Hostname: page-component-848d4c4894-5nwft Total loading time: 0 Render date: 2024-05-30T07:59:50.664Z Has data issue: false hasContentIssue false
  • English
  • Français

Impact dynamics of compound drops of fluids with density contrast

Published online by Cambridge University Press:  02 June 2023

Zhen Zhang ,
Chun-Yu Zhang Open the ORCID record for Chun-Yu Zhang [Opens in a new window] ,
Hao-Ran Liu Open the ORCID record for Hao-Ran Liu [Opens in a new window]  and
Hang Ding Open the ORCID record for Hang Ding [Opens in a new window]
Zhen Zhang
Affiliation:
Department of Modern Mechanics, University of Science and Technology of China, Hefei 230026, PR China
Chun-Yu Zhang
Affiliation:
Department of Modern Mechanics, University of Science and Technology of China, Hefei 230026, PR China
Hao-Ran Liu
Affiliation:
Department of Modern Mechanics, University of Science and Technology of China, Hefei 230026, PR China
Hang Ding*
Affiliation:
Department of Modern Mechanics, University of Science and Technology of China, Hefei 230026, PR China
*
†Email address for correspondence: hding@ustc.edu.cn
Get access Rights & Permissions [Opens in a new window]

Abstract

The dynamics of compound drops impacting on a flat substrate is numerically investigated using a ternary-fluid diffuse-interface method, with the aim of assessing the effect of a density difference between the inner and outer droplets (denoted by $\lambda$) on the evolution of the interfaces. With the help of numerical simulations, we find that, at the intermediate stage of drop impact, the inner droplet exhibits a self-similar deformation at $\lambda =1$ and relatively high Weber number, and experiences more or less a uniform acceleration for various $\lambda$. In particular, the acceleration magnitude at $\lambda \ne 1$ can be correlated with the acceleration at $\lambda =1$ and the Atwood number. When the inner droplet is denser than the outer one, a lamella occurs at the spreading front of the inner droplet. We present a scaling analysis of the thickness of the lamella, and the resultant theoretical prediction is in good agreement with numerical results. At the maximal spreading of the compound drop, a bulging structure is formed around the symmetry axis due to the presence of the inner droplet, thereby effectively reducing the liquid supply to the spreading front and leading to a decrease of maximal spreading ratio $\beta _{max}$ as compared with a pure drop. We proposed a corrected Weber number $We^*_\lambda$ by taking account of the combined effects of $\lambda$, volume fraction of the inner droplet, Weber number and morphology of the compound drop. Integrating $We^*_\lambda$ with the universal model of $\beta _{max}$ for impacting pure drops, we successfully build up a new model for predicting the maximal spreading ratio of impacting compound drops with various $\lambda$.

JFM classification

Drops and Bubbles: Drops Interfacial Flows (free surface): Contact lines
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 964 , 10 June 2023 , A34
Check for updates
Copyright
© The Author(s), 2023. Published by Cambridge University Press

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

Blanken, N., Saleem, M.S., Antonini, C. & Thoraval, M.J. 2020 Rebound of self-lubricating compound drops. Sci. Adv. 6, eaay3499.CrossRefGoogle ScholarPubMed
Blanken, N., Saleem, M.S., Thoraval, M.J. & Antonini, C. 2021 Impact of compound drops: a perspective. Curr. Opin. Colloid Interface Sci. 51, 101389.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
De Cock, L.J., De Koker, S., De Geest, B.G., Grooten, J., Vervaet, C., Remon, J.P., Sukhorukov, G.B. & Antipina, M.N. 2010 Polymeric multilayer capsules in drug delivery. Angew. Chem. Intl Ed. 49, 6954–6973.CrossRefGoogle ScholarPubMed
Delcea, M., Mohwald, H. & Skirtach, A.G. 2011 Stimuli-responsive LBL capsules and nanoshells for drug delivery. Adv. Drug Deliv. Rev. 63, 730–747.CrossRefGoogle ScholarPubMed
Derby, B. 2010 Inkjet printing of functional and structural materials: fluid property requirements, feature stability, and resolution. Annu. Rev. Mater. Res. 40, 395–414.CrossRefGoogle Scholar
Eggers, J., Fontelos, M.A., Josserand, C. & Zaleski, S. 2010 Drop dynamics after impact on a solid wall: theory and simulations. Phys. Fluids 22, 062101.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
Gulyaev, I.P. & Solonenko, O.P. 2013 Hollow droplets impacting onto a solid surface. Exp. Fluids 54, 1–12.CrossRefGoogle Scholar
Hendriks, J., Visser, C.W., Henke, S., Leijten, J., Saris, D.B.F., Sun, C., Lohse, D. & Karperien, M. 2015 Optimizing cell viability in droplet-based cell deposition. Sci. Rep. 5, 1–10.CrossRefGoogle ScholarPubMed
Josserand, C. & Thoroddsen, S.T. 2016 Drop impact on a solid surface. Annu. Rev. Fluid Mech. 48, 365–391.CrossRefGoogle Scholar
Lagubeau, G., Fontelos, M.A., Josserand, C., Maurel, A., Pagneux, V. & Petitjeans, P. 2012 Spreading dynamics of drop impacts. J. Fluid Mech. 713, 50–60.CrossRefGoogle Scholar
Liu, D. & Tran, T. 2018 Emergence of two lamellas during impact of compound droplets. Appl. Phys. Lett. 112, 203702.CrossRefGoogle Scholar
Liu, D. & Tran, T. 2019 The ejecting lamella of impacting compound droplets. Appl. Phys. Lett. 115, 073702.CrossRefGoogle Scholar
Liu, G., Wu, Q., Dwivedi, P., Hu, C., Zhu, Z., Shen, S., Chu, J., Zhao, G., Si, T. & Xu, R. 2018 a Hemoglobin-laden microcapsules for simulating oxygen dynamics of biological tissue. ACS Biomater. Sci. Engng 4, 3177–3184.CrossRefGoogle ScholarPubMed
Liu, H.R., Zhang, C.Y., Gao, P., Lu, X.Y. & Ding, H. 2018 b On the maximal spreading of impacting compound drops. J. Fluid Mech. 854, R6.CrossRefGoogle Scholar
Lohse, D. 2022 Fundamental fluid dynamics challenges in inkjet printing. Annu. Rev. Fluid Mech. 54, 349–382.CrossRefGoogle Scholar
Mitchell, B.R., Klewicki, J.C., Korkolis, Y.P. & Kinsey, B.L. 2019 The transient force profile of low-speed droplet impact: measurements and model. J. Fluid Mech. 867, 300–322.CrossRefGoogle Scholar
Murphy, S.V. & Atala, A. 2014 3D bioprinting of tissues and organs. Nat. Biotechnol. 32, 773–785.CrossRefGoogle ScholarPubMed
Riboux, G. & Gordillo, J.M. 2014 Experiments of drops impacting a smooth solid surface: a model of the critical impact speed for drop splashing. Phys. Rev. Lett. 113, 024507.CrossRefGoogle Scholar
Tasoglu, S., Kaynak, G., Szeri, A.J., Demirci, U. & Muradoglu, M. 2010 Impact of a compound droplet on a flat surface: a model for single cell epitaxy. Phys. Fluids 22, 082103.CrossRefGoogle Scholar
Wang, R., Shi, Y.Z., Zhang, C.Y. & Ding, H. 2022 On the maximal spreading of drops impacting onto a no-slip substrate. Phys. Fluids 34, 052103.CrossRefGoogle Scholar
Wei, Y. & Thoraval, M.J. 2021 Maximum spreading of an impacting air-in-liquid compound drop. Phys. Fluids 33, 061703.CrossRefGoogle Scholar
Wijshoff, H. 2018 Drop dynamics in the inkjet printing process. Curr. Opin. Colloid Interface Sci. 36, 20–27.CrossRefGoogle Scholar
Yarin, A.L. 2006 Drop impact dynamics: splashing, spreading, receding, bouncing. Annu. Rev. Fluid Mech. 38, 159–192.CrossRefGoogle Scholar
Zhang, C.Y., Ding, H., Gao, P. & Wu, Y.L. 2016 Diffuse interface simulation of ternary fluids in contact with solid. J. Comput. Phys. 309, 37–51.CrossRefGoogle Scholar
Zhang, J.M., Li, E.Q. & Thoroddsen, S.T. 2020 Fine radial jetting during the impact of compound drops. J. Fluid Mech. 883, A46.CrossRefGoogle Scholar

Zhang et al. Supplementary Movie 1

Impact dynamics of a compound drop at λ=0.1, α=0.064 and we=500

Download Zhang et al. Supplementary Movie 1(Video)
Video 4.6 MB

Zhang et al. Supplementary Movie 2

Impact dynamics of a compound drop at λ=1, α=0.064 and we=500

Download Zhang et al. Supplementary Movie 2(Video)
Video 4.7 MB

Zhang et al. Supplementary Movie 3

Impact dynamics of a compound drop at λ=4, α=0.064 and we=500

Download Zhang et al. Supplementary Movie 3(Video)
Video 4.8 MB