EI、Scopus 收录
中文核心期刊
Li Xiangwei, Hao Haohao, Tan Huanshu. Numerical study of solute gradient-induced self-propulsion of suspended droplets. Chinese Journal of Theoretical and Applied Mechanics, 2024, 56(5): 1223-1232. DOI: 10.6052/0459-1879-24-011
Citation: Li Xiangwei, Hao Haohao, Tan Huanshu. Numerical study of solute gradient-induced self-propulsion of suspended droplets. Chinese Journal of Theoretical and Applied Mechanics, 2024, 56(5): 1223-1232. DOI: 10.6052/0459-1879-24-011

NUMERICAL STUDY OF SOLUTE GRADIENT-INDUCED SELF-PROPULSION OF SUSPENDED DROPLETS

  • Received Date: January 01, 2024
  • Accepted Date: March 19, 2024
  • Available Online: March 19, 2024
  • Published Date: March 20, 2024
  • In the presence of solute concentration gradients, suspended droplets undergo spontaneous motion. The reason is that the non-uniform distribution of solutes at the droplet interface can cause an interfacial tension gradient at the fluid interface, inducing interfacial flow. This process involves the interface movement of the self-propelled droplet, the evolution of the near-interface flow field, the solute concentration field, and the coupling effects of multiple physical fields. Understanding this complex dynamic process holds significance. This paper constructs a multiphase-multicomponent fluid numerical model to describe solute-induced droplet migration phenomena by combining the conservation-type Allen-Cahn equation, incompressible Navier-Stokes equation, and the advection-diffusion equation for solute. The accuracy of the numerical model is validated through case studies and theoretical comparisons (Laplace pressure difference of stationary droplets, buoyancy driven bubble rise, and solute concentration driven droplets migration). The simulation investigates solute Marangonii effects under different Marangoni numbers, including phenomena of coalescence and separation of two droplets in different sizes. Results indicate that larger droplets exhibit faster movement, and an increased Marangoni number shifts the self-propelled droplet interface mass transfer from diffusion-dominated to advection-dominated, enhancing the impact of droplet movement on the ambient solute field. Meanwhile, the solute gradient at the interface is reduced, which weakens the Marangoni effect, and decreases the droplet migration speed. The larger the size of the droplet, the more significant decrease in its velocity. This study provides a reliable numerical model for solving physical problems in multiphase multi-component fluid systems in the future and provides reference data for the manipulation of multi-component micro-droplets.
  • [1]
    Moragues T, Arguijo D, Beneyton T, et al. Droplet-based microfluidics. Nature Reviews Methods Primers, 2023, 3(1): 32 doi: 10.1038/s43586-023-00212-3
    [2]
    陈晓东, 胡国庆. 微流控器件中的多相流动. 力学进展, 2015, 45(3): 56-110 (Chen Xiaodong, Hu Guoqing. Multiphase flow in microfluidic devices. Advances in Mechanics, 2015, 45(3): 56-110 (in Chinese)

    Chen Xiaodong, Hu Guoqing. Multiphase flow in microfluidic devices. Advances in Mechanics, 2015, 45(3): 56-110 (in Chinese)
    [3]
    Leung CM, De Haan P, Ronaldson-Bouchard K, et al. A guide to the organ-on-a-chip. Nature Reviews Methods Primers, 2022, 2(1): 33 doi: 10.1038/s43586-022-00118-6
    [4]
    Perazzo A, Tomaiuolo G, Preziosi V, et al. Emulsions in porous media: From single droplet behavior to applications for oil recovery. Advances in Colloid and Interface Science, 2018, 256: 305-325 doi: 10.1016/j.cis.2018.03.002
    [5]
    Gale B, Jafek A, Lambert C, et al. A review of current methods in microfluidic device fabrication and future commercialization prospects. Inventions, 2018, 3(3): 60 doi: 10.3390/inventions3030060
    [6]
    Chauhan VP, Stylianopoulos T, Boucher Y, et al. Delivery of molecular and nanoscale medicine to tumors: transport barriers and strategies. Annual Review of Chemical and Biomolecular Engineering, 2011, 2(1): 281-298 doi: 10.1146/annurev-chembioeng-061010-114300
    [7]
    Leal LG. Advanced Transport Phenomena: Fluid Mechanics and Convective Transport Processes. Cambridge: Cambridge University Press, 2007
    [8]
    Michelin S. Self-propulsion of chemically active droplets. Annual Review of Fluid Mechanics, 2023, 55(1): 77-101 doi: 10.1146/annurev-fluid-120720-012204
    [9]
    Suga M, Suda S, Ichikawa M, et al. Self-propelled motion switching in nematic liquid crystal droplets in aqueous surfactant solutions. Physical Review E, 2018, 97(6): 062703 doi: 10.1103/PhysRevE.97.062703
    [10]
    Li Y, Diddens C, Prosperetti A, et al. Bouncing oil droplet in a stratified liquid and its sudden death. Physical Review Letters, 2019, 122(15): 154502 doi: 10.1103/PhysRevLett.122.154502
    [11]
    Izri Z, van der Linden MN, Michelin S, et al. Self-propulsion of pure water droplets by spontaneous Marangonii-stress-driven motion. Physical Review Letters, 2014, 113(24): 248302 doi: 10.1103/PhysRevLett.113.248302
    [12]
    Tan H, Banerjee A, Shi N, et al. A two-step strategy for delivering particles to targets hidden within microfabricated porous media. Science Advances, 2021, 7(33): eabh0638 doi: 10.1126/sciadv.abh0638
    [13]
    Michelin S, Lauga E, Bartolo D. Spontaneous autophoretic motion of isotropic particles. Physics of Fluids, 2013, 25(6): 061701 doi: 10.1063/1.4810749
    [14]
    Li G. Swimming dynamics of a self-propelled droplet. Journal of Fluid Mechanics, 2022, 934: A20 doi: 10.1017/jfm.2021.1154
    [15]
    Morozov M, Michelin S. Self-propulsion near the onset of Marangoni instability of deformable active droplets. Journal of Fluid Mechanics, 2019, 860: 711-738 doi: 10.1017/jfm.2018.853
    [16]
    Manikantan H, Squires TM. Surfactant dynamics: Hidden variables controlling fluid flows. Journal of Fluid Mechanics, 2020, 892: P1 doi: 10.1017/jfm.2020.170
    [17]
    黄彦如, 黄睿雯, 马雪等. 溶质引起的自由液面Marangonii铺展研究综述. 力学学报, 2024, 出版中 (Huang Yanru, Huang Ruiwen, Ma Xue, et al. Review of solutal Marangonii spreading on free surface. Chinese Journal of Theoretical and Applied Mechanics, 2024, in press (in Chinese)

    Huang Yanru, Huang Ruiwen, Ma Xue, et al. Review of solutal Marangonii spreading on free surface. Chinese Journal of Theoretical and Applied Mechanics, 2024, in press (in Chinese)
    [18]
    叶致君, 段俐, 康琦. 激光驱动液滴迁移的机理研究. 力学学报, 2022, 54(2): 316-325 (Ye Zhijun, Duan Li, Kang Qi. Mechanistic study of laser-driven droplet migration. Chinese Journal of Theoretical and Applied Mechanics, 2022, 54(2): 316-325 (in Chinese)

    Ye Zhijun, Duan Li, Kang Qi. Mechanistic study of laser-driven droplet migration. Chinese Journal of Theoretical and Applied Mechanics, 2022, 54(2): 316-325 (in Chinese)
    [19]
    Ryazantsev YS, Velarde MG, Rubio RG, et al. Thermo- and soluto-capillarity: Passive and active drops. Advances in Colloid and Interface Science, 2017, 247: 52-80 doi: 10.1016/j.cis.2017.07.025
    [20]
    Tan H, Diddens C, Zhang X, et al. Evaporation of ternary sessile drops//David B, Khellil S, eds. Drying of complex fluid drops. The United Kingdom by CPI Group (UK) Ltd: The Royal Society of Chemistry, 2022: 33-46
    [21]
    Lai MC, Tseng YH, Huang H. An immersed boundary method for interfacial flows with insoluble surfactant. Journal of Computational Physics, 2008, 227(15): 7279-7293 doi: 10.1016/j.jcp.2008.04.014
    [22]
    Muradoglu M, Tryggvason G. A front-tracking method for computation of interfacial flows with soluble surfactants. Journal of Computational Physics, 2008, 227(4): 2238-2262 doi: 10.1016/j.jcp.2007.10.003
    [23]
    Stricker L. Numerical simulation of artificial microswimmers driven by Marangonii flow. Journal of Computational Physics, 2017, 347: 467-489 doi: 10.1016/j.jcp.2017.07.007
    [24]
    Xu JJ, Shi W, Lai MC. A level-set method for two-phase flows with soluble surfactant. Journal of Computational Physics, 2018, 353: 336-355 doi: 10.1016/j.jcp.2017.10.019
    [25]
    Yang J, Tan Z, Kim J. Linear and fully decoupled scheme for a hydrodynamics coupled phase-field surfactant system based on a multiple auxiliary variables approach. Journal of Computational Physics, 2022, 452: 110909 doi: 10.1016/j.jcp.2021.110909
    [26]
    Teigen KE, Song P, Lowengrub J, et al. A diffuse-interface method for two-phase flows with soluble surfactants. Journal of Computational Physics, 2011, 230(2): 375-393 doi: 10.1016/j.jcp.2010.09.020
    [27]
    Picardo JR, Radhakrishna TG, Pushpavanam S. Solutal Marangonii instability in layered two-phase flows. Journal of Fluid Mechanics, 2016, 793: 280-315 doi: 10.1017/jfm.2016.135
    [28]
    Yang C, Mao ZS. Numerical simulation of interphase mass transfer with the level set approach. Chemical Engineering Science, 2005, 60(10): 2643-2660 doi: 10.1016/j.ces.2004.11.054
    [29]
    Yang QJ, Mao Q, Cao W. Numerical simulation of the Marangonii flow on mass transfer from single droplet with different Reynolds numbers. Colloids and Surfaces A: Physicochemical and Engineering Aspects, 2022, 639: 128385 doi: 10.1016/j.colsurfa.2022.128385
    [30]
    Tryggvason G, Scardovelli R, Zaleski S. Direct Numerical Simulations of Gas-Liquid Multiphase Flows. 1st ed. Cambridge: Cambridge University Press, 2011
    [31]
    Sussman M, Almgren AS, Bell JB, et al. An adaptive level set approach for incompressible two-phase flows. Journal of Computational Physics, 1999, 148: 81-124 doi: 10.1006/jcph.1998.6106
    [32]
    Sethian JA, Smereka P. Level set methods for fluid interfaces. Annual Review of Fluid Mechanics, 2003, 35(1): 341-372 doi: 10.1146/annurev.fluid.35.101101.161105
    [33]
    Chiu PH, Lin YT. A conservative phase field method for solving incompressible two-phase flows. Journal of Computational Physics, 2011, 230(1): 185-204 doi: 10.1016/j.jcp.2010.09.021
    [34]
    Ding H, Peter DMS, Shu C. Diffuse interface model for incompressible two-phase flows with large density ratios. Journal of Computational Physics, 2007, 226(2): 2078-2095
    [35]
    Zhang C, Guo Z, Wang LP. Improved well-balanced free-energy lattice Boltzmann model for two-phase flow with high Reynolds number and large viscosity ratio. Physics of Fluids, 2022, 34: 012110 doi: 10.1063/5.0072221
    [36]
    Aihara S, Takaki T, Takada N. Multi-phase-field modeling using a conservative Allen-Cahn equation for multiphase flow. Computers & Fluids, 2019, 178: 141-151
    [37]
    Zhang C, Liang H, Guo Z, et al. Discrete unified gas-kinetic scheme for the conservative Allen-Cahn equation. Physical Review E, 2022, 105(4): 045317 doi: 10.1103/PhysRevE.105.045317
    [38]
    Kim J. A continuous surface tension force formulation for diffuse-interface models. Journal of Computational Physics, 2005, 204(2): 784-804 doi: 10.1016/j.jcp.2004.10.032
    [39]
    Jacqmin D. Calculation of two-phase Navier–Stokes flows using phase-field modeling. Journal of Computational Physics, 1999, 155(1): 96-127 doi: 10.1006/jcph.1999.6332
    [40]
    Demont THB, Stoter SKF, van Brummelen EH. Numerical investigation of the sharp-interface limit of the Navier-Stokes-Cahn-Hilliard equations. Journal of Fluid Mechanics, 2023, 970: A24 doi: 10.1017/jfm.2023.611
    [41]
    Aland S, Voigt A. Benchmark computations of diffuse interface models for two-dimensional bubble dynamics. International Journal for Numerical Methods in Fluids, 2012, 69(3): 747-761 doi: 10.1002/fld.2611
    [42]
    Wang Y, Shu C, Shao JY, et al. A mass-conserved diffuse interface method and its application for incompressible multiphase flows with large density ratio. Journal of Computational Physics, 2015, 290: 336-351 doi: 10.1016/j.jcp.2015.03.005
    [43]
    Young NO, Goldstein JS, Block MJ. The motion of bubbles in a vertical temperature gradient. Journal of Fluid Mechanics, 1959, 6: 350-356 doi: 10.1017/S0022112059000684
    [44]
    张朔婷, 胡良, 段俐等. 多液滴热毛细迁移的研究. 力学学报, 2014, 46(5): 802-806 (Zhang Shuoting, Hu Liang, Duan Li, et al. Droplet interactions in thermocapillary migration. Chinese Journal of Theoretical and Applied Mechanics, 2014, 46(5): 802-806 (in Chinese) doi: 10.6052/0459-1879-13-244

    Zhang Shuoting, Hu Liang, Duan Li, et al. Droplet interactions in thermocapillary migration. Chinese Journal of Theoretical and Applied Mechanics, 2014, 46(5): 802-806 (in Chinese) doi: 10.6052/0459-1879-13-244
    [45]
    Liu H, Wu L, Ba Y, et al. A lattice Boltzmann method for axisymmetric thermocapillary flows. International Journal of Heat and Mass Transfer, 2017, 104: 337-350 doi: 10.1016/j.ijheatmasstransfer.2016.08.068
    [46]
    Yin Z, Li Q. Thermocapillary migration and interaction of drops: Two non-merging drops in an aligned arrangement. Journal of Fluid Mechanics, 2015, 766: 436-467 doi: 10.1017/jfm.2015.10
    [47]
    Kalichetty SS, Sundararajan T, Pattamatta A. Thermocapillary migration and interaction dynamics of droplets in a constricted domain. Physics of Fluids, 2019, 31(2): 022106 doi: 10.1063/1.5084313
  • Related Articles

    [1]Gong Jingfeng, Chen Sicheng, Xuan Lingkuan, Li Chenqi, Zhang Yue. FUNCTIONALLY GRADED MATERIAL DATA DRIVEN CELL-VERTEX FINITE VOLUME METHOD[J]. Chinese Journal of Theoretical and Applied Mechanics, 2025, 57(1): 136-147. DOI: 10.6052/0459-1879-24-303
    [2]Feng Yixin, Peng Hui, Luo Wei. RESEARCH ON PARAMETER IDENTIFICATION OF COMPOSITE MATERIALS BY COMBINATION OF SELF-CONSISTENT CLUSTER ANALYSIS, NEURAL NETWORK AND BAYESIAN OPTIMIZATION[J]. Chinese Journal of Theoretical and Applied Mechanics, 2024, 56(11): 3333-3350. DOI: 10.6052/0459-1879-24-246
    [3]Ji Shunying. Preface of Theme Articles on Computation Mechanics of Granular Materials[J]. Chinese Journal of Theoretical and Applied Mechanics, 2021, 53(9): 2355-2356. DOI: 10.6052/0459-1879-21-428
    [4]Zhuo Xiaoxiang, Liu Hui, Chu Xihua, Xu Yuanjie. A GENERALIZED MULTISCALE FINITE ELEMENT METHOD FOR DYNAMIC ANALYSIS OF HETEROGENEOUS MATERIAL[J]. Chinese Journal of Theoretical and Applied Mechanics, 2016, 48(2): 378-386. DOI: 10.6052/0459-1879-15-211
    [5]Shengwang Hao, Ju Sun. A sensitive precursor to catastrophic failure in heterogeneous brittle materials[J]. Chinese Journal of Theoretical and Applied Mechanics, 2008, 40(3): 339-344. DOI: 10.6052/0459-1879-2008-3-2007-552
    [6]Jun Zhou, Youhe Zhou. A new simple method of implicit time integration for dynamic problems of engineering structures[J]. Chinese Journal of Theoretical and Applied Mechanics, 2007, 39(1): 91-99. DOI: 10.6052/0459-1879-2007-1-2006-167
    [7]Z.Y. Gao, Tongxi Yu, D. Karagiozova. Finite element simulation on the mechanical properties of MHS materials[J]. Chinese Journal of Theoretical and Applied Mechanics, 2007, 39(1): 65-75. DOI: 10.6052/0459-1879-2007-1-2006-198
    [8]Microscopic heterogeneity and macroscopic mechanical behavior of a polycrystalline material[J]. Chinese Journal of Theoretical and Applied Mechanics, 2004, 36(6): 714-723. DOI: 10.6052/0459-1879-2004-6-2003-444
    [9]HOMOGENIZATION METHOD OF STRESS ANALYSIS OF COMPOSITE STRUCTURES[J]. Chinese Journal of Theoretical and Applied Mechanics, 1997, 29(3): 306-313. DOI: 10.6052/0459-1879-1997-3-1995-230
    [10]基于变形动力学模型的黏弹性材料本构关系[J]. Chinese Journal of Theoretical and Applied Mechanics, 1993, 25(3): 375-379. DOI: 10.6052/0459-1879-1993-3-1995-655
  • Cited by

    Periodical cited type(2)

    1. 龚京风,陈思成,宣领宽,李晨琦,张跃. 功能梯度材料数据驱动格点型有限体积法. 力学学报. 2025(01): 136-147 . 本站查看
    2. 冯易鑫 ,彭辉 ,罗威 . 聚类分析-神经网络-贝叶斯优化联合识别复合材料参数研究. 力学学报. 2024(11): 3333-3350 . 本站查看

    Other cited types(0)

Catalog

    Article Metrics

    Article views (177) PDF downloads (81) Cited by(2)
    Related

    /

    DownLoad:  Full-Size Img  PowerPoint
    Return
    Return