Drop Impacts with Liquid Pools and Layers

Alexander L. Yarin; Ilia V. Roisman; Cameron Tropea

doi:10.1017/9781316556580.007

6 - Drop Impacts with Liquid Pools and Layers

from Part II - Drop Impacts onto Liquid Surfaces

Published online by Cambridge University Press: 13 July 2017

Alexander L. Yarin ,

Ilia V. Roisman and

Cameron Tropea

Show author details

Alexander L. Yarin: Affiliation:
University of Illinois, Chicago
Ilia V. Roisman: Affiliation:
Technische Universität, Darmstadt, Germany
Cameron Tropea: Affiliation:
Technische Universität, Darmstadt, Germany

Book contents

Get access

Summary

In this chapter drop impacts onto a liquid layer of the same liquid as in the drop are considered. The chapter begins with consideration of such weak drop impacts on a liquid layer that they result only in capillary waves propagating over the surface. An interesting feature of these waves is that they are self-similar (Section 6.1). In the following Section 6.2 crown formation in strong (high-velocity) impacts onto thin liquid films is considered. Normal and oblique impacts of a single drop onto a wet wall are studied, as well as crown–crown interaction in sprays impacting the wall. Also, the evolution of the free rim on top of the crown is described. Then, in Section 6.3 drop impacts onto a thick liquid layer are considered and the dynamics of the crater formation is explained. Drop impacts onto a wet wall leave a residual liquid film on the wall which is addressed in Section 6.4. Drop impacts onto deep liquid pools produce a plethora of interesting morphological structures considered in Section 6.5. In the following Section 6.6 bending instability of a free rim is considered and the splashing mechanism is discussed. Splashing resulting from impacts of drop trains one-by-one is discussed in Section 6.7, where its physical mechanism and the link to splashing of a single drop impacting onto a liquid layer are elucidated. Several other regimes of drop impact are also mentioned.

Drop Impact onto Thin Liquid Layer on a Wall: Weak Impacts and Self-similar Capillary Waves

Consider patterns of capillary waves propagating over the free surface of a thin liquid film from the point where it was impacted normally by a tiny droplet or a stick (Fig. 6.1), as an example of a relatively weak (low-velocity) impact. For scales of the order of several millimeters the gravity effect on these waves is negligibly small, and for time scales of the order of several milliseconds viscosity effects can also be neglected.

Type: Chapter
Information: Collision Phenomena in Liquids and Solids , pp. 255 - 320

DOI: https://doi.org/10.1017/9781316556580.007 [Opens in a new window]

Publisher: Cambridge University Press

Print publication year: 2017

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Book purchase

Temporarily unavailable

References

Agbaglah, G. and Deegan, R. D. (2014). Growth and instability of the liquid rim in the crown splash regime, J. Fluid Mech. 752: 485–496.Google Scholar

Ashgriz, N. and Poo, J. Y. (1990). Coalescence and separation in binary collisions of liquid drops, J. Fluid Mech. 221: 183–204.Google Scholar

Bagué, A., Zaleski, S. and Josserand, C. (2007). Droplet formation at the edge of a liquid sheet, in M., Sommerfeld (ed.), Proc. 6th International Conference on Multiphase Flow, Leipzig, Germany.

Bakshi, S., Roisman, I. V. and Tropea, C. (2007). Investigations on the impact of a drop onto a small spherical target, Phys. Fluids 19: 032102.Google Scholar

Bartolo, D., Josserand, C. and Bonn, D. (2005). Retraction dynamics of aqueous drops upon impact on non-wetting surfaces, J. Fluid Mech. 545: 329–338.Google Scholar

Berberović, E., van Hinsberg, N. P., Jakirlić, S., Roisman, I. V. and Tropea, C. (2009). Drop impact onto a liquid layer of finite thickness: Dynamics of the cavity evolution, Phys. Rev. E 79: 036306.Google Scholar

Birkhoff, G., MacDougall, D. P., Pugh, E. M. and Taylor, S. G. (1948). Explosives with lined cavities, J. Appl. Phys. 19: 563–582.Google Scholar

Bisighini, A., Cossali, G. E., Tropea, C. and Roisman, I. V. (2010). Crater evolution after the impact of a drop onto a semi-infinite liquid target, Phys. Rev. E 82: 036319.Google Scholar

Blanchard, D. and Woodcock, A. (1957). Bubble formation and modification in the sea and its meteorological significance, Tellus 9: 145–158.Google Scholar

Böhm, C., Weiss, D. A. and Tropea, C. (1999). Multi-droplet impact onto solid walls: droplet droplet interaction and collision of kinematic discontinuities, in C., Tropea and K., Heukelbach (eds.), Proc. 15th Ann. Conf. on Liquid Atomization and Spray Systems, ILASS-Europe, Darmstadt, pp. VII.7.1–VII.7.6.

Boussinesq, J. (1869a). Théorie des expériences de Savart, sur la forme que prend une veine liquide après s'être choquée contre un plan circulaire, C. R. Acad. Sci. Paris 69: 45–49.Google Scholar

Boussinesq, J. (1869b). Théories des expériences de Savart, sur la forme que prend une veine liquide après s'être choquée contre un plan circulaire (suite), C. R. Acad. Sci. Paris 69: 128–131.Google Scholar

Brenn, G., Valkovska, D. and Danov, K. D. (2001). The formation of satellite droplets by unstable binary drop collisions, Phys. Fluids 13: 2463–2477.Google Scholar

Brenner, M. P., Lister, J. R. and Stone, H. A. (1996). Pinching threads, singularities and the number 0.0304…, Phys. Fluids 8: 2827–2836.Google Scholar

Brochard-Wyart, F. and de Gennes, P.-G. (1997). Shocks in an inertial dewetting process, C. R. Acad. Sc. Paris 324-IIb: 257–260.Google Scholar

Brochard-Wyart, F., Di Meglio, J. and Quéré, D. (1987). Dewetting–growth of dry regions from a film covering a flat solid or a fiber, C. R. Acad. Sc. Paris 304-II-11: 553–558.Google Scholar

Brutin, D. (2003). Drop impingement on a deep liquid surface: study of a crater's sinking dynamics, C. R. Mec. 331: 61–67.Google Scholar

Bush, J.W.M. and Aristoff, J. M. (2003). The influence of surface tension on the circular hydraulic jump, J. Fluid Mech. 489: 229–238.Google Scholar

Bush, J. W. M. and Hasha, A. E. (2004). On the collision of laminar jets: fluid chains and fishbones, J. Fluid Mech. 511: 285–310.Google Scholar

Carroll, K. and Mesler, R. (1981). Part ii: Bubble entrainment by drop-formed vortex rings, AIChE J. 27: 853–856.Google Scholar

Clanet, C. (2001). Dynamics and stability of water bells, J. Fluid Mech. 430: 111–147.Google Scholar

Clanet, C. and Villermaux, E. (2002). Life of a smooth liquid sheet, J. Fluid Mech. 462: 307–340.Google Scholar

Clark, C. J. and Dombrowski, N. (1972). On the formation of drops from the rims of fan spray sheets, J. Aerosol Sci. 3: 173–183.Google Scholar

Cossali, G. E., Brunello, G., Coghe, A. and Marengo, M. (1999). Impact of a single drop on a liquid film: experimental analysis and comparison with empirical models, in Proc. Italian Congress of Thermofluid Dynamics UIT, Ferrara, Italy.

Cossali, G. E., Coghe, A. and Marengo, M. (1997). The impact of a single drop on a wetted surface, Exp. Fluids 22: 463–472.Google Scholar

Cossali, G. E., Marengo, M., Coghe, A. and Zhdanov, S. (2004). The role of time in single drop splash on thin film, Exp. Fluids 36: 888–900.Google Scholar

Culick, F. E. C. (1960). Comments on a ruptured soap film, J. Appl. Phys. 31: 1128–1129.Google Scholar

Deegan, R. D., Brunet, P. and Eggers, J. (2007). Complexities of splashing, Nonlinearity 21: C1–C11.Google Scholar

Eggers, J. (1997). Nonlinear dynamics and breakup of free-surface flows, Rev. Mod. Phys. 69: 865–929.Google Scholar

Eggers, J. and Villermaux, E. (2008). Physics of liquid jets, Rep. Prog. Phys. 71: 036601.Google Scholar

Engel, O. G. (1966). Crater depth in fluid impacts, J. Appl. Phys. 37: 1798–1808.Google Scholar

Engel, O. G. (1967). Initial pressure, initial flow velocity, and the time dependence of crater depth in fluid impacts, J. Appl. Phys. 38: 3935–3940.Google Scholar

Entov, V. M. (1982). On the dynamics of films of viscous and elastoviscous liquids, Arch. Mech. Stosow. 34: 395–407.Google Scholar

Entov, V. M., Rozhkov, A. N., Feizkhanov, U. F. and Yarin, A. L. (1986). Dynamics of liquid films. Plane films with free rims, J. Appl. Mech. Tech. Phys. 27: 41–47.Google Scholar

Entov, V. M. and Yarin, A. L. (1984). The dynamics of thin liquid jets in air, J. Fluid Mech. 140: 91–111.Google Scholar

Esmailizadeh, L. and Mesler, R. (1986). Bubble entrainment with drops, J. Colloid Interface Sci. 110: 561–574.Google Scholar

Fedorchenko, A. I. and Wang, A. B. (2004). On some common features of drop impact on liquid surfaces, Phys. Fluids 16: 1349–1365.Google Scholar

Frankel, I. and Weihs, D. (1985). Stability of a capillary jet with linearly increasing axial velocity (with application to shaped charges), J. Fluid Mech. 155: 289–307.Google Scholar

Franz, G. J. (1959). Splashes as sources of sound in liquids, J. Acoust. Soc. Am. 31: 1080–1096.Google Scholar

Fullana, J. M. and Zaleski, S. (1999). Stability of a growing end rim in a liquid sheet of uniform thickness, Phys. of Fluids 11: 952–954.Google Scholar

Gorokhovski, M. and Herrmann, M. (2008). Modeling primary atomization, Annu. Rev. Fluid Mech. 40: 343–366.Google Scholar

Harlow, H. and Shannon, J. P. (1967). The splash of a liquid drop, J. Appl. Phys. 38: 3855–3866.Google Scholar

Holsapple, K. A. and Schmidt, R. M. (1987). Point source solutions and coupling parameters in cratering mechanics, J. Geophys. Res. Solid Earth 92: 6350–6376.Google Scholar

Hsiang, L. P. and Faeth, G. M. (1992). Near-limit drop deformation and secondary breakup, Int. J. Multiph. Flow 18: 635–652.Google Scholar

Hsiang, L. P. and Faeth, G. M. (1995). Drop deformation and breakup due to shock wave and steady disturbances, Int. J. Multiph. Flow 21: 545–560.Google Scholar

Jayaratne, O. and Mason, B. (1964). The coalescence and bouncing of water drops at an air/water interface, Proc. R. Soc. London Ser. A-Math. 280: 545–565.Google Scholar

Josserand, C. and Thoroddsen, S. T. (2016). Drop impact on a solid surface, Annu. Rev. Fluid Mech. 48: 365–391.Google Scholar

Josserand, C. and Zaleski, S. (2003). Droplet splashing on a thin liquid film, Phys. Fluids 15: 1650–1657.Google Scholar

Khakhar, D. V. and Ottino, J. M. (1987). Breakup of liquid threads in linear flows, Int. J. Multiph. Flow 13: 71–86.Google Scholar

Kolbasov, A., Sinha-Ray, S., Joijode, A., Hassan, M. A., Brown, D., Maze, B., Pourdeyhimi, B. and Yarin, A. L. (2016). Industrial-scale solution blowing of soy protein nanofibers, Ind. Eng. Chem. Res. 58: 323–333.Google Scholar

Krechetnikov, R. and Homsy, G. M. (2009). Crown-forming instability phenomena in the drop splash problem, J. Colloid Interface Sci. 331: 555–559.Google Scholar

Lavergne, G. and Platet, B. (2000). Droplet impingement on gold and wet wall, ILASS-Europe, Sept. 2000 pp. 11–13.

Leng, L. J. (2001). Splash formation by spherical drops, J. Fluid Mech. 427: 73–105.Google Scholar

Levin, Z. and Hobbs, P. V. (1971). Splashing of water drops on solid and wetted surfaces: hydrodynamics and charge separation, Philos. Trans. R. Soc. Lond. Ser. A-Math. Phys. Eng. Sci. 269: 555–585.Google Scholar

Lin, S. and Reitz, R. (1998). Drop and spray formation from a liquid jet, Annu. Rev. Fluid Mech. 30: 85–105.Google Scholar

Macklin, W. C. and Metaxas, G. J. (1976). Splashing of drops on liquid layers, J. Appl. Phys. 47: 3963–3970.Google Scholar

Merzhievsky, L. A. (1997). Crater formation in a plastic target under hypervelocity impact, Int. J. Impact Eng. 20: 557.–568. Google Scholar

Mundo, C. H. R., Sommerfeld, M. and Tropea, C. (1995). Droplet-wall collisions: experimental studies of the deformation and breakup process, Int. J. Multiph. Flow 21: 151–173.Google Scholar

Mundo, C., Sommerfeld, M. and Tropea, C. (1998). On the modeling of liquid sprays impinging on surfaces, Atom. Sprays 8: 625–652.Google Scholar

Õguz, H. N. and Prosperetti, A. (1989). Surface-tension effects in the contact of liquid surfaces, J. Fluid Mech. 203: 149–171.Google Scholar

Õguz, H. N. and Prosperetti, A. (1990). Bubble entrainment by the impact of drops on liquid surfaces, J. Fluid Mech. 219: 143–179.Google Scholar

Olevson, K. L. R. (1969). Energy balances for transient water craters, US Geol. Surv. Prof. Paper 650-D: D189–D194.Google Scholar

Panão, M. R. O. and Moreira, A. L. N. (2005). Flow characteristics of spray impingement in PFI injection systems, Exp. Fluids 39: 364–374.Google Scholar

Peregrine, D. H. (1981). The fascination of fluid mechanics, J. Fluid Mech. 106: 59–80.Google Scholar

Prosperetti, A. and Õguz, H. N. (1993). The impact of drops on liquid surfaces and the underwater noise of rain, Annu. Rev. Fluid Mech. 25: 577–602.Google Scholar

Pumphrey, H. C. and Elmore, P. A. (1990). The entrainment of bubbles by drop impacts, J. Fluid Mech. 220: 539–567.Google Scholar

Range, K. and Feuillebois, F. (1998). Influence of surface roughness on liquid drop impact, J. Colloid Interface Sci. 203: 16–30.Google Scholar

Lord, Rayleigh (1878). On the instability of jets, Proc. Lond. Math. Soc. 1: 4–13.Google Scholar

Rein, M. (1993). Phenomena of liquid drop impact on solid and liquid surfaces, Fluid Dyn. Research 12: 61–93.Google Scholar

Rieber, M. and Frohn, A. (1999). A numerical study on the mechanism of splashing, Int. J. Heat Fluid Flow 20: 455–461.Google Scholar

Rioboo, R., Bauthier, C., Conti, J., Voué, M. and DeConinck, J. (2003). Experimental investigation of splash and crown formation during single drop impact on wetted surfaces, Exp. Fluids 35: 648–652.Google Scholar

Rodriguez, F. and Mesler, R. (1985). Some drops don't splash, J. Colloid Interface Sci. 106: 347–352.Google Scholar

Roisman, I. V. (2004). Dynamics of inertia dominated binary drop collisions, Phys. Fluids 16: 3438–3449.Google Scholar

Roisman, I. V. (2009). Inertia dominated drop collisions. II. An analytical solution of the Navier– Stokes equations for a spreading viscous film, Phys. Fluids 21: 052104.Google Scholar

Roisman, I. V. (2010). On the instability of a free viscous rim, J. Fluid Mech. 661: 206–228.Google Scholar

Roisman, I. V., Araneo, L., Marengo, M. and Tropea, C. (1999). Evaluation of drop impingement models: experimental and numerical analysis of a spray impact, in Proc. 15th Ann. Conf. on Liquid Atomization and Spray Systems, ILASS-Europe, Toulouse, France.

Roisman, I. V., Gambaryan-Roisman, T., Kyriopoulos, O., Stephan, P. and Tropea, C. (2007). Breakup and atomization of a stretching crown, Phys. Rev. E 76: 026302.Google Scholar

Roisman, I. V., Horvat, K. and Tropea, C. (2006). Spray impact: Rim transverse instability initiating fingering and splash, and description of a secondary spray, Phys. Fluids 18: 102104.Google Scholar

Roisman, I. V., Rioboo, R. and Tropea, C. (2002). Normal impact of a liquid drop on a dry surface: model for spreading and receding, Proc. R. Soc. London Ser. A-Math. 458: 1411–1430.Google Scholar

Roisman, I. V. and Tropea, C. (2002). Impact of a drop onto a wetted wall: description of crown formation and propagation, J. Fluid Mech. 472: 373–397.Google Scholar

Roisman, I. V., van Hinsberg, N. P. and Tropea, C. (2008). Propagation of a kinematic instability in a liquid layer: capillary and gravity effects, Phys. Rev. E 77: 046305.Google Scholar

Rozhkov, A. N., Prunet-Foch, B. and Vignes-Adler, M. (2002). Impact of water drops on small targets, Phys. Fluids 14: 3485–3501.Google Scholar

Savva, N. and Bush, J. W. M. (2009). Viscous sheet retraction, J. Fluid Mech. 626: 211–240.Google Scholar

Schelkle, von, M., Rieber, M. and Frohn, A. (1999). Numerische Simulation von Tropfenkollisionen, Spektrum der Wissenschaft pp. 72–79.

Schneider, L., Le Lostec, N., Villedieu, P. and Sadiki, A. (2010). A moment method for splashing and evaporation processes of polydisperse sprays, Int. J. Multiph. Flow 36: 261–272.Google Scholar

Shin, J. and McMahon, T. A. (1990). The tuning of a splash, Phys. Fluids A-Fluid 8: 1312–1317.Google Scholar

Stanton, D. W. and Rutland, C. J. (1998). Multi-dimensional modeling of thin liquid films and spray-wall interactions resulting from impinging sprays, Int. J. Heat Mass. Transf. 41: 3037–3054.Google Scholar

Sivakumar, D. and Tropea, C. (2002). Splashing impact of a spray onto a liquid film, Phys. Fluids 14: L85–L88.Google Scholar

Taylor, G. I. (1959a). The dynamics of thin sheets of fluid. I. Water bells, Proc. R. Soc. London Ser. A-Math. 253: 289–295.Google Scholar

Taylor, G. I. (1959b). The dynamics of thin sheets of fluid II. Waves on fluid sheets., Proc. R. Soc. London Ser. A-Math. 253: 296–312.Google Scholar

Taylor, G. I. (1959c). The dynamics of thin sheets of fluid. III. Disintegration of fluid sheets, 253: 313–321.

Thoroddsen, S. T. (2002). The ejecta sheet generated by the impact of a drop, J. Fluid Mech. 451: 373–381.Google Scholar

Tomotika, S. (1935). On the instability of a cylindrical thread of a viscous liquid surrounded by another viscous fluid, Proc. R. Soc. London Ser. A-Math. 150: 322–337.Google Scholar

Tropea, C. and Roisman, I. V. (2000). Modelling of spray impact on solid surfaces, Atom. Sprays 10: 387–408.Google Scholar

Trujillo, M. F. and Lee, C. F. (2001). Modeling crown formation due to the splashing of a droplet, Phys. Fluids 13: 2503–2516.Google Scholar

van Hinsberg, N. P., Budakli, M., Göhler, S., Berberović, E., Roisman, I. V., Gambaryan-Roisman, T., Tropea, C. and Stephan, P. (2010). Dynamics of the cavity and the surface film for impingements of single drops on liquid films of various thicknesses, J. Colloid Interface Sci. 350: 336–343.Google Scholar

Vander Wal, R. L., Berger, G. M. and Mozes, S. D. (2006). Droplets splashing upon films of the same fluid of various depths, Exp. Fluids 40: 33–52.Google Scholar

Villermaux, E. (2007). Fragmentation, Annu. Rev. Fluid Mech. 39: 419–446.Google Scholar

Visaria, M. and Mudawar, I. (2008). Theoretical and experimental study of the effects of spray inclination on two-phase spray cooling and critical heat flux, Int. J. Heat Mass Transf. 51: 2398.– 2410.Google Scholar

Walzel, P. (1980). Zerteilgrenze beim Tropfenaufprall, Chem. Ing. Tech. 52: 338–339.Google Scholar

Wang, A. B. and Chen, C. C. (2000). Splashing impact of a single drop onto very thin liquid films, Phys. Fluids 12: 2155–2158.Google Scholar

Wang, A. B., Kuan, C. C. and Tsai, P. H. (2013). Do we understand the bubble formation by a single drop impacting upon liquid surface?, Phys. Fluids 25: 101702.Google Scholar

Weber, C. (1931). Zum Zerfall eines Fluessigkeitsstrahles, Z. Angew. Math. Mech. 2: 136–154.Google Scholar

Weiss, D. A. and Yarin, A. L. (1999). Single drop impact onto liquid films: neck distortion, jetting, tiny bubble entrainment, and crown formation, J. Fluid Mech. 385: 229–254.Google Scholar

Worthington, A. M. (1908). A Study of Splashes, Longmans, Green, and Company, London.

Yarin, A. L. (1993). Free Liquid Jets and Films: Hydrodynamics and Rheology, Longman and John Wiley & Sons, Harlow and New York.

Yarin, A. L. (2006). Drop impact dynamics: splashing, spreading, receding, bouncing…, Annu. Rev. Fluid Mech. 38: 159–192.Google Scholar

Yarin, A. L. (2007). Self-similarity, in C., Tropea, A. L., Yarin and J. F., Foss (eds.), Springer Handbook of Experimental Fluid Mechanics, Springer, Berlin, pp. 57–82.

Yarin, A. L., Rubin, M. B. and Roisman, I. V. (1995). Penetration of a rigid projectile into an elastic-plastic target of finite thickness, Int. J. Impact Eng. 16: 801.– 831.Google Scholar

Yarin, A. L. and Weiss, D. A. (1995). Impact of drops on solid surfaces: Self-similar capillary waves, and splashing as a new type of kinematic discontinuity, J. Fluid Mech. 283: 141–173.Google Scholar

Yarin, L. P. (2012). The Pi-Theorem: Applications to Fluid Mechanics and Heat and Mass Transfer, Springer, Heidelberg.

Zhang, L. V., Brunet, P., Eggers, J. and Deegan, R. D. (2010). Wavelength selection in the crown splash, Phys. Fluids 22: 122105.Google Scholar