Droplet spreading on an oblique surface
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摘要: 液滴碰撞固体表面后铺展的现象广泛存在于航空航天领域和工农业生产中。在工程中，被撞击表面多不与液滴速度方向垂直，而前人对于液滴碰撞铺展的研究多基于垂直碰撞，其研究成果无法直接解决工程斜碰撞问题。通过实验研究液滴碰撞倾斜固体表面铺展形成液膜的演化过程，获得了不同表面倾斜角度和不同韦伯数条件下液膜形状的瞬态数据；基于新建立的液滴碰撞倾斜表面铺展理论，分析了液膜形状的瞬态变化过程，发现该理论可以合理预测小倾角下液滴的铺展，而对于大倾角下液膜在倾斜方向最大铺展宽度的预测，由于推导过程中将液膜上沿长度近似为常数，导致误差较大。为解决该问题，通过加入液膜上沿长度的细致理论分析，建立了一个预测液膜最大形状的解析模型，预测结果相对实验结果的误差可从前人61.8%的误差降至3.2%。Abstract: Droplet spreading on a surface is ubiquitous in a variety of applications including aerospace, industry, and agriculture. Majority of these impacts are oblique, while previous studies focused on orthogonal impacts. Oblique impacts cannot be understood directly by previous theories and/or models. Evolution of film formation following a droplet impacting an oblique surface is investigated experimentally. Evolution of the film shape is obtained under various inclination angles and Weber numbers. Based on a new theory of droplet spreading on oblique surfaces, evolution of the film shape is analyzed. It is found that the film shape at small inclination angles can be predicted reasonably, but the error between the predicted maximum lamella width along the inclination direction and the experimental data is relatively big at large inclination angles since the length of the upstream lamella is assumed as a constant in the theory. Modifications of the theory including more detailed analysis of the length of the upstream lamella lead to an analytical model which permits the theoretical determination of the maximum lamella shape. It is shown that the error between the predicted results and the experimental results can be reduced from 61.8% by the previous theory to 3.2%.
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Key words:
- droplet impact /
- oblique surface /
- spreading /
- prediction model /
- liquid film
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图 3 液滴斜碰撞铺展过程（We = 37.6）
Figure 3. Spreading process of droplets impacting on inclined sub-strates （We = 37.6）
图 4 水平方向最大铺展宽度与倾斜角度的关系
Figure 4. The variation of the maximum horizontal width as a function of the inclination angle
图 5 倾斜方向最大铺展宽度与倾斜角度的关系
Figure 5. The variation of the maximum oblique width as a function of the inclination angle
图 6 小倾角下液滴演化的实验与模型预测结果（We = 37.6）
注：图（a）中t = 1时的黄线区域为液滴拉伸形成的影像，不是液膜
Figure 6. Droplet evolution at small inclination angles from experiments and model prediction （We = 37.6）
图 7 大倾角下液滴演化的实验与模型预测结果（We = 37.6）
Figure 7. Droplet evolution at large inclination angles from experiments and model prediction （We = 37.6）
图 9 椭圆中心与碰撞点距离随表面倾斜角度的变化（We = 37.6）
Figure 9. Distance between the ellipse center and the impact point as a function of the inclination angle （We = 37.6）
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[1] LIANG G T, MUDAWAR I. Review of drop impact on heated walls[J]. International Journal of Heat and Mass Transfer, 2017, 106: 103–126. doi: 10.1016/j.ijheatmasstransfer.2016.10.031 [2] LYU S J, TAN H S, WAKATA Y, et al. On explosive boiling of a multicomponent Leidenfrost drop[J]. Proceed-ings of the National Academy of Sciences of the United States of America, 2021, 118(2): 1–6. doi: 10.1073/pnas.2016107118 [3] QIN M X, TANG C L, TONG S Q, et al. On the role of liquid viscosity in affecting droplet spreading on a smooth solid surface[J]. International Journal of Multiphase Flow, 2019, 117: 53–63. doi: 10.1016/j.ijmultiphaseflow.2019.05.002 [4] MAITRA T, ANTONINI C, TIWARI M K, et al. Super-cooled water drops impacting superhydrophobic textures[J]. Langmuir: the ACS Journal of Surfaces and Colloids, 2014, 30(36): 10855–10861. doi: 10.1021/la502675a [5] ZHANG R, HAO P F, ZHANG X W, et al. Supercooled water droplet impact on superhydrophobic surfaces with various roughness and temperature[J]. International Journal of Heat and Mass Transfer, 2018, 122: 395–402. doi: 10.1016/j.ijheatmasstransfer.2018.01.076 [6] YI H, QI L H, LUO J, et al. Effect of the surface morphology of solidified droplet on remelting between neighboring aluminum droplets[J]. International Journal of Machine Tools and Manufacture, 2018, 130-131: 1–11. doi: 10.1016/j.ijmachtools.2018.03.006 [7] 任彦霖, 刘赵淼, 逄燕, 等. 基于LBM的铝微滴斜柱沉积水平偏移研究[J]. 力学学报, 2021, 53(6): 1599–1608. doi: 10.6052/0459-1879-21-022REN Y L, LIU Z M, PANG Y, et al. A lattice-boltzmann method simulation of the horizontal offset in oblique column deposition of aluminum droplets[J]. Chinese Journal of Theoretical and Applied Mechanics, 2021, 53(6): 1599–1608. doi: 10.6052/0459-1879-21-022 [8] FERNÁNDEZ-TOLEDANO J C, BRAECKEVELDT B, MARENGO M, et al. How wettability controls nanoprinting[J]. Physical Review Letters, 2020, 124(22): 224503. doi: 10.1103/physrevlett.124.224503 [9] AQEEL A B, MOHASAN M, LV P Y, et al. Effects of the actuation waveform on the drop size reduction in drop-on-demand inkjet printing[J]. Acta Mechanica Sinica, 2020, 36(5): 983–989. doi: 10.1007/s10409-020-00991-y [10] BREITENBACH J, ROISMAN I V, TROPEA C. From drop impact physics to spray cooling models: a critical review[J]. Experiments in Fluids, 2018, 59(55): 1–3. doi: 10.1007/s00348-018-2514-3 [11] 尚超, 阳倦成, 张杰, 等. 镓铟锡液滴撞击泡沫金属表面的运动学特性研究[J]. 力学学报, 2019, 51(2): 380–391. doi: 10.6052/0459-1879-18-307SHANG C, YANG J C, ZHANG J, et al. Experimental study on the dynamic characteristics of galinstan droplet impacting on the metal foam surface[J]. Chinese Journal of Theoretical and Applied Mechanics, 2019, 51(2): 380–391. doi: 10.6052/0459-1879-18-307 [12] WEINSTEIN S J. Coating flows[J]. Annual Review of Fluid Mechanics, 2004, 36: 29–53. doi: 10.1146/annurev.fluid.36.050802.122049 [13] BLAKE T D, FERNANDEZ-TOLEDANO J C, DOYEN G, et al. Forced wetting and hydrodynamic assist[J]. Physics of Fluids, 2015, 27(11): 112101. doi: 10.1063/1.4934703 [14] SOTO D, GIRARD H L, LE HELLOCO A, et al. Droplet fragmentation using a mesh[J]. Physical Review Fluids, 2018, 3(8): 083602. doi: 10.1103/physrevfluids.3.083602 [15] YARIN A L. Drop Impact Dynamics: splashing, spreading, receding, bouncing…[J]. Annual Review of Fluid Mechanics, 2006, 38: 159–192. doi: 10.1146/annurev.fluid.38.050304.092144 [16] JOSSERAND C, THORODDSEN S T. Drop impact on a solid surface[J]. Annual Review of Fluid Mechanics, 2016, 48: 365–391. doi: 10.1146/annurev-fluid-122414-034401 [17] 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(6): 062101. doi: 10.1063/1.3432498 [18] 毕菲菲, 郭亚丽, 沈胜强, 等. 液滴撞击固体表面铺展特性的实验研究[J]. 物理学报, 2012, 61(18): 184702. doi: 10.7498/aps.61.184702BI F F, GUO Y L, SHEN S Q, et al. Experimental study of spread characteristics of droplet impacting solid surface[J]. Acta Physica Sinica, 2012, 61(18): 184702. doi: 10.7498/aps.61.184702 [19] LAAN N, DE BRUIN K G, BARTOLO D, et al. Maximum diameter of impacting liquid droplets[J]. Physical Review Applied, 2014, 2(4): 044018. doi: 10.1103/physrevapplied.2.044018 [20] HAO J G. Effect of surface roughness on droplet splashing[J]. Physics of Fluids, 2017, 29(12): 122105. doi: 10.1063/1.5005990 [21] TANG C L, QIN M X, WENG X Y, et al. Dynamics of droplet impact on solid surface with different roughness[J]. International Journal of Multiphase Flow, 2017, 96: 56–69. doi: 10.1016/j.ijmultiphaseflow.2017.07.002 [22] 沈胜强, 张洁珊, 梁刚涛. 液滴撞击加热壁面传热实验研究[J]. 物理学报, 2015, 64(13): 134704. doi: 10.7498/aps.64.134704SHEN S Q, ZHANG J S, LIANG G T. Exp erimental study of heat transfer from droplet impact on a heated surface[J]. Acta Physica Sinica, 2015, 64(13): 134704. doi: 10.7498/aps.64.134704 [23] 荣松, 沈世全, 王天友, 等. 液滴撞击加热壁面雾化弹起模式及驻留时间[J]. 物理学报, 2019, 68(15): 154701. doi: 10.7498/aps.68.20190097RONG S, SHEN S Q, WANG T Y, et al. Bouncing-with-spray mode and residence time of droplet impact on heated surfaces[J]. Acta Physica Sinica, 2019, 68(15): 154701. doi: 10.7498/aps.68.20190097 [24] WANG Y J, EL BOUHALI A, LYU S J, et al. Leidenfrost drop impact on inclined superheated substrates[J]. Physics of Fluids, 2020, 32(11): 112113. doi: 10.1063/5.0027115 [25] SHANG Y H, ZHANG Y H, HOU Y, et al. Effects of surface subcooling on the spreading dynamics of an impact water droplet[J]. Physics of Fluids, 2020, 32(12): 123309. doi: 10.1063/5.0028081 [26] GORDILLO J M, RIBOUX G, QUINTERO E S. A theory on the spreading of impacting droplets[J]. Journal of Fluid Mechanics, 2019, 866: 298–315. doi: 10.1017/jfm.2019.117 [27] 春江, 王瑾萱, 徐晨, 等. 液滴撞击超亲水表面的最大铺展直径预测模型[J]. 物理学报, 2021, 70(10): 242–252. doi: 10.7498/aps.70.20201918CHUN J, WANG J X, XU C, et al. Theoretical model of maximum spreading diameter on superhydrophilic surfaces[J]. Acta Physica Sinica, 2021, 70(10): 242–252. doi: 10.7498/aps.70.20201918 [28] AVEDISIAN S. On the collision of a droplet with a solid surface[J]. Proceedings Mathematical and Physical Sciences, 1991, 432(1884): 13–41. doi: 10.1098/rspa.1991.0002 [29] 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. doi: 10.1063/1.868850 [30] CLANET C, BÉGUIN C, RICHARD D, et al. Maximal deformation of an impacting drop[J]. Journal of Fluid Mechanics, 2004, 517: 199–208. doi: 10.1017/s0022112004000904 [31] 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(5): 052104. doi: 10.1063/1.3129283 [32] LEE J B, LAAN N, DE BRUIN K G, et al. Universal rescaling of drop impact on smooth and rough surfaces[J]. Journal of Fluid Mechanics, 2016, 786: 1–11. doi: 10.1017/jfm.2015.620 [33] 宋云超, 宁智, 孙春华, 等. 液滴撞击湿润壁面的运动形态及飞溅运动机制[J]. 力学学报, 2013, 45(6): 833–842. doi: 10.6052/0459-1879-13-053SONG Y C, NING Z, SUN C H, et al. Movement and splashing of a droplet impacting on a wet wall[J]. Chinese Journal of Theoretical and Applied Mechanics, 2013, 45(6): 833–842. doi: 10.6052/0459-1879-13-053 [34] 李春曦, 陈朋强, 叶学民. 二维微柱阵列壁面对活性剂液滴铺展的影响[J]. 力学学报, 2014, 46(5): 665–672. doi: 10.6052/0459-1879-14-099LI C X, CHEN P Q, YE X M. Effect of two-dimensional micropillar arrayed topography on spreading of insoluble surfactant-laden droplet[J]. Chinese Journal of Theoretical and Applied Mechanics, 2014, 46(5): 665–672. doi: 10.6052/0459-1879-14-099 [35] 焦云龙, 刘小君, 刘焜. 离散型织构表面液滴的铺展及其接触线的力学特性分析[J]. 力学学报, 2016, 48(2): 353–360. doi: 10.6052/0459-1879-15-257JIAO Y L, LIU X J, LIU K. Mechanical analysis of a droplet spreading on the discrete textured surfaces[J]. Chinese Journal of Theoretical and Applied Mechanics, 2016, 48(2): 353–360. doi: 10.6052/0459-1879-15-257 [36] ŠIKALO Š, TROPEA C, GANIĆ E N. Impact of droplets onto inclined surfaces[J]. Journal of Colloid and Interface Science, 2005, 286(2): 661–669. doi: 10.1016/j.jcis.2005.01.050 [37] HAO J G, LU J, LEE L N, et al. Droplet splashing on an inclined surface[J]. Physical Review Letters, 2019, 122(5): 054501. doi: 10.1103/PhysRevLett.122.054501 [38] GARCÍA-GEIJO P, RIBOUX G, GORDILLO J M. Inclined impact of drops[J]. Journal of Fluid Mechanics, 2020, 897: 1–44. doi: 10.1017/jfm.2020.373 [39] HAO J G, LU J, ZHANG Z H, et al. Asymmetric droplet splashing[J]. Physical Review Fluids, 2020, 5(7): 073603. doi: 10.1103/physrevfluids.5.073603 [40] BIRD J C, TSAI S S H, STONE H A. Inclined to splash: triggering and inhibiting a splash with tangential velocity[J]. New Journal of Physics, 2009, 11(6): 063017. doi: 10.1088/1367-2630/11/6/063017 [41] HAO J G, GREEN S I. Splash threshold of a droplet impacting a moving substrate[J]. Physics of Fluids, 2017, 29(1): 012103. doi: 10.1063/1.4972976 [42] ALMOHAMMADI H, AMIRFAZLI A. Understanding the drop impact on moving hydrophilic and hydrophobic surfaces[J]. Soft Matter, 2017, 13(10): 2040–2053. doi: 10.1039/c6sm02514e [43] WU Z H, HAO J G, LU J, et al. Small droplet bouncing on a deep pool[J]. Physics of Fluids, 2020, 32(1): 012107. doi: 10.1063/1.5132350 [44] XU L, JI W J, LU J, et al. Droplet impact on a prewetted mesh[J]. Physical Review Fluids, 2021, 6(10): L101602. doi: 10.1103/physrevfluids.6.l101602 [45] RIBOUX G, GORDILLO J M. Experiments of drops impacting a smooth solid surface: a model of the critical impact speed for drop splashing[J]. Physical Review Letters, 2014, 113(2): 024507. doi: 10.1103/PhysRevLett.113.024507 [46] RIBOUX G, GORDILLO J M. Maximum drop radius and critical Weber number for splashing in the dynamical Leidenfrost regime[J]. Journal of Fluid Mechanics, 2016, 803: 516–527. doi: 10.1017/jfm.2016.496 [47] RIBOUX G, GORDILLO J M. Boundary-layer effects in droplet splashing[J]. Physical Review E, 2017, 96(1): 013105. doi: 10.1103/PhysRevE.96.013105 [48] GORDILLO J M, RIBOUX G. A note on the aerodynamic splashing of droplets[J]. Journal of Fluid Mechanics, 2019, 871(2): 1–12. doi: 10.1017/jfm.2019.396 -
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