization/surfactants-enhanced absorption coupled with biological scrubbing. CIESC Journal, 2022, 73(10): 4692-4706 (in Chinese)

    Hou Xiaosong, Liu Chenxing, Ren Ailing, Guo Bin, Guo Yuanming. Study on purification of toluene waste gas by ultrasonic atomization/surfactants-enhanced absorption coupled with biological scrubbing. CIESC Journal, 2022, 73(10): 4692-4706 (in Chinese))
    [3]
    Li J, Li X. Numerical study of the impact of contact line with hysteresis on the Faraday instability. Physics of Fluids, 2022, 34(7): 072108 doi: 10.1063/5.0101956
    [4]
    魏卓, 姚井淳, 石小鑫等. 低频振动对超疏水电热除冰方法的增益效果探究. 航空科学技术, 2022, 33(11): 70-75 (Wei Zhuo, Yao Jingchun, Shi Xiaoxin, et al. Study on gain effect of low frequency vibration on superhydrophobic electrothermal de-icing method. Aeronautical Science & Technology, 2022, 33(11): 70-75 (in Chinese)

    Wei Zhuo, Yao Jingchun, Shi Xiaoxin, Chen Zenggui, Tang Yalin, Lyu Xianglian, He Yang. Study on Gain Effect of Low Frequency Vibration on Superhydrophobic Electrothermal De-icing Method. Aeronautical Science & Technology. 2022, 33(11): 70-75. (in Chinese))
    [5]
    Awada A, Younes R, Ilinca A. Optimization of wind turbine performance by vibration control and deicing, Journal of Wind Engineering & Industrial Aerodynamics, 2022, 229: 105143
    [6]
    Shen L, Fang G, Wang S, et al. Numerical study of the secondary atomization characteristics and droplet distribution of pressure swirl atomizers. Fuel, 2022, 324: 124643
    [7]
    Binks D, Water W. Nonlinear pattern formation of Faraday waves. Physical Review Letters, 1997, 78: 4043-4046
    [8]
    James AJ, Smith MK, Glezer A, et al. Vibration-induced drop atomization and the numerical simulation of low-frequency single-droplet ejection. Journal of Fluid Mechanics, 2003, 476: 29-62
    [9]
    James A, Vukasinovic B, Smith M, et al. Vibration-induced drop atomization and bursting. Journal of Fluid Mechanics, 2003, 476: 1-28
    [10]
    Chang CT, Bostwick JB, Steen PH, et al. Substrate constraint modifies the Rayleigh spectrum of vibrating sessile drops. Physical Review E, 2013, 88 : 023015
    [11]
    Singla T, Verma DK, Tovar JF, et al. Dynamics of a vertically vibrating mercury drop. AIP Advances, 2019, 9: 045204
    [12]
    王凯宇, 庞祥龙, 李晓光等. 超疏水表面液滴的振动特性及其与液滴体积的关系. 物理学报, 2021, 70(7): 282-290 (Wang Kaiyu, Pang Xianglong, Li Xiaoguang, et al. Oscillation properties of water droplets on a superhydrophobic surface and their correlations with droplet volume. Acta Physica Sinica, 2021, 70(7): 282-290 (in Chinese)

    Wang KaiYu, Pang XiangLong, Li Xiao Guang. Oscillation properties of water droplets on a superhydrophobic surface and their correlations with droplet volume. ActaPhysica Sinica, 2021, 70(07): 282-290. (in Chinese))
    [13]
    Noblin X, Buguin A, Brochard-Wyart F, et al. Vibrated sessile drops: Transition between pinned and mobile contact line oscillations. The European Physical Journal E, 2004, 14: 395-404
    [14]
    Shao X, Wilson P, Saylor JR, et al. Surface wave pattern formation in a cylindrical container. Journal of Fluid Mechanics, 2021, 915: A19
    [15]
    Faraday M. On a peculiar class of acoustical figures; and on certain forms assumed by groups of particles upon vibrating elastic surfaces//Abstracts of the Papers Printed in the Philosophical Transactions of the Royal Society of London, 1837, 3: 49-51
    [16]
    Kumar K. Linear theory of Faraday instability in viscous liquids. Mathematical, Physical and Engineering Sciences, 1996, 452: 1113-1126 doi: 10.1098/rspa.1996.0056
    [17]
    Adou AE, Tuckerman LS. Faraday instability on a sphere: Floquet analysis. Journal of Fluid Mechanics, 2016, 805: 591-610
    [18]
    Bronfort A, Caps H. Faraday instability at foam-water interface. Physical Review E, 2012, 86: 066313
    [19]
    Chen P. Nonlinear wave dynamics in Faraday instabilities. Physical Review E, 2002, 65: 036308
    [20]
    Li Y, Zhang M, Wu K, et al. Three-dimensional simulation of ligament formation and breakup caused by external vibration. Physics of Fluids, 2020, 32(8): 083605 doi: 10.1063/5.0006817
    [21]
    Dinesh B, Livesay J, Ignatius IB, et al. Pattern formation in Faraday instability—experimental validation of theoretical models. Philosophical Transactions of the Royal Society A, 2023, 381(2245): 20220081 doi: 10.1098/rsta.2022.0081
    [22]
    Yuan S, Zhang Y, Gao Y. Faraday instability of a liquid layer in ultrasonic atomization. Physical Review Fluids, 2022, 7(3): 033902 doi: 10.1103/PhysRevFluids.7.033902
    [23]
    Bestehorn M, Sharma D, Borcia R, et al. Faraday instability of binary miscible/immiscible fluids with phase field approach. Physical Review Fluids, 2021, 6(6): 064002 doi: 10.1103/PhysRevFluids.6.064002
    [24]
    Dong J, Liu Y, Xu Q, et al. Surface parametric instability of star-shaped oscillating liquid drops. Physics of Fluids, 2019, 31(8): 087104 doi: 10.1063/1.5112007
    [25]
    Kumar K, Tuckerman LS. Parametric instability of the interface between two fluids. Journal of Fluid Mechanics, 1994, 279: 49-68
    [26]
    姚慕伟, 富庆飞, 杨立军等. 受径向振荡激励的黏弹性液滴稳定性分析. 力学学报, 2021, 53(9): 2468-2476 (Yao Muwei, Fu Qingfei, Yang Lijun, et al. Stability analysis of viscoelastic liquid droplets excited by radial oscillations. Chinese Journal of Theoretical and Applied Mechanics, 2021, 53(9): 2468-2476 (in Chinese)

    Yao Muwei, Fu Qingfei, Yang Lijun. Stability analysis of viscoelastic liquid droplets excited by radial oscillations. Chinese Journal of Theoretical and Applied Mechanics, 2021, 53(09): 2468-2476(in Chinese)
    [27]
    康宁. Faraday不稳定性下液滴雾化的特性和机理研究. [博士论文]. 北京: 北京理工大学, 2019

    Kang Ning. Study on the characteristics and mechanisms of droplet atomization under Faraday instability. [PhD Thesis]. Beijing: Beijing Institute of Technology, 2019 (in Chinese)
    [28]
    Sussman M, Puckett EG. A coupled level set and volume-of-fluid method for computing 3D and axisymmetric incompressible two-phase flows. Journal of Computational Physics, 2000, 162: 301-337
    [29]
    Daryaei A, Hanafizadeh P, Akhavan-Behabadi MA, et al. Three-dimensional numerical investigation of a single bubble behavior against non-linear forced vibration in a microgravity environment. International Journal of Multiphase Flow, 2018, 109: 84-97
    [30]
    Duan G, Koshizuka S, Chen B, et al. A contoured continuum surface force model for particle methods. Journal of Computational Physics, 2015, 298: 280-304
    [31]
    Chorin AJ. On the convergence of discrete approximations to the Navier-Stokes equations. Mathematics of Computation, 1969, 23: 341-353
    [32]
    Popinet S. Gerris: a tree-based adaptive solver for the incompressible Euler equations in complex geometries. Journal of Computational Physics, 2003, 190: 572-600
    [33]
    Pang X, Duan M, Liu H, et al. Oscillation-Induced mixing advances the functionality of liquid marble microreactors. ACS Applied Materials & Interfaces, 2022, 14(9): 11999-12009
    [34]
    Vukasinovic B, Smith MK, Glezer A, et al. Dynamics of a sessile drop in forced vibration. Journal of Fluid Mechanics, 2007, 587: 395-423
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