Hostname: page-component-745bb68f8f-b95js Total loading time: 0 Render date: 2025-01-09T22:09:20.491Z Has data issue: false hasContentIssue false
  • English
  • Français

Drop impact of yield-stress fluids

Published online by Cambridge University Press:  27 July 2009

LI-HUA LUU  and
YOËL FORTERRE
LI-HUA LUU
Affiliation:
Laboratoire IUSTI, CNRS UMR 6595, Aix-Marseille Université, 5 rue Enrico Fermi, 13453 Marseille Cedex 13, France
YOËL FORTERRE*
Affiliation:
Laboratoire IUSTI, CNRS UMR 6595, Aix-Marseille Université, 5 rue Enrico Fermi, 13453 Marseille Cedex 13, France
*
†Email address for correspondence: [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

The normal impact of a drop of yield-stress fluid on a flat rigid surface is investigated experimentally. Using different model fluids (polymer microgels, clay suspensions) and impacted surfaces (partially wettable, super-hydrophobic), we find a rich variety of impact regimes from irreversible viscoplastic coating to giant elastic spreading and recoil. A minimal model of inertial spreading, taking into account an elasto-viscoplastic rheology, allows explaining in a single framework the different regimes and scaling laws. In addition, semi-quantitative predictions for the spread factor are obtained when the measured rheological parameters of the fluid (elasticity, yield stress, viscosity) are injected into the model. Our study offers a means to probe the short-time rheology of yield-stress fluids and highlights the role of elasticity on the unsteady hydrodynamics of these complex fluids. Movies are available with the online version of the paper (go to journals.cambridge.org/flm).

JFM classification

Drops and Bubbles: Drops Non-Newtonian Flows: Non-Newtonian Flows
Type
Papers
Information
Journal of Fluid Mechanics , Volume 632 , 10 August 2009 , pp. 301 - 327
Copyright
Copyright © Cambridge University Press 2009

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.)

References

REFERENCES

Awerbuch, N. J. & Bodner, S. R. 1974 Experimental investigation of normal perforation of projectile in metallic plates. Intl J. Solids Struct. 10, 685–699.CrossRefGoogle Scholar
Balmforth, N. J., Forterre, Y. & Pouliquen, O. 2009 The viscoplastic Stokes layer. J. Non-Newton. Fluid Mech. 158, 46–53.Google Scholar
Balmforth, N. J. & Frigaard, I. 2007 Viscoplastic fluids: from theory to application. J. Non-Newton. Fluid Mech. 142, 1–244.CrossRefGoogle Scholar
Barnes, H. A., Hutton, J. F. & Walters, K. 1989 An Introduction to Rheology. Elsevier.Google Scholar
Bartolo, D., Boudaoud, A., Narcy, G. & Bonn, D. 2007 Dynamics of non-Newtonian droplets. Phys. Rev. Lett. 99, 174502.Google Scholar
Bénito, S., Bruneau, C.-H., Colin, T., Gay, C. & Molino, F. 2008 An elasto-visco-plastic model for immortal foams or emulsions. Eur. Phys. J. E 25, 225–251.Google Scholar
Bird, R. B., Armstrong, R. C. & Hassager, O. 1987 Dynamics of Polymeric Liquids: Fluid Mechanics, vol. 1. John Wiley.Google Scholar
Bussmann, M., Chandra, S. & Mostaghimi, J. 2000 Modeling the splash of a droplet impacting a solid surface. Phys. Fluids 12, 3121–3132.Google Scholar
de Bruyn, J. R., Habdas, P. & Kim, S. 2002 Fingering instability of a sheet of yield-stress fluid. Phys. Rev. E 66, 031504.CrossRefGoogle ScholarPubMed
Chambon, G., Ghemmour, A. & Laigle, D. 2009 Gravity-driven surges of a viscoplastic fluid: an experimental study. J. Non-Newton. Fluid Mech. 158, 54–62.Google Scholar
Chandra, S. & Avedisian, C. T. 1991 On the collision of a droplet with a solid surface. Proc. R. Soc. Lond. A 432, 13–41.Google Scholar
Cheddadi, I., Saramito, P., Raufaste, C., Marmottant, P. & Graner, F. 2008 Numerical modelling of foam Couette flows. Eur. Phys. J. E 432, 123–133.CrossRefGoogle Scholar
Clanet, C., Béguin, C., Richard, D. & Quéré, D. 2004 Maximal deformation of an impacting drop. J. Fluid Mech. 517, 199–208.CrossRefGoogle Scholar
Cooper-White, J. J., Crooks, R. C. & Boger, D. V. 2002 A drop impact study of worm-like viscoelastic surfactants solutions. Colloids Surf. A 210, 105–123.Google Scholar
Coussot, P. 1994 Steady, laminar, flow of concentrated mud suspension in open channel. J. Hydraul. Res. 32, 535–559.Google Scholar
Coussot, P. 2005 Rheometry of Pastes, Suspensions and Granular Materials. Wiley Interscience.Google Scholar
Coussot, P. & Gaulard, F. 2005 Gravity flow instability of viscoplastic materials: The ketchup drip. Phys. Rev. E 72, 031409.CrossRefGoogle ScholarPubMed
Coussot, P., Roussel, N., Jarny, S. & Chanson, H. 2005 Continuous or catastrophic solid–liquid transition in jammed systems. Phys. Fluids 17, 011704.CrossRefGoogle Scholar
Crossland, B. 1982 Explosive Welding of Metals and Its Applications. Oxford Science.Google Scholar
Johnson, K. L. 1985 Contact Mechanics. Cambridge University Press.Google Scholar
Kim, H.-Y. & Chun, J.-H. 2001 The recoiling of liquid droplets upon collision with solid surfaces. Phys. Fluids 13, 643–659.Google Scholar
Larrieu, E., Staron, L. & Hinch, E. J. 2006 Raining into shallow water as a description of the collapse of a column of grains. J. Fluid Mech. 554, 259–270.CrossRefGoogle Scholar
Lewis, J. A. 2006 Direct ink writing of three-dimensional functional materials. Adv. Funct. Mater. 16, 2193–2204.Google Scholar
Magnin, A. & Piau, J. M. 1990 Cone-and-plate rheometry of yield stress fluids: study of an aqueous gel. J. Non-Newton. Fluid Mech. 36, 85–108.CrossRefGoogle Scholar
Marmottant, P. & Graner, F. 2007 An elastic, plastic, viscous model for slow shear of a liquid foam. Eur. Phys. J. E 23, 337–347.CrossRefGoogle ScholarPubMed
Meeker, S. P., Bonnecaze, R. T. & Cloitre, M. 2004 Slip and flow in soft particle pastes. Phys. Rev. Lett. 92, 198302.CrossRefGoogle ScholarPubMed
Melosh, H. J. 1989 Impact Cratering: A Geologic Process. Oxford University Press.Google Scholar
Mohamed Abdelhaye, Y. O., Chaouche, M. & Van Damme, H. 2008 The tackiness of smectite muds. Part 1. The dilute regime. Appl. Clay Sci. 42, 163–167.CrossRefGoogle Scholar
Mujumdar, A., Beris, A. N. & Metzner, A. B. 2002 Transient phenomena in thixotropic systems. J. Non-Newton. Fluid Mech. 102, 157–178.CrossRefGoogle Scholar
Nigen, S. 2005 Experimental investigation of the impact of an (apparent) yield-stress material. Atom. Sprays 15, 103–117.CrossRefGoogle Scholar
O'Brien, V. T. & Mackay, M. 2002 Shear and elongation flow properties of kaolin suspensions. J. Rheol. 46, 557–572.Google Scholar
van Olphen, H. 1977 An Introduction to Clay Colloid Chemistry, 2nd edn. Wiley.Google Scholar
Oppong, F. K., Rubatat, L., Friskein, B. J., Bailey, A. E. & de Bruyn, J. R. 2006 Microrheology and structure of a yield-stress polymer gel. Phys. Rev. E 73, 041405.CrossRefGoogle ScholarPubMed
Osmond, D. I. & Griffiths, R. W. 2001 The static shape of yield strength fluids slowly emplaced on slopes. J. Geophys. Res. 106, 16241–16250.Google Scholar
Peixinho, J., Nouar, C., Desaubry, C. & Théron, B. 2005 Laminar transitional and turbulent flow of yield stress fluid in a pipe. J. Non-Newton. Fluid Mech. 128, 172–184.CrossRefGoogle Scholar
Piau, J. M. 2007 Carbopol gels: elastoviscoplastic and slippery glasses made of individual swollen sponges; meso-and macroscopic properties, constitutive equations and scaling laws. J. Non-Newton. Fluid Mech. 144, 1–29.Google Scholar
Pignon, F., Magnin, A. & Piau, J.-M. 1996 Thixotropic colloidal suspensions and flow curves with minimum: identification of flow regimes and rheometric consequences. J. Rheol. 40, 573–587.CrossRefGoogle Scholar
Pignon, F., Magnin, A. & Piau, J.-M. 1997 Butterfly light scattering pattern and rheology of a sheared thixotropic clay gel. Phys. Rev. Lett. 79, 4689–4692.CrossRefGoogle Scholar
Rein, M. 1993 Phenomena of liquid drop impact on solid and liquid surfaces. Fluid. Dyn. Res. 12, 61–93.CrossRefGoogle Scholar
Renardy, Y., Popinet, S., Duchemin, L., Renardy, M., Zaleski, S., Josserand, C., Drumwright-Clarke, M. A., Richard, D., Clanet, C. & Quéré, D. 2003 Pyramidal and toroidal water drops after impact a solid surface. J. Fluid Mech. 484, 69–83.Google Scholar
Rieber, M. & Frohn, A. 1999 A numerical study of the mechanism of splashing. Intl J. Heat Fluid Flow 20, 455–461.Google Scholar
Roisman, I. V., Rioboo, R. & Tropea, C. 2002 Normal impact of a liquid drop on dry surface: model for spreading and receding. Proc. R. Soc. Lond. A 458, 1411–1430.Google Scholar
de Saint-Venant, A. J. C. 1871 Théorie du mouvement non-permanent des eaux, avec application aux crues des rivières et à l'introduction des marées dans leur lit. C. R. Acad. Sci. Paris 73, 147–154.Google Scholar
Saramito, P. 2007 A new constitutive equation for elastoviscoplastic fluid flows J. Non-Newton. Fluid Mech. 145, 1–14.CrossRefGoogle Scholar
Schwedoff, T. 1890 Experimental researches on the cohesion of liquids. Part 2. Viscosity of liquids. J. Phys. 9, 34–46.Google Scholar
Tabuteau, H., Coussot, P. & de Bruyn, J. R. 2007 Drag force on a sphere in steady motion through a yield-stress fluid. J. Rheol. 51, 125–137.CrossRefGoogle Scholar
Tanaka, Y., Yamazaki, Y. & Okumura, K. 2003 Bouncing gel balls: impact of soft gels onto rigid surface. Europhys. Lett. 63, 149–155.Google Scholar
Takeshi, O. & Sekimoto, K. 2005 Internal stress in a model elastoplastic fluid. Phys. Rev. Lett. 95, 108301.CrossRefGoogle Scholar
Thoroddsen, S. T. & Sakakibara, J. 1998 Evolution of the fingering pattern of an impacting drop. Phys. Fluids 10, 1359–1373.CrossRefGoogle Scholar
Tyabin, N. V. & Trusov, S. A. 1970 Theory of the flow of an elastoviscoplastic medium. J. Engng Thermophys. 18, 716–723.Google Scholar
White, J. L. 1979 A plastic-viscoelastic constitutive equation to represent the rheological behaviour of concentrated suspensions of small particles in polymer melts J. Non-Newton. Fluid Mech. 5, 177.Google Scholar
Witham, G. B. 1974 Linear and Nonlinear Waves. Wiley Interscience.Google Scholar
Xu, L., Zhang, W. W. & Nigel, S. R. 2005 Drop splashing on a dry smooth surface. Phys. Rev. Lett. 94, 184505.CrossRefGoogle ScholarPubMed
Yarin, A. L. 2006 Drop impact dynamics: splashing, spreading, receding, bouncing .–.–. Annu. Rev. Fluid. Mech. 38, 159–192.Google Scholar
Yarin, A. L., Rubin, M. B. & Roisman, I. V. 1995 Penetration of a rigid projectile into an elastic-plastic target of finite thickness. Intl J. Impact Engng 16, 801–831.Google Scholar
Yarin, A. L., Zussman, E., Theron, A., Rahimi, S., Sobe, Z. & Hasan, D. 2004 Elongational behaviour of gelled propellant simulants. J. Rheol. 48, 101–116.CrossRefGoogle Scholar
Yoshitake, Y., Mitani, S., Sakai, K. & Takagi, K. 2008 Surface tension and elasticity of gel studied with laser-induced surface deformation spectroscopy. Phys. Rev. E 78, 041405.CrossRefGoogle ScholarPubMed

Luu and Forterre supplementary movie

Movie 1. Typical impact dynamics of a drop of clay on a super-hydrophobic surface (55 wt% kaolin, L_0=26.5 mm, V_0=2.8 m.s^{-1}). Total time: 29 ms. After the rapid spreading phase, the drop `freezes' and irreversible coats the surface due to viscoplastic dissipation.

Download Luu and Forterre supplementary movie(Video)
Video 152.6 KB

Luu and Forterre supplementary movie

Movie 2. Typical impact dynamics of a Carbopol drop on a super-hydrophobic surface (1 wt% Carbopol, L_0=12 mm, V_0=2.8 m.s^{-1}). Total time: 75 ms. Strong elastic recoil and receding are observed after the spreading phase, despite the fact that drop deformations are far beyond the flow threshold. Note that during the impact, some hydrophobic sand grains are blown off the surface.

Download Luu and Forterre supplementary movie(Video)
Video 705.8 KB

Luu and Forterre supplementary movie

Movie 3. Bouncing of a 2 wt% Carbopol drop on a super-hydrophobic surface (L_0=17.5 mm, V_0=2.4 m.s^{-1}). Total time: 120 ms.

Download Luu and Forterre supplementary movie(Video)
Video 6.3 MB