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The role of viscoplastic drop shape in impact

Published online by Cambridge University Press:  27 December 2023

Kindness Isukwem ,
Julie Godefroid ,
Cécile Monteux ,
David Bouttes ,
Romain Castellani ,
Elie Hachem ,
Rudy Valette Open the ORCID record for Rudy Valette [Opens in a new window]  and
Anselmo Pereira Open the ORCID record for Anselmo Pereira [Opens in a new window]
Kindness Isukwem
Affiliation:
Mines Paris, PSL University, Centre for material forming (CEMEF), UMR CNRS 7635, rue Claude Daunesse, 06904 Sophia-Antipolis, France
Julie Godefroid
Affiliation:
Sciences et Ingénierie de la Matière Molle, ESPCI Paris, PSL Research University, UMR CNRS 7615, Sorbonne Université, Paris, France
Cécile Monteux
Affiliation:
Sciences et Ingénierie de la Matière Molle, ESPCI Paris, PSL Research University, UMR CNRS 7615, Sorbonne Université, Paris, France
David Bouttes
Affiliation:
Saint-Gobain CREE, 550 rue Alphonse Jauffret, Cavaillon 84300, France
Romain Castellani
Affiliation:
Mines Paris, PSL University, Centre for material forming (CEMEF), UMR CNRS 7635, rue Claude Daunesse, 06904 Sophia-Antipolis, France
Elie Hachem
Affiliation:
Mines Paris, PSL University, Centre for material forming (CEMEF), UMR CNRS 7635, rue Claude Daunesse, 06904 Sophia-Antipolis, France
Rudy Valette
Affiliation:
Mines Paris, PSL University, Centre for material forming (CEMEF), UMR CNRS 7635, rue Claude Daunesse, 06904 Sophia-Antipolis, France
Anselmo Pereira*
Affiliation:
Mines Paris, PSL University, Centre for material forming (CEMEF), UMR CNRS 7635, rue Claude Daunesse, 06904 Sophia-Antipolis, France
*
†Email address for correspondence: anselmo.soeiro_pereira@mines-paristech.fr
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Abstract

The impact of fluid drops on solid substrates is a cardinal fluid dynamics phenomenon intrinsically related to many fields. Although these impacting objects are very often non-spherical and non-Newtonian, previous studies have mainly focused on spherical Newtonian drops. As a result, both shape and rheological effects on the drop-spreading dynamics remain largely unexplored. In the present work we use a mixed approach combining experiments with multiphase three-dimensional numerical simulations to extend the work reported by Luu & Forterre (J. Fluid Mech., vol. 632, 2009, pp. 301–327) by highlighting the fundamental role of shape in the normal impact of viscoplastic drops. Such complex fluids are highly common in various industrial domains and ideally behave either like a rigid body or a shear-rate-dependent liquid, according to the stress solicitation. Spherical, prolate, cylindrical and prismatic drops are considered. The results show that, under negligible capillary effects, the impacting kinetic energy of the drop is dissipated through viscoplastic effects during the spreading process, giving rise to three flow regimes: (i) inertio-viscous, (ii) inertio-plastic, and (iii) mixed inertio-visco-plastic. These regimes are deeply affected by the drop initial aspect ratio, which in turn reveals the possibility of using drop shape to control spreading. The physical mechanisms driving the considered phenomenon are underlined by energy budget analyses and scaling laws. The results are summarised in a two-dimensional diagram linking the drop maximum spreading, minimum height and final shape with different spreading regimes through a single dimensionless parameter, here called the impact number.

JFM classification

Drops and Bubbles: Drops Multiphase and Particle-laden Flows: Multiphase flow Non-Newtonian Flows: Plastic materials
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 978 , 10 January 2024 , A1
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Copyright
© The Author(s), 2023. Published by Cambridge University Press

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References

Andrade, R., Osorio, F. & Skurtys, O. 2013 Drop impact behavior on food using spray coating: fundamentals and applications. Food Res. Intl 54, 397–405.CrossRefGoogle Scholar
Balmforth, N.J., Frigaard, I. & Ovarlez, G. 2014 Yielding to stress: recent developments in viscoplastic fluid mechanics. Annu. Rev. Fluid Mech. 46, 121–146.CrossRefGoogle Scholar
Balmforth, N.J., Forterre, Y. & Pouliquen, O. 2009 The viscoplastic Stokes layer. J. Non-Newtonian Fluid Mech. 158, 46–53.CrossRefGoogle Scholar
Blackwell, B.C., Deetjen, M.E., Gaudio, J.E. & Ewoldt, R.H. 2015 Sticking and splashing in yield-stress fluid drop impacts on coated surfaces. Phys. Fluids 27, 043101.CrossRefGoogle Scholar
Bonn, D., Eggers, J., Indekeu, J., Meunier, J. & Rolley, E. 2009 Wetting and spreading. Rev. Mod. Phys. 81, 739.CrossRefGoogle Scholar
Bordoloi, A.D. & Longmire, E.K. 2014 Drop motion through a confining orifice. J. Fluid Mech. 759, 520–545.CrossRefGoogle Scholar
Bottiglieri, P., de Sio, F., Fasanaro, G., Mojoli, G., Impembo, M. & Castaldo, D. 1991 Rheological characterization of ketchup. J. Food Quality 14, 497–512.CrossRefGoogle Scholar
Carlson, A., Do-Quang, M. & Amberg, G. 2011 Dissipation in rapid dynamic wetting. J. Fluid Mech. 682, 213–240.CrossRefGoogle Scholar
Chafe, N.P. & Bruyn, J.R. 2005 Drag and relaxation in a bentonite clay suspension. J. Non-Newtonian Fluid Mech. 131, 44–52.CrossRefGoogle Scholar
Chun, B., Kwon, I., Jung, H.W. & Hyun, J.C. 2017 Lattice Boltzmann simulation of shear-induced particle migration in plane Couette–Poiseuille flow: local ordering of suspension. Phys. Fluids 29, 121605.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
Cohen-Addad, S., Reinhard, H. & Pitois, O. 2013 Flow in foams and flowing foams. Annu. Rev. Fluid Mech. 45, 241–267.CrossRefGoogle Scholar
Coupez, T. & Hachem, E. 2013 Solution of high-Reynolds incompressible flow with stabilized finite element and adaptive anisotropic meshing. Comput. Meth. Appl. Mech. Engng 267, 65–85.CrossRefGoogle Scholar
Coussot, P. 2005 Rheometry of Pastes, Suspensions and Granular Materials. Wiley Interscience.CrossRefGoogle Scholar
Coussot, P. 2007 Rheophysics of pastes: a review of microscopic modelling approaches. Soft Matt. 3, 528–540.CrossRefGoogle ScholarPubMed
Coussot, P. & Gaulard, F. 2005 Gravity flow instability of viscoplastic materials: the ketchup drip. Phys. Rev. E 72 (031409), 1–5.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
Dages, N., Lidon, P., Pignon, F., Manneville, S. & Gibaud, T. 2021 Mechanics and structure of carbon black gels under high-power ultrasound. J. Rheol. 65, 477–490.CrossRefGoogle Scholar
Derkach, S.R. 2009 Rheology of emulsions. Adv. Colloid Interface Sci. 151, 1–23.CrossRefGoogle ScholarPubMed
Duez, C., Ybert, C., Clanet, C. & Bocquet, L. 2010 Wetting controls separation of inertial flows from solid surfaces. Phys. Rev. Lett. 104, 084503.CrossRefGoogle ScholarPubMed
de Gennes, P.-G., Brochard-Wyart, F. & Quéré, D. 2005 Gouttes, Bulles, Perles et Ondes. Belin.Google Scholar
German, G. & Bertola, V. 2009 Impact of shear-thinning and yield-stress drops on solid substrates. J. Phys.: Condens. Matter 21, 1–16.Google ScholarPubMed
Godefroid, J. 2019 Complex fluids dripped into a liquid bath: impact, relaxation and gelation dynamics. PhD thesis, ESPCI Paris.Google Scholar
Guazzelli, E. & Pouliquen, O. 2018 Rheology of dense granular suspensions. J. Fluid Mech. 852, 1–61.CrossRefGoogle Scholar
Hachem, E., Khalloufi, M., Bruchon, J., Valette, R. & Mesri, Y. 2016 Unified adaptive variational multiscale method for two phase compressible and incompressible flows. Comput. Meth. Appl. Mech. Engng 308, 238–255.CrossRefGoogle Scholar
Herschel, V.W.H. & Bulkley, R. 1926 Konsistenz-messungen von gummi-benzollosungen. Kolloidn. Z. 39, 291–300.CrossRefGoogle Scholar
Jalaal, M., Kemper, D. & Lohse, D. 2019 Viscoplastic water entry. J. Fluid Mech. 864, 596–613.CrossRefGoogle Scholar
Jørgensen, L., Forterre, Y. & Lhuissier, H. 2020 Deformation upon impact of a concentrated suspension drop. J. Fluid Mech. 896, 1–11.CrossRefGoogle Scholar
Josserand, C. & Thoroddsen, S.T. 2016 Drop impact on a solid surface. Annu. Rev. Fluid Mech. 48, 365–391.CrossRefGoogle Scholar
Kim, E. & Baek, J. 2012 Numerical study of the parameters governing the impact dynamics of yield-stress fluid droplets on a solid surface. J. Non-Newtonian Fluid Mech. 173–174, 62–71.CrossRefGoogle Scholar
Koocheki, A., Ghandi, A., Razavi, S.M.A., Mortazavi, S.A. & Vasiljevic, T. 2009 The rheological properties of ketchup as a function of different hydrocolloids and temperature. Intl J. Food Sci. Technol. 44, 596–602.CrossRefGoogle Scholar
Kumar, A., Tripathy, A., Nam, Y., Lee, C. & Sen, P. 2018 Effect of geometrical parameters on rebound of impacting droplets on leaky superhydrophobic meshes. Soft Matt. 14, 1571–1580.CrossRefGoogle ScholarPubMed
Laan, N., de Bruin, K.G., Bartolo, D., Josserand, C. & Bonn, D. 2014 Maximum diameter of impacting liquid droplets. Phys. Rev. Appl. 2, 044018.CrossRefGoogle Scholar
Lin, Y., Zhu, H., Wang, W., Chen, J., Phan-Thien, N. & Pan, D. 2019 Rheological behavior for laponite and bentonite suspensions in shear flow. J. Food Quality 14, 125233.Google Scholar
Liu, Q., Lo, J.H.Y., Li, U., Liu, Y., Zhao, J. & Xu, L. 2021 The role of drop shape in impact and splash. Nat. Commun. 12, 1–8.Google ScholarPubMed
Loisel, V., Abbas, M., Masbernat, O. & Climent, E. 2015 Inertia-driven particle migration and mixing in a wall-bounded laminar suspension flow. Phys. Fluids 27, 123304.CrossRefGoogle Scholar
Lorenceau, E. & Quéré, D. 2003 Drops impacting a sieve. J. Colloid Interface Sci. 263, 244–249.CrossRefGoogle ScholarPubMed
Luu, L.-H. & Forterre, Y. 2009 Drop impact of yield-stress fluids. J. Fluid Mech. 632, 301–327.CrossRefGoogle Scholar
Luu, L.-H. & Forterre, Y. 2014 Giant drag reduction in complex fluid drops on rough hydrophobic surfaces. Phys. Rev. Lett. 110, 184501.CrossRefGoogle Scholar
Ma, M. & Barbosa-Cánovas, G.V. 1995 a Rheological characterization of mayonnaise. Part I: slippage at different oil and xanthan gum concentrations. J. Food Engng 25, 397–408.CrossRefGoogle Scholar
Ma, M. & Barbosa-Cánovas, G.V. 1995 b Rheological characterization of mayonnaise. Part II: flow and viscoelastic properties at different oil and xanthan gum concentrations. J. Food Engng 25, 409–425.CrossRefGoogle Scholar
Modak, C.D., Kumar, A., Tripathy, A. & Sen, P. 2020 Drop impact printing. Nat. Commun. 11, 1–11.CrossRefGoogle ScholarPubMed
Murphy, S.V. & Atala, A. 2020 3D bioprinting of tissues and organs. Nat. Biotechnol. 32, 773–785.CrossRefGoogle Scholar
Mwasame, P.M., Wagner, N.J. & Beris, A.N. 2016 Modeling the viscosity of polydisperse suspensions: improvements in prediction of limiting behavior. Phys. Fluids 28, 061701.CrossRefGoogle Scholar
Ness, C., Seto, R. & Mari, R. 2022 The physics of dense suspensions. Annu. Rev. Condens. Matter Phys. 13, 97–117.CrossRefGoogle Scholar
Nigen, S. 2005 Experimental investigation of the impact of an (apparent) yield-stress material. Atomiz. Sprays 15, 103–117.CrossRefGoogle Scholar
Oishi, C.M., Thompson, R.L. & Martins, F.P. 2019 Normal and oblique drop impact of yield stress fluids with thixotropic effects. J. Fluid Mech. 876, 642–679.CrossRefGoogle Scholar
Paiu, 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-Newtonian Fluid Mech. 144, 1–29.CrossRefGoogle Scholar
Papanastasiou, T.C. 1987 Flows of materials with yield. J. Rheol. 31, 385–404.CrossRefGoogle Scholar
Pereira, A., Hachem, E. & Valette, R. 2020 Inertia-dominated coiling instabilities of power-law fluids. J. Non-Newtonian Fluid Mech. 282, 104321.CrossRefGoogle Scholar
Pereira, A., Larcher, A., Hachem, E. & Valette, R. 2019 Capillary, viscous, and geometrical effects on the buckling of power-law fluid filaments under compression stresses. Comput. Fluids 190, 514–519.CrossRefGoogle Scholar
Peters, I.R., Xu, Q. & Jaeger, H.M. 2013 Splashing onset in dense suspension droplets. Phys. Rev. Lett. 111, 028301.CrossRefGoogle ScholarPubMed
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
Quéré, D. 2008 Wetting and roughness. Annu. Rev. Fluid Mech. 38, 71–99.Google Scholar
Quetzeri-Santiago, M.A., Yokoi, K., Castrejon-Pita, A.A. & Castrejon-Pita, R. 2019 Role of the dynamic contact angle on splashing. Phys. Rev. Lett. 122, 1–6.CrossRefGoogle ScholarPubMed
Rein, M. 1993 Phenomena of liquid drop impact on solid and liquid surfaces. Fluid Dyn. Res. 12, 61–93.CrossRefGoogle Scholar
Riber, S., Valette, R., Mesri, Y. & Hachem, E. 2016 Adaptive variational multiscale method for Bingham flows. Comput. Fluids 138, 51–60.CrossRefGoogle Scholar
Richard, D., Clanet, C. & Quéré, D. 2002 Contact time of a bouncing drop. Nature 417, 811.CrossRefGoogle ScholarPubMed
Ryu, S., Sen, P., Nam, Y. & Lee, C. 2017 Water penetration through a superhydrophobic mesh during a drop impact. Phys. Rev. Lett. 118, 14501.CrossRefGoogle ScholarPubMed
Sanjay, V., Lohse, D. & Jalaal, M. 2021 Bursting bubble in a viscoplastic medium. J. Fluid Mech. 922, A2.CrossRefGoogle Scholar
Sen, S., Morales, A.G. & Ewoldt, R.H. 2020 Viscoplastic drop impact on thin films. J. Fluid Mech. 891, A27.CrossRefGoogle Scholar
Soto, D., Girard, H.-L., Le Helloco, A., Binder, T., Quéré, D. & Varanasi, K.K. 2018 Droplet fragmentation using a mesh. Phys. Rev. Fluids 3, 083602.CrossRefGoogle Scholar
Su, M.-J., Luo, Y., Chu, G.-W., Cai, Y., Le, Y., Zhang, L.-L. & Chen, J.-F. 2020 Dispersion behaviors of droplet impacting on wire mesh and process intensification by surface micro/nano-structure. Chem. Engng Sci. 219, 1–13.CrossRefGoogle Scholar
Tanner, R.I. 2018 Review article: aspects of non-colloidal suspension rheology. Phys. Fluids 30, 101301.CrossRefGoogle Scholar
Tenorio-Garcia, A., Araiza-Calahorra, A., Simone, E. & Sarkar, A. 2022 Recent advances in design and stability of double emulsions: trends in pickering stabilization. Food Hydrocolloid 128, 107601.CrossRefGoogle Scholar
Thompson, R.L., Sica, L.U.R. & de Souza Mendes, P.R. 2018 The yield stress tensor. J. Non-Newtonian Fluid Mech. 261, 211–219.CrossRefGoogle Scholar
Thompson, R.L. & Soares, E.J. 2016 Viscoplastic dimensionless numbers. J. Non-Newtonian Fluid Mech. 238, 57–64.CrossRefGoogle Scholar
Valette, R., Hachem, E., Khalloufi, M., Pereira, A.S., Mackley, M.R. & Butler, S.A. 2019 The effect of viscosity, yield stress, and surface tension on the deformation and breakup profiles of fluid filaments stretched at very high velocities. J. Non-Newtonian Fluid Mech. 263, 130–139.CrossRefGoogle Scholar
Valette, R., Pereira, A., Riber, S., Sardo, L., Larcher, A. & Hachem, E. 2021 Viscoplastic dam-breaks. J. Non-Newtonian Fluid Mech. 287, 1–21.CrossRefGoogle Scholar
Vázquez-Quesada, A. & Ellero, M. 2016 Analytical solution for the lubrication force between two spheres in a bi-viscous fluid. Phys. Fluids 28, 073101.CrossRefGoogle Scholar
Vijayavenkataraman, S., Yan, W.-C., Lu, W.F., Wang, C.-H. & Fuh, J.Y.H. 2018 3D bioprinting of tissues and organs for regenerative medicine. Adv. Drug Deliv. Rev. 132, 296–332.CrossRefGoogle ScholarPubMed
Wildeman, S., Visser, C.W., Sun, C. & Lohse, D. 2016 On the spreading of impacting drops. J. Fluid Mech. 805, 636–655.CrossRefGoogle Scholar
Worthington, A.M. 1883 On impact with a liquid surface. Proc. R. Soc. Lond. 34, 217–230.Google Scholar
Yarin, A.L. 2006 Drop impact dynamics: splashing, spreading, receding, bouncing.... Annu. Rev. Fluid Mech. 38, 159–192.CrossRefGoogle Scholar
Yumoto, M., Hemmi, N., Sato, N., Kawashima, Y., Arikawa, K., Ide, K., Hosokawa, M., Seo, M. & Takeyama, H. 2020 Evaluation of the effects of cell-dispensing using an inkjet-based bioprinter on cell integrity by RNA-seq analysis. Sci. Rep. 10, 1–10.CrossRefGoogle ScholarPubMed
Zhang, H.P. & Makse, H.A. 2005 Jamming transition in emulsions and granular materials. Phys. Rev. E 72, 011301.CrossRefGoogle ScholarPubMed
Supplementary material: File

Isukwem et al. supplementary movie 1

a typical experiment showing a ketchup prolate drop impacting an acrylic plate (U0 = 1.25m/s, D0 = 5mm, H0 = 7.5mm, ρ = 1250kg/m3, k = 10Pa.sm, m = 0.5, τ0 = 12Pa, and Dmax/D0 = 1.82). It is recorded by a high-speed camera [𝒪(104) frames per second] with the aid of a LED backlight panel.
Download Isukwem et al. supplementary movie 1(File)
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Supplementary material: File

Isukwem et al. supplementary movie 2

a typical numerical simulation illustrating the impact of a prolate drop on a solid (U0 = 1.5m/s, D0 = 3.15mm, H0 = 12.6mm, ρ = 1585kg/m3, k = 0.1Pa.sm, m = 1, τ0 = 948Pa).
Download Isukwem et al. supplementary movie 2(File)
File 16.1 MB