×

On the splashing of high-speed drops impacting a dry surface. (English) Zbl 1460.76779

Summary: When a drop impacts a dry surface at high velocity, it atomises into secondary droplets. These small droplets are generated by one of two types of splashes: either by a prompt splash from the spreading rim at the surface or by a thin corona splash, which levitates from the surface. This study investigates the splashing mechanisms experimentally using multiple high-resolution cameras and characterises the outcome of both splashing types at high Weber and Reynolds numbers. We demonstrate that the prompt splash is well described by the Rayleigh-Taylor instability of the rapidly advancing liquid lamella and determine the boundaries defining this splashing regime, which allows us to distinguish the prompt from the corona splash. Furthermore, we provide an expression to estimate the elapsed time during which the secondary droplets are generated, which is then implemented in the theory of G. Riboux and J. M. Gordillo [“Experiments of drops impacting a smooth solid surface: a model of the critical impact speed for drop splashing”, Phys. Rev. Lett. 113, No. 2, Article ID 024507, 5 p. (2014; doi:10.1103/PhysRevLett.113.024507)]. This theoretical approach together with detailed quantification of the splashing outcome allows us to completely predict the outcome of both splashing types, which includes the mean size, velocity and total ejected volume of the secondary droplets. The detailed model proposed here can be indeed used to understand, characterise and predict more accurately the underlying physics in several applications.

MSC:

76T10 Liquid-gas two-phase flows, bubbly flows
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Aboud, D. G. K. & Kietzig, A.-M.2015Splashing threshold of oblique droplet impacts on surfaces of various wettability. Langmuir31 (36), 10100-10111.
[2] Agbaglah, G., Josserand, C. & Zaleski, S.2013Longitudinal instability of a liquid rim. Phys. Fluids25 (2), 022103.
[3] Berg, T., Deppe, J., Michaelis, D., Voges, H. & Wissel, S.2006Comparison of particle size and velocity investigations in sprays carried out by means of different measurement techniques. In ICLASS 2006, 10th Internation Conference on Liquid Atomization and Spray Systems, Kyoto, Japan, ICLASS06-151.
[4] Bird, J. C., Tsai, S. S. H. & Stone, H. A.2009Inclined to splash: triggering and inhibiting a splash with tangential velocity. New J. Phys.11 (6), 063017.
[5] Boelens, A. M. P. & De Pablo, J. J.2018Simulations of splashing high and low viscosity droplets. Phys. Fluids30 (7), 072106.
[6] Burzynski, D. A. & Bansmer, S. E.2018High speed visualization of droplets impacting with a dry surface at high weber numbers. In New Results in Numerical and Experimental Fluid Mechanics XI, pp. 511-521. Springer.
[7] Burzynski, D. A. & Bansmer, S. E.2019Role of surrounding gas in the outcome of droplet splashing. Phys. Rev. Fluids4, 073601.
[8] Chandrasekhar, S.2013Hydrodynamic and Hydromagnetic Stability. Courier Corporation.
[9] Chen, H., Marengo, M. & Amirfazli, A.2019Drop impact onto semi-infinite solid surfaces with different wettabilities. Phys. Rev. Fluids4 (8), 083601.
[10] Cimpeanu, R. & Moore, M. R.2018Early-time jet formation in liquid-liquid impact problems: theory and simulations. J. Fluid Mech.856, 764-796. · Zbl 1415.76628
[11] Cimpeanu, R. & Papageorgiou, D. T.2018Three-dimensional high speed drop impact onto solid surfaces at arbitrary angles. Intl J. Multiphase Flow107, 192-207.
[12] De Goede, T. C., Laan, N., De Bruin, K. G. & Bonn, D.2017Effect of wetting on drop splashing of newtonian fluids and blood. Langmuir34 (18), 5163-5168.
[13] Duchemin, L. & Josserand, C.2011Curvature singularity and film-skating during drop impact. Phys. Fluids23 (9), 091701. · Zbl 1308.76280
[14] Entov, V. M., Sultanov, F. M. & Yarin, A. L.1985Breakup of liquid films under the action of a pressure drop in the ambient gas. Sov. Phys. Dokl.30 (10), 882-884. · Zbl 0638.76116
[15] Entov, V. M., Sultanov, F. M. & Yarin, A. L.1986Disintegration of liquid films subjected to an ambient gas pressure difference. Fluid Dyn.21 (3), 376-383.
[16] Faßmann, B. W., Bansmer, S. E., Möller, T. J., Radespiel, R. & Hartmann, M.2013High velocity impingement of single droplets on a dry smooth surface. Exp. Fluids54 (5), 1516.
[17] Fukai, J., Shiiba, Y., Yamamoto, T., Miyatake, O., Poulikakos, D., Megaridis, C. M. & Zhao, Z.1995Wetting effects on the spreading of a liquid droplet colliding with a flat surface: experiment and modeling. Phys. Fluids7 (2), 236-247.
[18] Garcia-Magariño, A., Sor, S. & Velazquez, A.2018Droplet breakup criterion in airfoils leading edge vicinity. J. Aircraft55 (5), 1867-1876.
[19] Gordillo, J. M. & Riboux, G.2019A note on the aerodynamic splashing of droplets. J. Fluid Mech.871, R3. · Zbl 1419.76633
[20] Guo, Y., Lian, Y. & Sussman, M.2016Investigation of drop impact on dry and wet surfaces with consideration of surrounding air. Phys. Fluids28 (7), 073303.
[21] Hao, J. & Green, S. I.2017Splash threshold of a droplet impacting a moving substrate. Phys. Fluids29 (1), 012103.
[22] Honsek, R., Habashi, W. G. & Aubé, M. S.2008Eulerian modeling of in-flight icing due to supercooled large droplets. J. Aircraft45 (4), 1290-1296.
[23] Howison, S. D., Ockendon, J. R., Oliver, J. M., Purvis, R. & Smith, F. T.2005Droplet impact on a thin fluid layer. J. Fluid Mech.542, 1-23. · Zbl 1080.76012
[24] Howland, C. J., Antkowiak, A., Castrejón-Pita, J. R., Howison, S. D., Oliver, J. M., Style, R. W. & Castrejón-Pita, A. A.2016Its harder to splash on soft solids. Phys. Rev. Lett.117 (18), 184502.
[25] Huang, J. C. P.1970The break-up of axisymmetric liquid sheets. J. Fluid Mech.43 (2), 305-319.
[26] Jian, Z., Josserand, C., Popinet, S., Ray, P. & Zaleski, S.2018Two mechanisms of droplet splashing on a solid substrate. J. Fluid Mech.835, 1065-1086. · Zbl 1419.76635
[27] Josserand, C. & Thoroddsen, S. T.2016Drop impact on a solid surface. Annu. Rev. Fluid Mech.48, 365-391. · Zbl 1356.76380
[28] Kapulla, R., Tuchtenhagen, J., Müller, A., Dullenkopf, K. & Bauer, H.2008Droplet sizing performance of different shadow sizing codes. Lasermethoden Strömungsmesstechnik16, 38.
[29] Kim, K. S. & Kim, S. S.1994Drop sizing and depth-of-field correction in TV imaging. Atomiz. Sprays4 (1), 65-78.
[30] Kittel, H. M., Roisman, I. V. & Tropea, C.2018Splash of a drop impacting onto a solid substrate wetted by a thin film of another liquid. Phys. Rev. Fluids3 (7), 073601.
[31] Krechetnikov, R.2010Stability of liquid sheet edges. Phys. Fluids22 (9), 092101.
[32] Krechetnikov, R. & Homsy, G. M.2009Crown-forming instability phenomena in the drop splash problem. J. Colloid Interface Sci.331 (2), 555-559.
[33] Lagubeau, G., Fontelos, M. A., Josserand, C., Maurel, A., Pagneux, V. & Petitjeans, P.2012Spreading dynamics of drop impacts. J. Fluid Mech.713, 50-60. · Zbl 1284.76021
[34] Latka, A., Strandburg-Peshkin, A., Driscoll, M. M., Stevens, C. S. & Nagel, S. R.2012Creation of prompt and thin-sheet splashing by varying surface roughness or increasing air pressure. Phys. Rev. Lett.109 (5), 054501.
[35] Lejeune, S. & Gilet, T.2019Drop impact close to the edge of an inclined substrate: liquid sheet formation and breakup. Phys. Rev. Fluids4 (5), 053601.
[36] Li, E. Q., Thoraval, M.-J., Marston, J. O. & Thoroddsen, S. T.2018Early azimuthal instability during drop impact. J. Fluid Mech.848, 821-835.
[37] Liang, G. & Mudawar, I.2016Review of mass and momentum interactions during drop impact on a liquid film. Intl J. Heat Mass Transfer101, 577-599.
[38] Liang, G. & Mudawar, I.2017Review of drop impact on heated walls. Intl J. Heat Mass Transfer106, 103-126.
[39] Liu, M. & Bothe, D.2016Numerical study of head-on droplet collisions at high Weber numbers. J. Fluid Mech.789, 785-805.
[40] Mandre, S. & Brenner, M. P.2012The mechanism of a splash on a dry solid surface. J. Fluid Mech.690, 148-172. · Zbl 1241.76074
[41] Marengo, M., Antonini, C., Roisman, I. V. & Tropea, C.2011Drop collisions with simple and complex surfaces. Curr. Opin. Colloid Interface Sci.16 (4), 292-302.
[42] Mehdizadeh, N. Z., Chandra, S. & Mostaghimi, J.2004Formation of fingers around the edges of a drop hitting a metal plate with high velocity. J. Fluid Mech.510, 353-373. · Zbl 1058.76515
[43] Moore, M. R., Howison, S. D., Ockendon, J. R. & Oliver, J. M.2012Three-dimensional oblique water-entry problems at small deadrise angles. J. Fluid Mech.711, 259-280. · Zbl 1275.76044
[44] Moore, M. R., Whiteley, J. P. & Oliver, J. M.2018On the deflection of a liquid jet by an air-cushioning layer. J. Fluid Mech.846, 711-751. · Zbl 1404.76076
[45] Moreira, A. L. N., Moita, A. S. & Panao, M. R.2010Advances and challenges in explaining fuel spray impingement: How much of single droplet impact research is useful?Prog. Energy Combust. Sci.36 (5), 554-580.
[46] Mundo, C. H. R., Sommerfeld, M. & Tropea, C.1995Droplet-wall collisions: experimental studies of the deformation and breakup process. Intl J. Multiphase Flow21 (2), 151-173. · Zbl 1134.76617
[47] Palacios, J., Hernández, J., Gómez, P., Zanzi, C. & López, J.2013Experimental study of splashing patterns and the splashing/deposition threshold in drop impacts onto dry smooth solid surfaces. Exp. Therm. Fluid Sci.44, 571-582.
[48] Pan, K. L., Tseng, K. C. & Wang, C. H.2010Breakup of a droplet at high velocity impacting a solid surface. Exp. Fluids48 (1), 143-156.
[49] Pasandideh-Fard, M., Bhola, R., Chandra, S. & Mostaghimi, J.1998Deposition of tin droplets on a steel plate: simulations and experiments. Intl J. Heat Mass Transfer41 (19), 2929-2945.
[50] Pegg, M., Purvis, R. & Korobkin, A.2018Droplet impact onto an elastic plate: a new mechanism for splashing. J. Fluid Mech.839, 561-593. · Zbl 1419.76071
[51] Philippi, J., Lagrée, P. & Antkowiak, A.2016Drop impact on a solid surface: short-time self-similarity. J. Fluid Mech.795, 96-135. · Zbl 1359.76095
[52] Quetzeri-Santiago, M. A., Yokoi, K., Castrejón-Pita, A. A. & Castrejón-Pita, J. R.2019Role of the dynamic contact angle on splashing. Phys. Rev. Lett.122 (22), 228001.
[53] Quintero, E. S., Riboux, G. & Gordillo, J. M.2019Splashing of droplets impacting superhydrophobic substrates. J. Fluid Mech.870, 175-188.
[54] Rein, M. & Delplanque, J. P.2008The role of air entrainment on the outcome of drop impact on a solid surface. Acta Mechanica201 (1-4), 105. · Zbl 1155.76332
[55] Riboux, G. & Gordillo, J. M.2014Experiments of drops impacting a smooth solid surface: a model of the critical impact speed for drop splashing. Phys. Rev. Lett.113 (2), 024507.
[56] Riboux, G. & Gordillo, J. M.2015The diameters and velocities of the droplets ejected after splashing. J. Fluid Mech.772, 630-648.
[57] Riboux, G. & Gordillo, J. M.2017Boundary-layer effects in droplet splashing. Phys. Rev. E96 (1), 013105. · Zbl 1419.76633
[58] Rioboo, R., Marengo, M. & Tropea, C.2002Time evolution of liquid drop impact onto solid, dry surfaces. Exp. Fluids33 (1), 112-124.
[59] Rioboo, R., Tropea, C. & Marengo, M.2001Outcomes from a drop impact on solid surfaces. Atomiz. Sprays11 (2), 155-165.
[60] Roisman, I. V.2009Inertia dominated drop collisions. II. An analytical solution of the Navier-Stokes equations for a spreading viscous film. Phys. Fluids21 (5), 052104. · Zbl 1183.76438
[61] Roisman, I. V.2010On the instability of a free viscous rim. J. Fluid Mech.661, 206-228. · Zbl 1205.76118
[62] Roisman, I. V., Gambaryan-Roisman, T., Kyriopoulos, O., Stephan, P. & Tropea, C.2007Breakup and atomization of a stretching crown. Phys. Rev. E76 (2), 026302.
[63] Roisman, I. V., Horvat, K. & Tropea, C.2006Spray impact: rim transverse instability initiating fingering and splash and description of a secondary spray. Phys. Fluids18 (10), 102104. · Zbl 1185.76567
[64] Roisman, I. V., Lembach, A. & Tropea, C.2015Drop splashing induced by target roughness and porosity: the size plays no role. Adv. Colloid Interface Sci.222, 615-621.
[65] Roisman, I. V., Prunet-Foch, B., Tropea, C. & Vignes-Adler, M.2002aMultiple drop impact onto a dry solid substrate. J. Colloid Interface Sci.256 (2), 396-410.
[66] Roisman, I. V., Rioboo, R. & Tropea, C.2002bNormal impact of a liquid drop on a dry surface: model for spreading and receding. Proc. R. Soc. Lond. A458 (2022), 1411-1430. · Zbl 1056.76008
[67] Rozhkov, A., Prunet-Foch, B. & Vignes-Adler, M.2002Impact of water drops on small targets. Phys. Fluids14 (10), 3485-3501. · Zbl 1185.76318
[68] De Ruiter, J., Pepper, R. E. & Stone, H. A.2010Thickness of the rim of an expanding lamella near the splash threshold. Phys. Fluids22 (2), 022104. · Zbl 1183.76170
[69] Sahu, R. P., Sinha-Ray, S., Yarin, A. L. & Pourdeyhimi, B.2012Drop impacts on electrospun nanofiber membranes. Soft Matt.8 (14), 3957-3970.
[70] Sivakumar, D. & Tropea, C.2002Splashing impact of a spray onto a liquid film. Phys. Fluids14 (12), L85-L88. · Zbl 1185.76345
[71] Staat, H. J. J., Tran, T., Geerdink, B., Riboux, G., Sun, C., Gordillo, J. M. & Lohse, D.2015Phase diagram for droplet impact on superheated surfaces. J. Fluid Mech.779, R3.
[72] Stevens, C. S.2014Scaling of the splash threshold for low-viscosity fluids. Europhys. Lett.106 (2), 24001.
[73] Stevens, C. S., Latka, A. & Nagel, S. R.2014Comparison of splashing in high-and low-viscosity liquids. Phys. Rev. E89 (6), 063006.
[74] Stow, C. D. & Stainer, R. D.1977The physical products of a splashing water drop. J. Met. Soc. Japan55 (5), 518-531.
[75] Tan, C., Papadakis, M., Miller, D., Bencic, T., Tate, P. & Laun, M.2007Experimental study of large droplet splashing and breakup. In 45th AIAA Aerospace Sciences Meeting and Exhibit, p. 904.
[76] Taylor, G. I.1959The dynamics of thin sheets of fluid II. Waves on fluid sheets. Proc. R. Soc. Lond. A253 (1274), 296-312. · Zbl 0087.19602
[77] Thoroddsen, S. T. & Sakakibara, J.1998Evolution of the fingering pattern of an impacting drop. Phys. Fluids10 (6), 1359-1374.
[78] Thoroddsen, S. T., Takehara, K. & Etoh, T. G.2012Micro-splashing by drop impacts. J. Fluid Mech.706, 560-570. · Zbl 1275.76032
[79] Tsai, P., Van Der Veen, R. C. A., Van De Raa, M. & Lohse, D.2010How micropatterns and air pressure affect splashing on surfaces. Langmuir26 (20), 16090-16095.
[80] Villermaux, E.2007Fragmentation. Annu. Rev. Fluid Mech.39, 419-446. · Zbl 1296.76164
[81] Villermaux, E. & Bossa, B.2011Drop fragmentation on impact. J. Fluid Mech.668, 412-435. · Zbl 1225.76099
[82] Visser, C. W., Tagawa, Y., Sun, C. & Lohse, D.2012Microdroplet impact at very high velocity. Soft Matt.8 (41), 10732-10737.
[83] Wagner, H.1932Über Stoß-und Gleitvorgänge an der Oberfläche von Flüssigkeiten. Z. Angew. Math. Mech.12 (4), 193-215. · Zbl 0005.12601
[84] Wang, Y. & Bourouiba, L.2018Unsteady sheet fragmentation: droplet sizes and speeds. J. Fluid Mech.848, 946-967.
[85] Xu, L., Barcos, L. & Nagel, S. R.2007Splashing of liquids: interplay of surface roughness with surrounding gas. Phys. Rev. E76 (6), 066311.
[86] Xu, L., Zhang, W. W. & Nagel, S. R.2005Drop splashing on a dry smooth surface. Phys. Rev. Lett.94 (18), 184505.
[87] Yarin, A. L.1993Free Liquid Jets and Films: Hydrodynamics and Rheology. Longman & Wiley. · Zbl 0872.76002
[88] Yarin, A. L.2006Drop impact dynamics: splashing, spreading, receding, bouncing. Annu. Rev. Fluid Mech.38, 159-192. · Zbl 1097.76012
[89] Yarin, A. L., Roisman, I. V. & Tropea, C.2017Collision Phenomena in Liquids and Solids. Cambridge University Press. · Zbl 1365.74003
[90] Yarin, A. L. & Weiss, D. A.1995Impact of drops on solid surfaces: self-similar capillary waves and splashing as a new type of kinematic discontinuity. J. Fluid Mech.283, 141-173.
[91] Zhang, C. & Liu, H.2016Effect of drop size on the impact thermodynamics for supercooled large droplet in aircraft icing. Phys. Fluids28 (6), 062107.
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.