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Deformation upon impact of a concentrated suspension drop

Published online by Cambridge University Press:  01 June 2020

Loren Jørgensen Open the ORCID record for Loren Jørgensen [Opens in a new window] ,
Yoël Forterre Open the ORCID record for Yoël Forterre [Opens in a new window]  and
Henri Lhuissier Open the ORCID record for Henri Lhuissier [Opens in a new window]
Loren Jørgensen
Affiliation:
Aix Marseille Université, CNRS, IUSTI, Marseille, France
Yoël Forterre
Affiliation:
Aix Marseille Université, CNRS, IUSTI, Marseille, France
Henri Lhuissier*
Affiliation:
Aix Marseille Université, CNRS, IUSTI, Marseille, France
*
†Email address for correspondence: [email protected]
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Abstract

We study the impact between a plate and a drop of non-colloidal solid particles suspended in a Newtonian liquid, paying specific attention to the case when the particle volume fraction, $\unicode[STIX]{x1D719}$, is close to – or even exceeds – the critical volume fraction, $\unicode[STIX]{x1D719}_{c}$, at which the steady effective viscosity of the suspension diverges. We use a specific concentration protocol together with an accurate determination of $\unicode[STIX]{x1D719}$ for each drop, and we measure the deformation $\unicode[STIX]{x1D6FD}$ for different liquid viscosities, impact velocities and particle sizes. At low volume fractions, $\unicode[STIX]{x1D6FD}$ is found to follow closely an effective Newtonian behaviour, which we determine by documenting the low-deformation limit for a highly viscous Newtonian drop and characterizing the effective shear viscosity of our suspensions. By contrast, whereas the effective Newtonian approach predicts that $\unicode[STIX]{x1D6FD}$ vanishes at $\unicode[STIX]{x1D719}_{c}$, a finite deformation is observed for $\unicode[STIX]{x1D719}>\unicode[STIX]{x1D719}_{c}$. This finite deformation remains controlled by the suspending liquid viscosity and increases with increasing particle size, which suggests that the dilatancy of the particle phase is a key factor in the dissipation process close to and above $\unicode[STIX]{x1D719}_{c}$.

JFM classification

Complex Fluids: Suspensions Drops and Bubbles: Drops Multiphase and Particle-laden Flows: Particle/fluid flow
Type
JFM Rapids
Information
Journal of Fluid Mechanics , Volume 896 , 10 August 2020 , R2
Copyright
© The Author(s), 2020. Published by Cambridge University Press

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References

Bertola, V. & Haw, M. 2015 Impact of concentrated colloidal suspension drops on solid surfaces. Powder Technol. 270, 412–417.CrossRefGoogle Scholar
Boyer, F., Sandoval-Nava, E., Snoeijer, J., Dijksman, J. & Lohse, D. 2016 Drop impact of shear thickening liquids. Phys. Rev. Fluids 1, 013901.CrossRefGoogle Scholar
Chandra, S. & Avedisian, C. 1991 On the collision of a droplet with a solid surface. Proc. R. Soc. Lond. A 432, 13–41.Google Scholar
Derby, B. 2011 Inkjet printing ceramics: from drops to solid. J. Eur. Ceram. Soc. 31, 2543–2550.CrossRefGoogle Scholar
Gordillo, L., Sun, T.-P. & Cheng, X. 2018 Dynamics of drop impact on solid surfaces: evolution of impact force and self-similar spreading. J. Fluid Mech. 840, 190–214.CrossRefGoogle Scholar
Grishaev, V., Iorio, C., Dubois, F. & Amirfalzi, A. 2015 Complex drop impact morphology. Langmuir 31, 9833–9844.CrossRefGoogle ScholarPubMed
Guazzelli, É. & Pouliquen, O. 2018 Rheology of dense granular suspension. J. Fluid Mech. 852, P1.CrossRefGoogle Scholar
Hertz, H. 1896 On the contact of elastic solids. J. Reine Angew. Math. 92, 156–171.Google Scholar
Ingold, C. 1971 Fungal Spores. Their Libération and Dispersal. Clarendon.Google Scholar
Jerome, J., Vandenberghe, N. & Forterre, Y. 2016 Unifying impacts in granular matter from quicksand to cornstarch. Phys. Rev. Lett. 117, 098003.CrossRefGoogle ScholarPubMed
Josserand, C. & Thoroddsen, S. 2016 Drop impact on a solid surface. Annu. Rev. Fluid Mech. 48, 365–391.CrossRefGoogle Scholar
Korkut, S., Saville, D. & Aksay, I. 2008 Collodial cluster arrays by electrohydrodynamic printing. Langmuir 24, 12196–12201.CrossRefGoogle ScholarPubMed
Laan, N., de Bruin, K., Bartolo, D., Josserand, C. & Bonn, D. 2014 Maximum diameter of impacting liquid droplets. Phys. Rev. Appl. 2, 044018.CrossRefGoogle Scholar
Lagubeau, G., Fontelos, M., C, J., Maurel, A., Pagneux, V. & Petitjeans, P. 2012 Spreading dynamics of drop impacts. J. Fluid Mech. 713, 50–60.CrossRefGoogle Scholar
Lubbers, L., Xu, Q., Wilken, S., Zhang, W. & Jaeger, H. 2014 Dense suspension splat: monolayer spreading and hole formation after impact. Phys. Rev. Lett. 113, 044502.CrossRefGoogle ScholarPubMed
Madejski, J. 1976 Solidification of droplets on a surface. Intl J. Heat Mass Transfer 19, 1009–1013.CrossRefGoogle Scholar
Morris, J. 2020 Spreading dynamics of drop impacts. Annu. Rev. Fluid Mech. 52, 121–144.CrossRefGoogle Scholar
Nicolas, M. 2005 Spreading of a drop of neutrally buoyant suspension. J. Fluid Mech. 545, 271–280.CrossRefGoogle Scholar
Palma, S. & Lhuissier, H. 2019 Dip-coating with a particulate suspension. J. Fluid Mech. 869, R3.CrossRefGoogle Scholar
Peters, I., Xu, Q. & Jaeger, H. 2013 Splashing onset in dense suspension droplets. Phys. Rev. Lett. 111, 028301.CrossRefGoogle ScholarPubMed
Qi, L., McMurry, P., Norris, D. & Girshick, S. 2011 Impact dynamics of colloidal quantum dot solids. Langmuir 27, 12677–12683.CrossRefGoogle ScholarPubMed
Raux, P., Troger, A., Jop, P. & Sauret, A. 2020 Spreading and fragmentation of particle-laden liquid sheets. Phys. Rev. Fluids 5, 044004.CrossRefGoogle Scholar
Reynolds, O. 1885 On the dilatancy of media composed of rigid particles in contact, with experimental illustrations. Phil. Mag. 20, 449–481.CrossRefGoogle Scholar
Schaarsberg, M., Peters, I., Stern, M., Dodge, K., Zhang, W. & Jaeger, H. 2016 From splashing to bouncing. Phys. Rev. E 93, 062609.Google Scholar
Stickel, J. & Powell, R. 2005 Fluid mechanics and rheology of dense suspensions. Annu. Rev. Fluid Mech. 37, 129–149.CrossRefGoogle Scholar
Wildeman, S., Visser, C. W., Sun, C. & Lohse, D. 2016 On the spreading of impacting drops. J. Fluid Mech. 805, 636–655.CrossRefGoogle Scholar
Zarraga, I., Hill, D. & Leighton, D. 2000 The characterization of the total stress of concentrated suspensions of noncolloidal spheres in Newtonian fluids. J. Rheol. 44, 185–220.CrossRefGoogle Scholar
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