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From drop impact physics to spray cooling models: a critical review

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A Publisher Correction to this article was published on 26 April 2018

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Abstract

Spray–wall interaction is an important process encountered in a large number of existing and emerging technologies and is the underlying phenomenon associated with spray cooling. Spray cooling is a very efficient technology, surpassing all other conventional cooling methods, especially those not involving phase change and not exploiting the latent heat of vaporization. However, the effectiveness of spray cooling is dependent on a large number of parameters, including spray characteristics like drop size, velocity and number density, the surface morphology, but also on the temperature range and thermal properties of the materials involved. Indeed, the temperature of the substrate can have significant influence on the hydrodynamics of drop and spray impact, an aspect which is seldom considered in model formulation. This process is extremely complex, thus most design rules to date are highly empirical in nature. On the other hand, significant theoretical progress has been made in recent years about the interaction of single drops with heated walls and improvements to the fundamentals of spray cooling can now be anticipated. The present review has the objective of summarizing some of these recent advances and to establish a framework for future development of more reliable and universal physics-based correlations to describe quantities involved in spray cooling.

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Adapted from Breitenbach et al. (2017b)

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  • 26 April 2018

    The article category has been published incorrectly due to processing error. The correct category should read “Review Article”. We apologize for this lapse.

References

  • Aamir M, Qiang L, Hong W, Xun Z, Wang J, Sajid M (2017) Transient heat transfer performance of stainless steel structured surfaces combined with air-water spray evaporative cooling at high temperature scenarios. Appl Thermal Eng 115:418–434

    Article  Google Scholar 

  • Abu-Zaid M (2004) An experimental study of the evaporation characteristics of emulsified liquid droplets. Heat Mass Transf 40(9):737–741

    Google Scholar 

  • Bai C, Gosman AD (1995) Development of methodology for spray impingement simulation. Technical Report 950283. SAE Technical Paper

  • Bai C, Gosman AD (1996) Mathematical modelling of wall films formed by impinging sprays. Technical Report 960626. SAE Technical Paper

  • Bar-Cohen A, Arik M, Ohadi M (2006) Direct liquid cooling of high flux micro and nano electronic components. Proc IEEE 94(8):1549–1570

    Article  Google Scholar 

  • Batzdorf S, Breitenbach J, Schlawitschek C, Roisman IV, Tropea C, Stephan P, Gambaryan-Roisman T (2017) Heat transfer during simultaneous impact of two drops onto a hot solid substrate. Int J Heat Mass Transf 113:898–907

    Article  Google Scholar 

  • Berberović E, van Hinsberg NP, Jakirlić S, Roisman IV, Tropea C (2009) Drop impact onto a liquid layer of finite thickness: dynamics of the cavity evolution. Phys Rev E 79(3):036306

    Article  MathSciNet  Google Scholar 

  • Berberović E, Roisman IV, Jakirlić S, Tropea C (2011) Inertia dominated flow and heat transfer in liquid drop spreading on a hot substrate. Int J Heat Fluid Flow 32(4):785–795

    Article  MATH  Google Scholar 

  • Berenson PJ (1961) Film-boiling heat transfer from a horizontal surface. J Heat Transf 83(3):351–356

    Article  Google Scholar 

  • Bernardin JD, Mudawar I (1997) Film boiling heat transfer of droplet streams and sprays. Int J Heat Mass Transf 40(11):2579–2593

    Article  Google Scholar 

  • Bernardin JD, Mudawar I (1999) The Leidenfrost point: experimental study and assessment of existing models. J Heat Transf 121:894–903

    Article  Google Scholar 

  • Bernardin JD, Mudawar I (2004) A Leidenfrost point model for impinging droplets and sprays. J Heat Transf 126(2):272–278

    Article  Google Scholar 

  • Bernardin JD, Stebbins CJ, Mudawar I (1996) Effects of surface roughness on water droplet impact history and heat transfer regimes. Int J Heat Mass Transf 40(1):73–88

    Article  Google Scholar 

  • Bernardin JD, Stebbins CJ, Mudawar I (1997) Mapping of impact and heat transfer regimes of water drops impinging on a polished surface. Int J Heat Mass Transf 40(2):247–267

    Article  Google Scholar 

  • Bertola V (2015) An impact regime map for water drops impacting on heated surfaces. Int J Heat Mass Transf 85:430–437

    Article  Google Scholar 

  • Biance AL, Pirat C, Ybert C (2011) Drop fragmentation due to hole formation during Leidenfrost impact. Phys Fluids 23(2):022104

    Article  Google Scholar 

  • Bird JC, Tsai SS, Stone HA (2009) Inclined to splash: triggering and inhibiting a splash with tangential velocity. New J Phys 11(6):063017

    Article  Google Scholar 

  • Bisighini A, Cossali GE, Tropea C, Roisman IV (2010) Crater evolution after the impact of a drop onto a semi-infinite liquid target. Phys Rev E 82(3):036319

    Article  Google Scholar 

  • Bolle L, Moureau JC (1982) Spray cooling of hot surfaces. Multiphase Sci Technol 1(1–4)

  • Breitenbach J, Roisman IV, Tropea C (2017) Drop collision with a hot, dry solid substrate: Heat transfer during nucleate boiling. Phys Rev Fluids 2(7):074301

    Article  Google Scholar 

  • Breitenbach J, Roisman IV, Tropea C (2017) Heat transfer in the film boiling regime: single drop impact and spray cooling. Int J Heat Mass Transf 110:34–42

    Article  Google Scholar 

  • Brutin D (ed) (2015) Droplet wetting and evaporation: from pure to complex fluids. Academic Press, London

  • Buchmüller I (2014) Influence of pressure on Leidenfrost effect. Ph.D. thesis. TU Darmstadt. Darmstadt

  • Butt HJ, Roisman IV, Brinkmann M, Papadopoulos P, Vollmer D, Semprebon C (2014) Characterization of super liquid-repellent surfaces. Curr Opin Colloid Interface Sci 19(4):343–354

    Article  Google Scholar 

  • Carey VP (1992) Liquid-vapor phase-change phenomena: an introduction to the thermophysics of vaporization and condensation processes in heat transfer equipment. Series in Chemical and Mechanical Engineering. Taylor & Francis, Bristol

    Google Scholar 

  • Castanet G, Caballina O, Lemoine F (2015) Drop spreading at the impact in the Leidenfrost boiling. Phys Fluids 27(6):063302

    Article  Google Scholar 

  • Cazabat AM, Guena G (2010) Evaporation of macroscopic sessile droplets. Soft Matter 6(12):2591–2612

    Article  Google Scholar 

  • Celata GP, Cumo M, Mariani A, Zummo G (2006) Visualization of the impact of water drops on a hot surface: effect of drop velocity and surface inclination. Heat Mass Transf 42(10):885–890

    Article  Google Scholar 

  • Chandra S, Avedisian CT (1991) On the collision of a droplet with a solid surface. Proc R Soc Lond A Math Phys Sci 432(1884):13–41

    Article  Google Scholar 

  • Chaze W, Caballina O, Castanet G, Lemoine F (2016) The saturation of the fluorescence and its consequences for laser-induced fluorescence thermometry in liquid flows. Exp Fluids 57(4):58

    Article  Google Scholar 

  • Chaze W, Caballina O, Castanet G, Lemoine F (2017) Spatially and temporally resolved measurements of the temperature inside droplets impinging on a hot solid surface. Exp Fluids 58(8):96

    Article  Google Scholar 

  • Chen RH, Chow LC, Navedo JE (2002) Effects of spray characteristics on critical heat flux in subcooled water spray cooling. Int J Heat Mass Transf 45(19):4033–4043

    Article  Google Scholar 

  • Chen SJ, Tseng AA (1992) Spray and jet cooling in steel rolling. Int J Heat Mass Transf 13(4):358–369

    Google Scholar 

  • Cheng L (1977) Dynamic spreading of drops impacting onto a solid surface. Ind Eng Chem Process Des Dev 16(2):192–197

    Article  Google Scholar 

  • Cheng WL, Zhang WW, Chen H, Hu L (2016) Spray cooling and flash evaporation cooling: the current development and application. Renew Sust Energ Rev 55:614–628

    Article  Google Scholar 

  • Cho J, Goodson KE (2015) Thermal transport: cool electronics. Nat Mater 14:136–137

    Article  Google Scholar 

  • Choi K, Yao S (1987) Mechanisms of film boiling heat transfer of normally impacting spray. Int J Heat Mass Transf 30(2):311–318

    Article  Google Scholar 

  • Clanet C, Béguin C, Richard D, Quéré D (2004) Maximal deformation of an impacting drop. J Fluid Mech 517:199

    Article  MATH  Google Scholar 

  • Collings EW, Markworth JK, McCoy JK, Saunders JH (1990) Splat-quench solidification of freely falling liquid-metal drops by impact on a planar substrate. J Mater Sci 25:3677–3682

    Article  Google Scholar 

  • Cossali GE, Coghe A, Marengo M (1997) The impact of a single drop on a wetted surface. Exp Fluids 22:463–472

    Article  Google Scholar 

  • Cossali GE, Marengo M, Coghe A, Zhdanov S (2004) The role of time in single drop splash on thin film. Exp Fluids 36(6):888–900

    Article  Google Scholar 

  • Cossali GE, Marengo M, Santini M (2005) Single-drop empirical models for spray impact on solid walls: a review. Atom Sprays 15:699–736

    Article  Google Scholar 

  • van Dam DB, Clerc CL (2004) Experimental study of the impact of an ink-jet printed droplet on a solid substrate. Phys Fluids 16(9):3403–3414

    Article  MATH  Google Scholar 

  • Datrice N, Ramirez-San-Juan J, Zhang R, Meshkinpour A, Aguilar G, Nelson JS, Kelly KM (2006) Cutaneous effects of cryogen spray cooling on in vivo human skin. Dermatol Surg 32(8):1007–1012

    Google Scholar 

  • Deng W, Gomez A (2011) Electrospray cooling for microelectronics. Int J Heat Mass Transf 54(11):2270–2275

    Article  Google Scholar 

  • Elston LJ, Yerkes KL, Thomas SK, McQuillen J (2009) Cooling performance of a 16-Nozzle array in variable gravity. J Thermophys Heat Transf 23(3):571

    Article  Google Scholar 

  • Erbil HY (2012) Evaporation of pure liquid sessile and spherical suspended drops: a review. Adv Colloid Interface Sci 170(1–2):67–86

    Article  Google Scholar 

  • Estes KA, Mudawar I (1995) Correlation of Sauter mean diameter and critical heat flux for spray cooling of small surfaces. Int J Heat Mass Transf 38(16):2985–2996

    Article  Google Scholar 

  • Fabbri M, Jiang S, Dhir VK (2005) A comparative study of cooling of high power density electronics using sprays and microjets. J Heat Transf 127(1):38–48

    Article  Google Scholar 

  • Fedorchenko AI, Wang AB (2004) On some common features of drop impact on liquid surfaces. Phys Fluids 16(5):1349–1365

    Article  MathSciNet  MATH  Google Scholar 

  • Forster HK, Zuber N (1954) Growth of a vapor bubble in a superheated liquid. J Appl Phys 25(4):474–478

    Article  MathSciNet  MATH  Google Scholar 

  • Foucart H, Habchi C, Le Coz JF, Baritaud T (1998) Development of a three dimensional model of wall fuel liquid film for internal combustion engines. Technical Report 980133. SAE Technical Paper

  • Fukai J, Shiiba Y, Yamamoto T, Miyatake O, Poulikakos D, Megaridis CM, Zhao Z (1995) Wetting effects on the spreading of a liquid droplet colliding with a flat surface: experiment and modeling. Phys Fluids 7:236–247

    Article  Google Scholar 

  • Ghodbane M, Holman J (1991) Experimental study of spray cooling with Freon-113. Int J Heat Mass Transf 34(4):1163–1174

    Article  Google Scholar 

  • Griffith P (1958) Bubble growth rates in boiling. J Heat Transf 80:721–726

    Google Scholar 

  • Gross KA, Berndt CC (1998) Thermal processing of hydroxyapatite for coating production. J Biomed Mater Res 39(4):580–587

    Article  Google Scholar 

  • Hall DD, Mudawar I (1995) Experimental and numerical study of quenching complex-shaped metallic alloys with multiple, overlapping sprays. Int J Heat Mass Transf 38(7):1201–1216

    Article  Google Scholar 

  • Herbert S, Fischer S, Gambaryan-Roisman T, Stephan P (2013) Local heat transfer and phase change phenomena during single drop impingement on a hot surface. Int J Heat Mass Transf 61:605–614

    Article  Google Scholar 

  • van Hinsberg NP, Budakli M, Göhler S, Berberović E, Roisman IV, Gambaryan-Roisman T, Tropea C, 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(1):336–343

    Article  Google Scholar 

  • Holman J, Kendall C (1993) Extended studies of spray cooling with Freon-113. Int J Heat Mass Transf 36(8):2239–2241

    Article  Google Scholar 

  • Hong K, Lee SH, Ryou HS (2001) Modelling of wall films formed by impinging diesel sprays. Technical Report 2001-01-3228. SAE Technical Paper

  • Hsieh CC, Yao SC (2006) Evaporative heat transfer characteristics of a water spray on micro-structured silicon surfaces. Int J Heat Mass Transf 49(5):962–974

    Article  Google Scholar 

  • Hsieh SS, Fan TC, Tsai HH (2004) Spray cooling characteristics of water and R-134a. Part I: nucleate boiling. Int J Heat Mass Transf 47(26):5703–5712

    Article  Google Scholar 

  • Hsieh SS, Hsu YF, Wang ML (2014) A microspray-based cooling system for high powered LEDs. Energy Convers Manag 78:338–346

    Article  Google Scholar 

  • Huddle JJ, Chow LC, Lei S, Marcos A, Rini D, Lindauer S, Bass M, Delfyett P (2000) Thermal management of diode laser arrays. In 16th Annual IEEE Semiconductor Thermal Measurement and Management Symposium, 2000. IEEE. (pp 154–160)

  • Itaru M, Kunihide M (1978) Heat transfer characteristics of evaporation of a liquid droplet on heated surfaces. Int J Heat Mass Transf 21(5):605–613

    Article  Google Scholar 

  • Josserand C, Thoroddsen ST (2016) Drop impact on a solid surface. Annu Rev Fluid Mech 48(1):365–391

    Article  MathSciNet  MATH  Google Scholar 

  • Karbalaei A, Kumar R, Cho HJ (2016) Thermocapillarity in microfluidics: a review. Micromachines 7(1):13

    Article  Google Scholar 

  • Karl A, Anders K, Rieber M, Frohn A (1996) Deformation of liquid droplets during collisions with hot walls: experimental and numerical results. Part Part Syst Charact 13(3):186–191

    Article  Google Scholar 

  • Karwa N, Kale SR, Subbarao P (2007) Experimental study of non-boiling heat transfer from a horizontal surface by water sprays. Exp Therm Fluid Sci 32(2):571–579

    Article  Google Scholar 

  • Kato M, Abe Y, Mori YH, Nagashima A (1995) Spray cooling characteristics under reduced gravity. J Thermophys Heat Transf 9(2):378–380

    Article  Google Scholar 

  • Kelly KM, Nelson JS, Lask GP, Geronemus RG, Bernstein LJ (1999) Cryogen spray cooling in combination with nonablative laser treatment of facial rhytides. Arch Dermatol 135(6):691–694

    Article  Google Scholar 

  • Khavari M, Sun C, Lohse D, Tran T (2015) Fingering patterns during droplet impact on heated surfaces. Soft Matter 11(17):32983303

    Article  Google Scholar 

  • Kim J (2007) Spray cooling heat transfer: the state of the art. Int J Heat Fluid Flow 28(4):753–767

    Article  Google Scholar 

  • Kim J, You S, Choi SU (2004) Evaporative spray cooling of plain and microporous coated surfaces. Int J Heat Mass Transf 47(14):3307–3315

    Article  Google Scholar 

  • Klinzing WP, Rozzi JC, Mudawar I (1992) Film and transition boiling correlations for quenching of hot surfaces with water sprays. J Heat Treat 9(2):91–103

    Article  Google Scholar 

  • Kovalchuk NM, Trybala A, Starov VM (2014) Evaporation of sessile droplets. Curr Opin Colloid Interface Sci 19(4):336–342

    Article  Google Scholar 

  • Kunkelmann C, Ibrahem K, Schweizer N, Herbert S, Stephan P, Gambaryan-Roisman T (2012) The effect of three-phase contact line speed on local evaporative heat transfer: experimental and numerical investigations. Int J Heat Mass Transf 55(7):1896–1904

    Article  Google Scholar 

  • Kyriopoulos ON (2010) Gravity effect on liquid film hydrodynamics and spray cooling. Ph.d. thesis. Technische Universität Darmstadt. Darmstadt, Germany

  • Labergue A, Gradeck M, Lemoine F (2015) Comparative study of the cooling of a hot temperature surface using sprays and liquid jets. Int J Heat Mass Transf 81(Supplement C):889–900

    Article  Google Scholar 

  • Lagubeau G, Fontelos MA, Josserand C, Maurel A, Pagneux V, Petitjeans P (2012) Spreading dynamics of drop impacts. J Fluid Mech 713:5060

    Article  MATH  Google Scholar 

  • Leidenfrost JG (1756) De aquae Communis Nonnullis Qualitatibus Tractatus. Ovenius, Duisburg ad Rhenum. See the translation in Int J Heat Mass Transf 9:1153–1166 (1966)

  • Lembach AN, Tan HB, Roisman IV, Gambaryan-Roisman T, Zhang Y, Tropea C, Yarin AL (2010) Drop impact, spreading, splashing, and penetration into electrospun nanofiber mats. Langmuir 26(12):9516–9523

    Article  Google Scholar 

  • Liang G, Mudawar I (2017a) Review of drop impact on heated walls. Int J Heat Mass Transf 106:103–126

    Article  Google Scholar 

  • Liang G, Mudawar I (2017) Review of spray cooling – Part 1: single-phase and nucleate boiling regimes, and critical heat flux. Int J Heat Mass Transf 115(Part A):1174–1205

    Article  Google Scholar 

  • Liang G, Mudawar I (2017) Review of spray cooling – Part 2: high temperature boiling regimes and quenching applications. Int J Heat Mass Transf 115(Part A):1206–1222

    Article  Google Scholar 

  • Lin L, Ponnappan R (2003) Heat transfer characteristics of spray cooling in a closed loop. Int J Heat Mass Transf 46(20):3737–3746

    Article  Google Scholar 

  • Liu H, Lee CF (2014) Numerical study on wall film formation and evaporation. Technical Report 2014-01-1112. SAE Technical Paper

  • Lopes MC, Bonaccurso E, Gambaryan-Roisman T, Stephan P (2013) Influence of the substrate thermal properties on sessile droplet evaporation: effect of transient heat transport. Colloids and Surf A: Physicochem Eng Aspects 432:64–70

    Article  Google Scholar 

  • Manzello SL, Yang JC (2002) On the collision dynamics of a water droplet containing an additive on a heated solid surface. Proc R Soc Lond A Math Phys Sci 458(2026):2417–2444

    Article  Google Scholar 

  • Marengo M, Antonini C, Roisman IV, Tropea C (2011) Drop collisions with simple and complex surfaces. Curr Opin Colloid Interface Sci 16(4):292–302

    Article  Google Scholar 

  • Marmanis H, Thoroddsen ST (1996) Scaling of the fingering pattern of an impacting drop. Phys Fluids 8(6):1344–1346

    Article  Google Scholar 

  • Mathur P, Apelian D, Lawley A (1989) Analysis of the spray deposition process. Acta Metall 37(2):429–443

    Article  Google Scholar 

  • Michalak TE, Yerkes KL, Thomas SK, McQuillen JB (2010) Acceleration effects on the cooling performance of a partially confined FC-72 spray. J Thermophys Heat Transf 24(3):463–479

    Article  Google Scholar 

  • Mikic BB, Rohsenow WM (1969) Bubble growth rates in non-uniform temperature field. Prog Heat Mass Transf 2:283–292

    Google Scholar 

  • Moita AS, Moreira AL (2012) Scaling the effects of surface topography in the secondary atomization resulting from droplet/wall interactions. Exp Fluids 52(3):679–695

    Article  Google Scholar 

  • Moreira A, Moita A, Panao M (2010) Advances and challenges in explaining fuel spray impingement: how much of single droplet impact research is useful? Prog Energy Combust Sci 36(5):554–580

    Article  Google Scholar 

  • Mudawar I, Deiters TA (1994) A universal approach to predicting temperature response of metallic parts to spray quenching. Int J Heat Mass Transf 37(3):347–362

    Article  Google Scholar 

  • Mudawar I, Valentine WS (1989) Determination of the local quench curve for spray-cooled metallic surfaces. J Heat Treat 7(2):107–121

    Article  Google Scholar 

  • Mühlbauer M (2010) Modelling wall interactions of a high-pressure, hollow cone spray. Ph.D. thesis. Technische Universität Darmstadt. Darmstadt, Germany

  • Mundo C, Sommerfeld M, Tropea C (1995) Droplet-wall collisions: experimental studies of the deformation and breakup process. Int J Multiph Flow 21(2):151–173

    Article  MATH  Google Scholar 

  • Nelson JS, Milner TE, Anvari B, Tanenbaum BS, Kimel S, Svaasand LO, Jacques SL (1995) Dynamic epidermal cooling during pulsed laser treatment of port-wine stain: a new methodology with preliminary clinical evaluation. Arch Dermatol 131(6):695–700

    Article  Google Scholar 

  • Nishio S, Kim YC (1998) Heat transfer of dilute spray impinging on hot surface (simple model focusing on rebound motion and sensible heat of droplets). Int J Heat Mass Transf 41(24):4113–4119

    Article  MATH  Google Scholar 

  • Ohtake H, Koizumi Y (2004) Study on propagative collapse of a vapor film in film boiling (mechanism of vapor-film collapse at wall temperature above the thermodynamic limit of liquid superheat). Int J Heat Mass Transf 47(8):1965–1977

    Article  Google Scholar 

  • Oliphant K, Webb B, McQuay M (1998) An experimental comparison of liquid jet array and spray impingement cooling in the non-boiling regime. Exp Therm Fluid Sci 18(1):1–10

    Article  Google Scholar 

  • Opfer L (2014) Controlling Liquid Atomization using Dilute Emulsions: Mitigation of Pesticide Spray Drift. Ph.D. thesis. Technische Universität Darmstadt. Darmstadt, Germany

  • O’Rourke PJ, Amsden A (2000) A spray/wall interaction submodel for the KIVA-3 wall film model. Technical Report 2000-01-0271. SAE Technical Paper

  • Pais MR, Chow LC, Mahefkey ET (1992) Surface roughness and its effects on the heat transfer mechanism in spray cooling. J Heat Transf 114(1):211–219

    Article  Google Scholar 

  • Palacios J, Hernández J, Gómez P, Zanzi C, López J (2013) Experimental study of splashing patterns and the splashing/deposition threshold in drop impacts onto dry smooth solid surfaces. Exp Therm Fluid Sci 44:571–582

    Article  Google Scholar 

  • Pan KL, Tseng KC, Wang CH (2010) Breakup of a droplet at high velocity impacting a solid surface. Exp Fluids 48(1):143–156

    Article  Google Scholar 

  • Pasandideh-Fard M, Qiao YM, Chandra S, Mostaghimi J (1996) Capillary effects during droplet impact on a solid surface. Phys Fluids 8:650–659

    Article  Google Scholar 

  • Puschmann F (2003) Experimentelle Untersuchung der Spraykühlung zur Qualitätsverbesserung durch definierte Einstellung des Wärmeübergangs. Ph.D. thesis. Otto-von-Guericke-Universität Magdeburg, Universitätsbibliothek

  • Quere D (2013) Leidenfrost dynamics. Annu Rev Fluid Mech 45:197–215

    Article  MathSciNet  MATH  Google Scholar 

  • Rieber M, Frohn A (1999) A numerical study on the mechanism of splashing. Int J Heat Fluid Flow 20(5):455–461

    Article  Google Scholar 

  • Rini DP, Chen RH, Chow LC (2002) Bubble behavior and nucleate boiling heat transfer in saturated FC-72 spray cooling. ASME J Heat Transf 124(1):63–72

    Article  Google Scholar 

  • Rioboo R, Marengo M, Tropea C (2001) Outcomes from a drop impact on solid surfaces. Atom Sprays 11:155–165

    Google Scholar 

  • Rioboo R, Voué M, Vaillant A, De Coninck J (2008) Drop impact on porous superhydrophobic polymer surfaces. Langmuir 24(24):14074–14077

    Article  Google Scholar 

  • Roisman IV (2009) Inertia dominated drop collisions. II. An analytical solution of the Navier–Stokes equations for a spreading viscous film. Phys Fluids 21(5):052104

    Article  MATH  Google Scholar 

  • Roisman IV (2010) Fast forced liquid film spreading on a substrate: flow, heat transfer and phase transition. J Fluid Mech 656:189–204

    Article  MathSciNet  MATH  Google Scholar 

  • Roisman IV, Berberović E, Tropea C (2009) Inertia dominated drop collisions. I: on the universal flow in the lamella. Phys Fluids 21(5):052103

    Article  MATH  Google Scholar 

  • Roisman IV, Breitenbach J, Tropea C (2017) Thermal atomisation of a liquid drop after impact onto a hot substrate. J Fluid Mech (accepted)

  • Roisman IV, van Hinsberg NP, Tropea C (2008) Propagation of a kinematic instability in a liquid layer: capillary and gravity effects. Phys Rev E 77(4):046305

    Article  Google Scholar 

  • Roisman IV, Horvat K, Tropea C (2006) Spray impact: rim transverse instability initiating fingering and splash, and description of a secondary spray. Phys Fluids 18:102–104

    Article  MathSciNet  MATH  Google Scholar 

  • Roisman IV, Lembach A, Tropea C (2015) Drop splashing induced by target roughness and porosity: the size plays no role. Adv Colloid Interface Sci 222:615–621

    Article  Google Scholar 

  • Roisman IV, Rioboo R, Tropea C (2002) Normal impact of a liquid drop on a dry surface: model for spreading and receding. Proc R Soc Lond A Math Phys Sci 458(2022):1411–1430

    Article  MATH  Google Scholar 

  • Roisman IV, Tropea C (2005) Fluctuating flow in a liquid layer and secondary spray created by an impacting spray. Int J Multiph Flow 31(2):179–200

    Article  MATH  Google Scholar 

  • Rybicki JR, Mudawar I (2006) Single-phase and two-phase cooling characteristics of upward-facing and downward-facing sprays. Int J Heat Mass Transf 49(1):5–16

    Article  Google Scholar 

  • Saski K, Sugitani Y, Kawasaki M (1979) Heat transfer in spray cooling on hot surface. Tetsu-to-Hagane 65(1):90–96

    Article  Google Scholar 

  • Sawan ME, Carbon MW (1975) Spray-cooling and bottom-flooding work for LWR cores. Nucl Eng Des 32(2):191–207

    Article  Google Scholar 

  • Scheller BL, Bousfield DW (1995) Newtonian drop impact with a solid surface. AIChE J 41(6):1357–1367

    Article  Google Scholar 

  • Schmehl R, Rosskamp H, Willmann M, Wittig S (1999) CFD analysis of spray propagation and evaporation including wall film formation and spray/film interactions. Int J Heat Fluid Flow 20(5):520–529

    Article  Google Scholar 

  • Schremb M, Borchert S, Berberovic E, Jakirlic S, Roisman IV, Tropea C (2017) Computational modelling of flow and conjugate heat transfer of a drop impacting onto a cold wall. Int J Heat Mass Transf 109:971–980

    Article  Google Scholar 

  • Sehmbey MS, Chow LC, Hahn OJ, Pais MR (1995) Spray cooling of power electronics at cryogenic temperatures. J Thermophys Heat Transf 9(1):123–128

    Article  Google Scholar 

  • Senda J, Kanda T, Al-Roub M, Farrell PV, Fukami T, Fujimoto H (1997) Modeling spray impingement considering fuel film formation on the wall. Technical Report 970047. SAE Technical Paper

  • Senda J, Yamada K, Fujimoto H, Miki H (1988) The heat-transfer characteristics of a small droplet impinging upon a hot surface. JSME Int J II 31(1):105–111

    Google Scholar 

  • Shedd TA (2007) Next generation spray cooling: high heat flux management in compact spaces. Heat Transf Eng 28(2):87–92

    Article  Google Scholar 

  • Shirota M, van Limbeek MAJ, Sun C, Prosperetti A, Lohse D (2016) Dynamic Leidenfrost effect: relevant time and length scales. Phys Rev Lett 116:064501

    Article  Google Scholar 

  • Siemons N, Bruining H, Castelijns H, Wolf KH (2006) Pressure dependence of the contact angle in a CO2–H2O-coal system. J Colloid Interface Sci 297(2):755–761

    Article  Google Scholar 

  • Silk EA, Kim J, Kiger K (2006) Spray cooling of enhanced surfaces: impact of structured surface geometry and spray axis inclination. Int J Heat Mass Transf 49(25):4910–4920

    Article  Google Scholar 

  • Sinha-Ray S, Yarin AL (2014) Drop impact cooling enhancement on nano-textured surfaces. Part I: theory and results of the ground (1g) experiments. Int J Heat Mass Transf 70:1095–1106

    Article  Google Scholar 

  • Sivakumar D, Tropea C (2002) Splashing impact of a spray onto a liquid film. Phys Fluids 14(12):L85–L88

    Article  MATH  Google Scholar 

  • Sodtke C, Stephan P (2007) Spray cooling on micro structured surfaces. Int J Heat Mass Transf 50(19):4089–4097

    Article  Google Scholar 

  • Srikar R, Gambaryan-Roisman T, Steffes C, Stephan P, Tropea C, Yarin A (2009) Nanofiber coating of surfaces for intensification of drop or spray impact cooling. Int J Heat Mass Transf 52(25):5814–5826

    Article  MATH  Google Scholar 

  • Staat HJJ, Tran T, Geerdink B, Sun C, Gordillo JM, Lohse D (2015) Phase diagram for droplet impact on superheated surfaces. J Fluid Mech 779:R3

    Article  Google Scholar 

  • Stanton DW, Rutland CJ (1996) Modeling fuel film formation and wall interaction in diesel engines. Technical Report 960628. SAE Technical Paper

  • Stanton DW, Rutland CJ (1998) Multi-dimensional modeling of heat and mass transfer of fuel films resulting from impinging sprays. Technical Report 980132. SAE Technical Paper

  • Tartarini P, Lorenzini G, Randi MR (1999) Experimental study of water droplet boiling on hot, non-porous surfaces. Heat Mass Transf 34(6):437–447

    Article  Google Scholar 

  • Taylor GI (1959) The dynamics of thin sheets of fluid. II. Waves on fluid sheets. Proc R Soc Lond A Math Phys Sci 253(1274):296–312

    Article  MathSciNet  MATH  Google Scholar 

  • Testa P, Nicotra L (1986) Influence of pressure on the Leidenfrost temperature and on extracted heat fluxes in the transient mode and low pressure. J Heat Transf 108(4):916–921

    Article  Google Scholar 

  • Tilton DE, Kearns DA, Tilton CL (1994) Liquid nitrogen spray cooling of a simulated electronic chip. In Advances in cryogenic engineering. Springer, Boston, pp 1779–1786

  • Tran T, Staat HJJ, Prosperetti A, Sun C, Lohse D (2012) Drop impact on superheated surfaces. Phys Rev Lett 108(3):036101

    Article  Google Scholar 

  • Tropea C, Roisman IV (2000) Modelling of spray impact on solid surfaces. Atom Sprays 10:387–408

    Article  Google Scholar 

  • Tsui YC, Clyne TW (1997) An analytical model for predicting residual stresses in progressively deposited coatings. 1. Planar geometry. Thin Solid Films 306(1):23–33

    Article  Google Scholar 

  • Ukiwe C, Kwok DY (2005) On the maximum spreading diameter of impacting droplets on well-prepared solid surfaces. Langmuir 21:666–673

    Article  Google Scholar 

  • Vander Wal RL, Berger GM, Mozes SD (2006) The splash/non-splash boundary upon a dry surface and thin fluid film. Exp Fluids 40(1):53–59

    Article  Google Scholar 

  • Visaria M, Mudawar I (2008a) Effects of high subcooling on two-phase spray cooling and critical heat flux. Int J Heat Mass Transf 51(21):5269–5278

    Article  MATH  Google Scholar 

  • Visaria M, Mudawar I (2008b) 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(9):2398–2410

    Article  MATH  Google Scholar 

  • Visser CW, Frommhold PE, Wildeman S, Mettin R, Lohse D, Sun C (2015) Dynamics of high-speed micro-drop impact: numerical simulations and experiments at frame-to-frame times below 100 ns. Soft Matter 11(9):1708–1722

    Article  Google Scholar 

  • Walzel P (1980) Zerteilgrenze beim tropfenprall. Chemie Ingenieur Technik 52(4):338–339

    Article  Google Scholar 

  • Wang H, Wu J, Yang Q, Zhu X, Liao Q (2016) Heat transfer enhancement of ammonia spray cooling by surface modification. Int J Heat Mass Transf 101:60–68

    Article  Google Scholar 

  • Wang Y, Liu M, Liu D, Xu K, Chen Y (2010) Experimental study on the effects of spray inclination on water spray cooling performance in non-boiling regime. Exp Therm Fluid Sci 34(7):933–942

    Article  Google Scholar 

  • Weickgenannt CM, Zhang Y, Lembach AN, Roisman IV, Gambaryan-Roisman T, Yarin AL, Tropea C (2011) Nonisothermal drop impact and evaporation on polymer nanofiber mats. Phys Rev E 83(3):036305

    Article  Google Scholar 

  • Weiss C (2005) The liquid deposition fraction of sprays impinging vertical walls and flowing films. Int J Multiph Flow 31(1):115–140

    Article  MATH  MathSciNet  Google Scholar 

  • Wendelstorf J, Spitzer KH, Wendelstorf R (2008a) Spray water cooling heat transfer at high temperatures and liquid mass fluxes. Int J Heat Mass Transf 51(19):4902–4910

    Article  MATH  Google Scholar 

  • Wendelstorf R, Spitzer KH, Wendelstorf J (2008b) Effect of oxide layers on spray water cooling heat transfer at high surface temperatures. Int J Heat Mass Transf 51(19):4892–4901

    Article  MATH  Google Scholar 

  • Wildeman S, Visser CW, Sun C, Lohse D (2016) On the spreading of impacting drops. J Fluid Mech 805:636655

    Article  MathSciNet  Google Scholar 

  • Worthington AM (1876) On the forms assumed by drops of liquids falling vertically on a horizontal plate. Proc R Soc Lond 25(171–178):261–272

    Article  Google Scholar 

  • Worthington AM (1895) The splash of a drop. S.P.C.K, London

    Google Scholar 

  • Worthington AM, Cole RS (1897) Impact with a liquid surface, studied by the aid of instantaneous photography. Phil Trans R Soc Lond A 189:137–148

    Article  MATH  Google Scholar 

  • Xie JL, Tan YB, Duan F, Ranjith K, Wong TN, Toh KC, Choo KF, Chan PK (2013) Study of heat transfer enhancement for structured surfaces in spray cooling. Appl Thermal Eng 59(1):464–472

    Article  Google Scholar 

  • Xu L, Zhang WW, Nagel SR (2005) Drop splashing on a dry smooth surface. Phys Rev Lett 94(18):184505

    Article  Google Scholar 

  • Yamanouc A (1968) Effect of core spray cooling in transient state after loss of coolant accident. J Nucl Sci Technol 5(11):547–558

    Article  Google Scholar 

  • Yang J, Chow LC, Pais MR (1996) Nucleate boiling heat transfer in spray cooling. ASME J Heat Transf 118(3):668–671

    Article  Google Scholar 

  • Yao S, Choit K (1987) Heat transfer experiments of mono-dispersed vertically impacting sprays. Int J Multiph Flow 13(5):639–648

    Article  Google Scholar 

  • Yao SC, Cai KY (1988) The dynamics and Leidenfrost temperature of drops impacting on a hot surface at small angles. Exp Therm Fluid Sci 1(4):363–371

    Article  Google Scholar 

  • Yao SC, Cox TL (2002) A general heat transfer correlation for impacting water sprays on high-temperature surfaces. Exp Heat Transf 15(4):207–219

    Article  Google Scholar 

  • Yao SC, Henry RE (1978) An investigation of the minimum film boiling temperature on horizontal surfaces. J Heat Transf 100(2):260–267

    Article  Google Scholar 

  • Yarin AL (2006) Drop impact dynamics: splashing, spreading, receding, bouncing. Annu Rev Fluid Mech 38:159–192

    Article  MathSciNet  MATH  Google Scholar 

  • Yarin AL, Roisman IV, Tropea C (2017) Collision phenomena in liquids and solids. Cambridge University Press, Cambridge

    Book  MATH  Google Scholar 

  • Yarin AL, Weiss DA (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

    Article  Google Scholar 

  • Zenzie HH, Altshuler GB, Smirnov MZ, Anderson RR (2000) Evaluation of cooling methods for laser dermatology. Lasers Surg Med 26(2):130–144

    Article  Google Scholar 

  • Zhang Y, Jia M, Liu H, Xie M (2016) Development of an improved liquid film model for spray/wall interaction under engine-relevant conditions. Int J Multiph Flow 79:74–87

    Article  MathSciNet  Google Scholar 

  • Zhang Z, Jiang PX, Ouyang XL, Chen JN, Christopher DM (2014) Experimental investigation of spray cooling on smooth and micro-structured surfaces. Int J Heat Mass Transf 76:366–375

    Article  Google Scholar 

  • Zhang Z, Li J, Jiang PX (2013) Experimental investigation of spray cooling on flat and enhanced surfaces. Appl Therm Eng 51(1):102–111

    Article  Google Scholar 

  • Zhong L, Guo Z (2017) Effect of surface topography and wettability on the Leidenfrost effect. Nanoscale 9(19):6219–6236

    Article  Google Scholar 

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Acknowledgements

This work was supported by the German Research Foundation (Deutsche Forschungsgemeinschaft) in the framework of the SFB-TRR 75 Collaborative Research Center, subproject C4.

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  1. Institute for Fluid Mechanics and Aerodynamics, Technische Universität Darmstadt, Darmstadt, Germany

    Jan Breitenbach, Ilia V. Roisman & Cameron Tropea

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  1. Jan Breitenbach
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  2. Ilia V. Roisman
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  3. Cameron Tropea
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Correspondence to Ilia V. Roisman.

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Breitenbach, J., Roisman, I.V. & Tropea, C. From drop impact physics to spray cooling models: a critical review. Exp Fluids 59, 55 (2018). https://doi.org/10.1007/s00348-018-2514-3

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