Abstract
This chapter gives an overview of the interfacial dynamics of complex fluids, with focus on non-Newtonian drop impact phenomena and non-Newtonian sprays. After a general introduction about Newtonian drops and sprays, the impact dynamics of viscoelastic and viscoplastic drops on both homothermal and heated surfaces is discussed. Finally, capillary instabilities and the atomisation process of non-Newtonian fluids are described.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Attané P, Girard F, Morin V (2007) An energy balance approach of the dynamics of drop impact on a solid surface. Phys Fluids 19(1):012101
Barnes HA (1995) A review of the slip (wall depletion) of polymer solutions, emulsions and particle suspensions in viscometers: its cause, character, and cure. J Non-Newton Fluid Mech 56(3):221–251
Barnes AC, Neilson GW, Enderby JE (1995) The structure and dynamics of aqueous solutions containing complex molecules. J Mol Liq 65–66:99–106
Bartolo D, Boudaoud A, Narcy G, Bonn D (2007) Dynamics of non-newtonian droplets. Phys Rev Lett 99(17)
Bazilevskii AV, Voronkov SI, Entov VM, Rozhkov AN (1981) On orientational effects at breakup of jets and threads of dilute polymer-solutions. Dokl Akad Nauk SSSR 257(2):336–339
Bechtel SE, Bogy DB, Talke FE (1981) Impact of a liquid drop against a flat surface. IBM J Res Dev 25(6):963–971
Bergeron V, Martin J-Y, Vovelle L (1998) Interaction of droplets with a surface: impact and adhesion. In: Fifth international symposium on adjuvants and agrochemicals memphis, Tennessee, USA, 17–21 Aug 1998
Bergeron V, Bonn D, Martin J-Y, Vovelle L (2000) Controlling droplet deposition with polymer additives. Nature 405:772–775
Bergeron V, Martin J-Y, Vovelle L (2003) Use of polymers as sticking agents. US Pat 6:534–563
Bernardin JD, Mudawar I (2002) A cavity activation and bubble growth model of the leidenfrost point. J Heat Transf 124(5):864–874
Bertola V (2004) Drop impact on a hot surface: effect of a polymer additive. Experiments in fluids 37(5):653–664
Bertola V (2009a) Wicking with a yield stress fluid. J Phys Condens Matter 21(3)
Bertola V (2009b) An experimental study of bouncing leidenfrost drops: comparison between newtonian and viscoelastic liquids. Int J Heat Mass Transf 52(7):1786–1793
Bertola V (2010) Effect of polymer additives on the apparent dynamic contact angle of impacting drops. Colloids Surf A: Physicochem Eng Asp 363(1–3):135–140
Bertola V (2013) Dynamic wetting of dilute polymer solutions: the case of impacting droplets. Adv Colloid Interface Sci 193–194:1–11
Bertola V (2014) Effect of polymer concentration on the dynamics of dilute polymer solution drops impacting on heated surfaces in the leidenfrost regime. Exp Therm Fluid Sci 52:259–269
Bertola V (2015) An impact regime map for water drops impacting on heated surfaces. Int J Heat Mass Transf 85:430–437
Bertola V, Sefiane K (2005) Controlling secondary atomization during drop impact on hot surfaces by polymer additives. Phys Fluids 17(10):108104
Bertola V, Wang M (2015) Dynamic contact angle of dilute polymer solution drops impacting on a hydrophobic surface. Colloids Surf A: Physicochem Eng Asp 481:600–608
Biance A-L, Chevy F, Clanet C, Lagubeau G, Quéré D (2006) On the elasticity of an inertial liquid shock. J Fluid Mech 554(1):47–66
Biolè D, Bertola V (2015a) The fuzzy interface of a drop. Comput Vis Sci 17(1):19–32
Biolè D, Bertola V (2015b) A goniometric mask to measure contact angles from digital images of liquid drops. Colloids Surf A: Physicochem Eng Asp 467:149–156
Biolè D, Bertola V (2015c) The role of the microscale contact line dynamics in the wetting behaviour of complex fluids. Arch Mech 67(5):401–414
Biolè D, Wang M, Bertola V (2016) Assessment of direct image processing methods to measure the apparent contact angle of liquid drops. Exp Therm Fluid Sci 76:296–305
Black K, Bertola V (2013) Non-newtonian leidenfrost drops. At Sprays 23(3):233–247
Bonhoeffer B, Kwade A, Juhnke M (2017) Impact of formulation properties and process parameters on the dispensing and depositioning of drug nanosuspensions using micro-valve technology. J Pharmaceut Sci 106(4):1102–1110
Borodin O, Smith GD (2000) Molecular dynamics simulations of poly(ethylene oxide)/lii melts. 2. dynamic properties. Macromolecules 33(6):2273–2283
Bousfield DW, Keunings R, Marrucci G, Denn MM (1986) Nonlinear analysis of the surface tension driven breakup of viscoelastic filaments. J Non-Newton Fluid Mech 21:79–97
Brandrup J, Immergut EH, Grulke EA, Abe A, Bloch DR (2005) Polymer handbook, 4th edn. Wiley
Brenn G, Plohl G (2015) The oscillating drop method for measuring the deformation retardation time of viscoelastic liquids. J Non-Newton Fluid Mech 223:88–97
Brenn G, Plohl G (2017) The formation of drops from viscoelastic liquid jets and sheets—an overview. At Sprays 27:285–302
Brenn G, Liu ZB, Durst F (2000) Linear analysis of the temporal instability of axisymmetrical non-newtonian liquid jets. Int J Multiph Flow 26:1621–1644
Chandra S, Avedisian CT (1991) On the collision of a droplet with a solid surface. Proc R Soci Lond A: Math Phys Eng Sci 432:13–41
Chandrasekhar S (1961) Hydrodynamic and hydromagnetic stability. International series of monographs on physics. Clarendon Press
Chen L, Wang Y, Peng X, Zhu Q, Zhang K (2018) Impact dynamics of aqueous polymer droplets on superhydrophobic surfaces. Macromolucles 51(19):7817–7827
Chen S, Bertola V (2016a) The impact of viscoplastic drops on a heated surface in the leidenfrost regime. Soft Matter 12:7624–7631
Chen S, Bertola V (2016b) Jumps, somersaults, and symmetry breaking in leidenfrost drops. Phys Rev E 94(2)
Chibowski E (2003) Surface free energy of a solid from contact angle hysteresis. Adv Colloid Interface Sci 103(2):149–172
Chibowski E (2007) On some relations between advancing, receding and Young’s contact angles. Adv Colloid Interface Sci 133(1):51–59
Christanti Y, Walker LM (2001) Surface tension driven jet break up of strain-hardening polymer solutions. J Non-Newton Fluid Mech 100:9–26
Christanti Y, Walker LM (2002) Effect of fluid relaxation time of dilute polymer solutions on jet breakup due to a forced disturbance. J Rheol 46:733–748
Clanet C, Béguin C, Richard D, Quéré D (2004) Maximal deformation of an impacting drop. J Fluid Mech 517:199–208
Coussot P, Gaulard F (2005) Gravity flow instability of viscoplastic materials: the ketchup drip. Phys Rev E 72:031409
Crooks R, Cooper-White J, Boger DV (2001) The role of dynamic surface tension and elasticity on the dynamics of drop impact. Chem Eng Sci 56:5575–5592
de Gennes PG (1974) Coil-stretch transition of dilute flexible polymers under ultrahigh velocity gradients. J Chem Phys 60(12):5030–5042
de Gennes PG (1985) Wetting: statics and dynamics. Rev Mod Phys 57(3):827–863
Dexter RW (1996) Measurement of extensional viscosity of polymer solutions and its effects on atomization from a spray nozzle. At Sprays 6:167–191
Dombrowski N, Johns WR (1963) The aerodynamic instability and disintegration of viscous liquid sheets. Chem Eng Sci 18:203–214
Dussan EB (1985) On the ability of drops or bubbles to stick to non-horizontal surfaces of solids. Part 2. small drops or bubbles having contact angles of arbitrary size. J Fluid Mech 151:1–20
Eggers J (1997) Nonlinear dynamics and breakup of free-surface flows. Rev Mod Phys 69:865–930
Eggers J, Fontelos MA, Josserand C, Zaleski S (2010) Drop dynamics after impact on a solid wall: theory and simulations. Phys Fluids 22(6):062101
Entov VM, Hinch EJ (1997) Effect of a spectrum of relaxation times on the capillary thinning of a filament of elastic liquid. J Non-Newton Fluid Mech 72:31–53
Ford RE, Furmidge CGL (1967) Impact and spreading of spray drops on foliar surfaces. Soc Chem Ind Monogr 25:32–417
Fujimoto H, Oku Y, Ogihara T, Takuda H (2010) Hydrodynamics and boiling phenomena of water droplets impinging on hot solid. Int J Multiph Flow 36(8):620–642. ISSN 0301-9322
German G, Bertola V (2009a) Impact of shear-thinning and yield-stress drops on solid substrates. J Phys: Condens Matter 21(37):375111
German G, Bertola V (2009b) Review of drop impact models and validation with high-viscosity newtonian fluids. At Sprays 19(8)
German G, Bertola V (2010a) The free-fall of viscoplastic drops. J Non-Newton Fluid Mech 165(13–14):825–828
German G, Bertola V (2010b) Formation of viscoplastic drops by capillary breakup. Phys Fluids 22(3):033101
Goldin M, Yerushalmi J, Pfeffer R, Shinnar R (1969) Breakup of a laminar capillary jet of a viscoelastic fluid. J Fluid Mech 38:689–711
Gottfried BS, Lee CJ, Bell KJ (1966) The leidenfrost phenomenon: film boiling of liquid droplets on a flat plate. Int J Heat Mass Transf 9(11):1167–1188
Harrison GM, Mun R, Cooper G, Boger DV (1999) A note on the effect of polymer rigidity and concentration on spray atomisation. J Non-Newton Fluid Mech 85:93–104
Hartnett JP, Hu RYZ (1986) Role of rheology in boiling studies of viscoelastic liquids. Int Commun Heat Mass Transf 13(6):627–637. ISSN 0735-1933
Josserand C, Thoroddsen ST (2016) Drop impact on a solid surface. Ann Rev Fluid Mech 48(1):365–391
Kalashnikov VN, Askarov AN (1989) Relaxation time of elastic stresses in liquids with small additions of soluble polymers of high molecular weights. J Eng Phys Thermophys 57(2):874–878
Keshavarz B, Sharma V, Houze EC, Koerner MR, Moore JR, Cotts PM, Threlfall-Holmes P, McKinley GH (2015) Studying the effects of extensional properties on atomization of weakly viscoelastic solutions using rayleigh ohnesorge jetting extensional rheometry (rojer). J Non-Newton Fluid Mech 222:171–189
Kim KY, Kang SL, Kwak H-Y (2004) Bubble nucleation and growth in polymer solutions. Polym Eng Sci 44(10):1890–1899
Kim JH, Shi W-X, Larson RG (2007) Methods of stretching dna molecules using flow fields. Langmuir 23(2):755–764
Kroesser FW, Middleman S (1969) Viscoelastic jet stability. AIChE J 15:383–386
Kroger M (2015) Simple, admissible, and accurate approximants of the inverse langevin and brillouin functions, relevant for strong polymer deformations and flows. J Non-Newton Fluid Mech 223:77–87
Lefebvre A (1988) At Sprays. Combustion (Hemisphere Publishing Corporation). Taylor & Francis. ISBN 9780891166030
Lin SP, Reitz RD (1998) Drop and spray formation from a liquid jet. Ann Rev Fluid Mech 30(1):85–105
Lindner A, Vermant J, Bonn D (2003) How to obtain the elongational viscosity of dilute polymer solutions? Physica A 319:125–133
Lumley JL (1973) Drag reduction in turbulent flow by polymer additives. J Polym Sci: Macromol Rev 7(1):263–290
Luu L-H, Forterre Y (2009) Drop impact of yield-stress fluids. J Fluid Mech 632:301–327
Mao T, Kuhn D, Tran H (1997) Spread and rebound of liquid droplets upon impact on flat surfaces. AIChE J 43(9):2169–2179
Marmottant P, Villermaux E (2004) Fragmentation of stretched liquid ligaments. Phys Fluids 16:2732–2741
Moreira ALN, Moita AS, Panao MR (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
Mun RP, Byars JA, Boger DV (1998) The effects of polymer concentration and molecular weight on the breakup of laminar capillary jets. J Non-Newton Fluid Mech 74:285–297
Mun RP, Young BW, Boger DV (1999) Atomisation of dilute polymer solutions in agricultural spray nozzles. J Non-Newton Fluid Mech 83:163–178
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
Negri M, Ciezki HK (2015) Effect of elasticity of boger fluids on the atomization behaviour of an impinging jet injector. At Sprays 25:695–714
Nigen S (2005) Experimental investigation of the impact of an apparent yield-stress material. At Sprays 15:103–117
Oliveira MSN, Yeh R, McKinley GH (2006) Iterated stretching, extensional rheology and formation of beads-on-a-string structures in polymer solutions. J Non-Newton Fluid Mech 137(1):137–148. Extensional Flow
Papageorgiou DT (1995) On the breakup of viscous liquid threads. Phys Fluids 7(7):1529–1544
Park GY, Harrison GM (2008) Effects of elasticity on the spraying of a non-newtonian fluid. At Sprays 18:243–271
Pasandideh-Fard M, Qiao YM, Chandra S, Mostaghimi J (1996) Capillary effects during droplet impact on a solid surface. Phys fluids 8(3):650–659
Pedersen CO (1970) An experimental study of the dynamic behavior and heat transfer characteristics of water droplets impinging upon a heated surface. Int J Heat Mass Transf 13(2):369–381. ISSN 0017-9310
Peterlin A (1966) Hydrodynamics of linear macromolecules. Pure Appl Chem 12(1–4):563–586
Plateau J (1867) Lettre au sujet de la transformation spontanée d’un cylindre liquide en sphères isolées. Comptes Rendus des Séances de l’Académie des Sciences 65:290–291
Quéré D (2013) Leidenfrost dynamics. Ann Rev Fluid Mech 45:197–215
Rayleigh L (1878) On the instability of jets. Proc Lond Math Soc 10:4–13
Rayleigh L (1879) On the capillary phenomena of jets. Proc R Soc Lon Ser A Math Phys Sci 29:71–97
Rayleigh L (1892) On the instability of a cylinder of viscous liquid under capillary force. Philos Mag 34:145–154
Rein M (1993) Phenomena of liquid drop impact on solid and liquid surfaces. Fluid Dyn Res 12(2):61–93
Rein M (ed) (2003) Drop-Surface interactions, CISM courses and lectures no. 456. Springer, Wien-New York
Rogers GP, Barnes HA (2001) New measurements of the flow-curves for carbopol dispersions without slip artefacts. Rheologica Acta 40:499–503
Roisman IV (2009) Inertia dominated drop collisions. ii. An analytical solution of the navierstokes equations for a spreading viscous film. Phys Fluids 21(5):052104
Roisman IV, Berberović E, Tropea C (2009) Inertia dominated drop collisions. i. On the universal flow in the lamella. Phys Fluids 21(5):052103
Romagnoli V, Felton P, Prudhomme RK (2000) Control of drop size by rheology. In: Proceedings of the eighth international conference on liquid atomization and spray systems (ICLASS), Pasadena (CA, USA), pp 34–38
Rozhkov AN (1983) Dynamics of threads of diluted polymer solutions. J Eng Phys 45(1):768–774
Rozhkov AN, Prunet-Foch B, Vignes-Adler M (2003) Impact of drops of polymer solutions on small targets. Phys Fluids 15:2006–2019
Saidi A, Martin C, Magnin A (2010) Influence of yield stress on the fluid droplet impact control. J Non-Newton Fluid Mech 165:596–606
Saïdi A, Martin C, Magnin A (2011) Effects of surface properties on the impact process of a yield stress fluid drop. Exp Fluids 51(1):211–224
Schiaffino S, Sonin AA (1997) Molten droplet deposition and solidification at low weber numbers. Phys Fluids 9(11):3172–3187
Schümmer P, Tebel KH (1983) A new elongational rheometer for polymer solutions. J Non-Newton Fluid Mech 12:331–347
Smith MI, Bertola V (2010a) Effect of polymer additives on the wetting of impacting droplets. Phys Rev Lett 104(15)
Smith MI, Bertola V (2010b) The anti-rebound effect of flexible polymers on impacting drops. In: Proceedings of the 23rd European conference on liquid atomization and spray systems, Brno, Czech Republic, 6–8 Sept 2010
Smith MI, Bertola V (2011) Particle velocimetry inside newtonian and non-newtonian droplets impacting a hydrophobic surface. Exp Fluids 50(5):1385–1391
Smith MI, Sharp JS (2014) Origin of contact line forces during the retraction of dilute polymer solution drops. Langmuir 30:5455–5459
Stelter M (2001) Das Zerstäubungsverhalten nicht-Newtonscher Flüssigkeiten (The atomization behaviour of non-Newonian liquids - in German). Phdthesis, Friedrich-Alexander University Erlangen-Nürnberg
Stelter M, Brenn G, Yarin AL, Singh RP, Durst F (2000) Validation and application of a novel elongational device for polymer solutions. J Rheol 44:595–616
Stelter M, Brenn G, Yarin AL, Singh RP, Durst F (2002a) Investigation of the elongational behavior of polymer solutions by means of an elongational rheometer. J Rheol 46:507–527
Stelter M, Brenn G, Durst F (2002b) The influence of viscoelastic fluid properties on spray formation from flat-fan and pressure-swirl atomizers. At Sprays 12:299–327
Stow CD, Hadfield MG (1981) An experimental investigation of fluid flow resulting from the impact of a water drop with an unyielding dry surface. Proc R Soc Lond A: Math Phys Eng Sci 373(1755):419–441
Tadmor R (2011) Approaches in wetting phenomena. Soft Matter 7:1577–1580
Teske ME, Bilanin AJ (1994) Drop size scaling analysis of non-newtonian fluids. At Sprays 4:473–483
Thompson JC, Rothstein JP (2007) The atomization of viscoelastic fluids in flat-fan and hollow-cone spray nozzles. J Non-Newton Fluid Mech 147:11–22
Tirtaatmadja V, Sridhar T (1993) A filament stretching device for measurement of extensional viscosity. J. Rheol 37:1081–1102
Wachters LHJ, Westerling NAJ (1966) The heat transfer from a hot wall to impinging water drops in the spheroidal state. Chem Eng Sci 21(11):1047–1056
Wang A-B, Lin C-H, Chen C-C (2000) The critical temperature of dry impact for tiny droplet impinging on a heated surface. Phys Fluids 12(6):1622–1625
Wang Y, Minh D-Q, Amberg G (2017) Impact of viscoelastic droplets. Journal of Non-Newtonian Fluid Mechanics 243:38–46
Weber C (1931) Zum zerfall eines flssigkeitsstrahles. ZAMM—J Appl Math Mech/Zeitschrift für Angewandte Mathematik und Mechanik 11(2):136–154
Williams PA, English RJ, Blanchard RL, Rose SA, Lyons L, Whitehead M (2008) The influence of the extensional viscosity of very low concentrations of high molecular mass water-soluble polymers on atomisation and droplet impact. Pest Manag Sci 64(5):497–504
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
Yao S-C, 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. ISSN 0894-1777
Yarin AL (1990) Strong flows of polymeric liquids. Part 1. Rheological behaviour. J Non-Newton Fluid Mech 37:113–138
Yarin AL (1993) Free liquid jets and films—hydrodynamics and rheology. Longman Sci Tech
Yarin AL (2006) Drop impact dynamics: splashing, spreading, receding, bouncing. Annu Rev Fluid Mech 38:159–192
Zhu H, Dexter RW, Fox RD, Reichard DL, Brazee RD, Ozkan HE (1997) Effects of polymer composition and viscosity on droplet size of recirculated spray solutions. J Agric Eng Res 67:35–45
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2020 CISM International Centre for Mechanical Sciences, Udine
About this chapter
Cite this chapter
Bertola, V., Brenn, G. (2020). Transport Phenomena Across Interfaces of Complex Fluids: Drops and Sprays. In: Burghelea, T., Bertola, V. (eds) Transport Phenomena in Complex Fluids. CISM International Centre for Mechanical Sciences, vol 598. Springer, Cham. https://doi.org/10.1007/978-3-030-35558-6_7
Download citation
DOI: https://doi.org/10.1007/978-3-030-35558-6_7
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-030-35557-9
Online ISBN: 978-3-030-35558-6
eBook Packages: EngineeringEngineering (R0)