Numerical study of the effect of fluid properties on droplet impacts
DU Yuxuan, MIN Qi, LI Yanzhi, DU Jiayu
Key Laboratory of Advanced Reactor Engineering and Safety of Ministry of Education, Collaborative Innovation Center of Advanced Nuclear Energy Technology, Institute of Nuclear and New Energy Technology, Tsinghua University, Beijing 100084, China
Abstract:Previous research on droplet impact dynamics has yielded different results, and the types of fluids studied are not sufficiently diverse. This project numerically modeled droplet impact dynamics with nine kinds of fluids including water, glycerite, silicone oil, and liquid metals at room temperature with viscosities of 1-970 mPa·s and surface tensions of 20-500 mN/m. The phase-field model was used to supplement the data at low Reynolds numbers to explore the applicability of existing theories. The results show that at the beginning of the impact, the existing law for the spread factor, β, varying with the dimensionless time, τ, is applicable for Re>100. The simulation results are consistent with existing theory that the maximum spread factor, βmax, scales as βmax∝Web in the capillary regime and βmax∝Reb in the viscous regime. The effect of wall wettability on the exponent b was also analyzed. The minimum center thickness, hmin*, is consistent with the existing theory of hmin*∝Re-0.5 only when We ≥ 10. For We < 10, the wall wettability and surface tension strongly influence hmin*. As Re tends to 1, βmax and hmin* are determined by the initial kinetic energy of droplet and wettability of target surface, but they deviate from the above power function laws.
杜宇轩, 闵琪, 李衍智, 都家宇. 流体性质对液滴碰撞壁面影响的数值研究[J]. 清华大学学报(自然科学版), 2022, 62(2): 294-302.
DU Yuxuan, MIN Qi, LI Yanzhi, DU Jiayu. Numerical study of the effect of fluid properties on droplet impacts. Journal of Tsinghua University(Science and Technology), 2022, 62(2): 294-302.
[1] KIM J. Spray cooling heat transfer:The state of the art[J]. International Journal of Heat and Fluid Flow, 2007, 28:753-767. [2] CHEN Y F, WANG J L. Radiological consequences of the startup timing of a containment spray system[J]. Journal of Tsinghua University (Science and Technology), 2013, 53(4):442-446. (in Chinese)陈迎锋, 王建龙. 喷淋系统启动时机对辐射后果的影响[J]. 清华大学学报(自然科学版), 2013, 53(4):442-446. [3] BARTOLO D, JOSSERAND C, BONN D. Retraction dynamics of aqueous drops upon impact on non-wetting surfaces[J]. Journal of Fluid Mechanics, 2005, 545:329-338. [4] XU L, ZHANG W W, NAGEL S R. Drop splashing on a dry smooth surface[J]. Physical Review Letters, 2005, 94(18):184505. [5] ANTONINI C, AMIRFAZLI A, MARENGO M. Drop impact and wettability:From hydrophilic to superhydrophobic surfaces[J]. Physics of Fluids, 2012, 24(10):673-687. [6] WANG X, CHEN L Q, BONACCURSO E. Comparison of spontaneous wetting and drop impact dynamics of aqueous surfactant solutions on hydrophobic polypropylene surfaces:Scaling of the contact radius[J]. Colloid and Polymer Science, 2015, 293(1):257-265. [7] LIN S J, ZHAO B Y, ZOU S, et al. Impact of viscous droplets on different wettable surfaces:Impact phenomena, the maximum spreading factor, spreading time and post-impact oscillation[J]. Journal of Colloid and Interface Science, 2018, 516:86-97. [8] YAO Y N, LI C, TAO Z X, et al. Experimental study of the dynamic characteristics of an oblique impact of a water droplet[J]. Journal of Tsinghua University (Science and Technology), 2019, 59(2):129-134. (in Chinese)姚一娜, 李聪, 陶振翔, 等. 液滴碰撞倾斜壁面的动力学特性[J]. 清华大学学报(自然科学版), 2019, 59(2):129-134. [9] YARIN A L. Drop impact dynamics:Splashing, spreading, receding, bouncing …[J]. Annual Review of Fluid Mechanics, 2006, 38(1):159-192. [10] THORODDSEN S T, ETOH T G, TAKEHARA K. High-speed imaging of drops and bubbles[J]. Annual Review of Fluid Mechanics, 2008, 40(1):257-285. [11] JOSSERAND C, THORODDSEN S T. Drop impact on a solid surface[J]. Annual Review of Fluid Mechanics, 2016, 48(1):365-391. [12] KHOJASTEH D, KAZEROONI M, SALARIAN S, et al. Droplet impact on superhydrophobic surfaces:A review of recent developments[J]. Journal of Industrial and Engineering Chemistry, 2016, 42:1-14. [13] RIOBOO R, MARENGO M, TROPEA C. Time evolution of liquid drop impact onto solid, dry surfaces[J]. Experiments in Fluids, 2002, 33(1):112-124. [14] CLANET C, BÉGUIN C, RICHARD D, et al. Maximal deformation of an impacting drop[J]. Journal of Fluid Mechanics, 2004, 517:199-208. [15] RICHARD D, QUÉRÉ D. Bouncing water drops[J]. Europhysics Letters, 2000, 50(6):769-775. [16] RICHARD D, CLANET C, QUÉRÉ D. Surface phenomena:Contact time of a bouncing drop[J]. Nature, 2002, 417:811. [17] MUNDO C, SOMMERFELD M, TROPEA C. Droplet-wall collisions:Experimental studies of the deformation and breakup process[J]. International Journal of Multiphase Flow, 1995, 21(2):151-173. [18] VANDERWAL R L, BERGER G M, MOZES S D. The splash/non-splash boundary upon a dry surface and thin fluid film[J]. Experiments in Fluids, 2006, 40:53-59. [19] GUPTA A, KUMAR R. Droplet impingement and breakup on a dry surface[J]. Computers and Fluids, 2010, 39(9):1696-1703. [20] ZHANG D, PAPADIKIS K, GU S. Application of a high density ratio Lattice-Boltzmann model for the droplet impingement on flat and spherical surfaces[J]. International Journal of Thermal Sciences, 2014, 84:75-85. [21] FENG J. A computational study of high-speed microdroplet impact onto a smooth solid surface[J]. Journal of Applied Fluid Mechanics, 2017, 10(1):243-256. [22] DU J Y, ZHANG Y Y, MIN Q. Numerical investigations of the spreading and retraction dynamics of viscous droplets impact on solid surfaces[J]. Colloids and Surfaces A, 2020, 125649. [23] PASANDIDEH-FARD M, QIAO Y M, CHANDRA S, et al. Capillary effects during droplet impact on a solid surface[J]. Physics of Fluids, 1996, 8(3):650-659. [24] ROISMAN I V. Inertia dominated drop collisions. Ⅱ. An analytical solution of the Navier-Stokes equations for a spreading viscous film[J]. Physics of Fluids, 2009, 21:052104. [25] FEDORCHENKO A I, WANG A B, WANG Y H. Effect of capillary and viscous forces on spreading of a liquid drop impinging on a solid surface[J]. Physics of Fluids, 2005, 17:093104. [26] EGGERS J, FONTELOS M A, JOSSERAND C, et al. Drop dynamics after impact on a solid wall:Theory and simulations[J]. Physics of Fluids, 2010, 22:062101. [27] ROISMAN I V, RIOBOO R, TROPEA C. Normal impact of a liquid drop on a dry surface:Model for spreading and receding[J]. Proceedings of the Royal Society A, 2002, 458:1411-1430. [28] SCHROLL R D, JOSSERAND C, ZALESKI S, et al. Impact of a viscous liquid drop[J]. Physical Review Letters, 2010, 104:034504. [29] LAGUBEAU G, FONTELOS M A, JOSSERAND C, et al. Spreading dynamics of drop impacts[J]. Journal of Fluid Mechanics, 2012, 713:50-60. [30] ZHU Y, LIU H R, MU K, et al. Dynamics of drop impact onto a solid sphere:Spreading and retraction[J]. Journal of Fluid Mechanics, 2017, 824(3). [31] HIRT C W, NICHOLS B D. Volume of fluid (VOF) method for the dynamics of free boundaries[J]. Journal of Computational Physics, 1981, 39(1):201-225. [32] OSHER S. Fronts propagating with curvature-dependent speed:Algorithms based on Hamilton-Jacobi formulations[J]. Journal of Computational Physics, 1988, 79(1):12-49. [33] UNVERDI S O, TRYGGVASON G. A front-tracking method for viscous, incompressible, multi-fluid flows[J]. Journal of Computational Physics, 1992, 100(1):25-37. [34] JACQMIN D. Calculation of two-phase Navier-Stokes flows using phase-field modeling[J]. Journal of Computational Physics, 1999, 155(1):96-127. [35] WANG Z C, DONG S C, TRIANTAFYLLOU M S, et al. A stabilized phase-field method for two-phase flow at high Reynolds number and large density/viscosity ratio[J]. Journal of Computational Physics, 2019, 397:108832. [36] LIM C Y, LAM Y C. Phase-field simulation of impingement and spreading of micro-sized droplet on heterogeneous surface[J]. Microfluidics and Nanofluidics, 2014, 17:131-148. [37] ASHOKE RAMAN K, JAIMAN K R, LEE T S, et al. Dynamics of simultaneously impinging drops on a dry surface:Role of impact velocity and air inertia[J]. Journal of Colloid and Interface Science, 2017, 486:265-276. [38] XIAO J, PAN F, XIA H T, et al. Computational study of single droplet deposition on randomly rough surfaces:Surface morphological effect on droplet impact dynamics[J]. Industrial and Engineering Chemistry Research, 2018, 57:7664-7675. [39] CAHN J W, HILLIARD J E. Free energy of a nonuniform system. Ⅲ. Nucleation in a two-component incompressible fluid[J]. The Journal of Chemical Physics, 1959, 31(3):688-699. [40] WÖRNER M. Numerical modeling of multiphase flows in microfluidics and micro process engineering:A review of methods and applications[J]. Microfluidics and Nanofluidics, 2012, 12(6):841-886. [41] YUE P T, ZHOU C F, FENG J J, et al. Phase-field simulations of interfacial dynamics in viscoelastic fluids using finite elements with adaptive meshing[J]. Journal of Computational Physics, 2006, 219:47-67. [42] ŠIKALO Š, WILHELM H D, ROISMAN I V, et al. Dynamic contact angle of spreading droplets:Experiments and simulations[J]. Physics of Fluids, 2005, 17:062103. [43] VADILLO D C, SOUCEMARIANADIN A, DELATTRE C, et al. Dynamic contact angle effects onto the maximum drop impact spreading on solid surfaces[J]. Physics of Fluids, 2009, 21:122002. [44] WANG F J, FANG T G. Post-impact drop vibration on a hydrophilic surface[J]. Experimental Thermal and Fluid Science, 2018, 98:420-428.