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The influence of temporal heating modulation on non-isothermal floating droplet dynamics

Published online by Cambridge University Press:  07 October 2022

Alexander Nepomnyashchy  and
Ilya Simanovskii Open the ORCID record for Ilya Simanovskii [Opens in a new window]
Alexander Nepomnyashchy
Affiliation:
Department of Mathematics, Technion – Israel Institute of Technology, 32000 Haifa, Israel
Ilya Simanovskii*
Affiliation:
Department of Mathematics, Technion – Israel Institute of Technology, 32000 Haifa, Israel
*
†Email address for correspondence: [email protected]
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Abstract

The action of temporal heating modulation on Marangoni flows in a droplet on a liquid substrate is investigated. The problem is studied numerically in the framework of long-wave amplitude equations and precursor model. It is shown that temporal modulation can lead to a change of the droplet shape. Specifically, rhombic droplets have been obtained. A modulated cooling from below can lead to periodic or quasiperiodic oscillations or the droplet's decomposition.

JFM classification

Instability: Nonlinear instability
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 949 , 25 October 2022 , A51
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Copyright
© The Author(s), 2022. Published by Cambridge University Press

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References

REFERENCES

Buffone, C. 2019 Formation, stability and hydrothermal waves in evaporating liquid lenses. Soft Matt. 15, 1970–1978.CrossRefGoogle ScholarPubMed
Chen, Y.Z, Zhou, T.J., Li, Y.Y., Zhu, L.F., Handschuh-Wang, S., Zhu, D.Y., Zhou, X.H., Liu, Z., Gan, T.S. & Zhou, X.C. 2018 Robust fabrication of nonstick, noncorrosive, conductive graphene-coated liquid metal droplets for droplet-based, floating electrodes. Adv. Funct. Mat. 28, 1706277.CrossRefGoogle Scholar
Craster, R.V. & Matar, O.K. 2006 On the dynamics of liquid lenses. J. Colloid Interface Sci. 303, 503–516.CrossRefGoogle ScholarPubMed
Fisher, L.S. & Golovin, A.A. 2005 Nonlinear stability analysis of a two-layer thin liquid film: dewetting and autophobic behavior. J. Colloid Interface Sci. 291, 515–528.CrossRefGoogle ScholarPubMed
Géoris, P., Hennenberg, M., Lebon, G. & Legros, J.C. 1999 Investigation of thermocapillary convection in a three-liquid-layer systems. J. Fluid Mech. 389, 209–228.CrossRefGoogle Scholar
Gershuni, G.Z. & Lyubimov, D.V. 1998 Thermal Vibrational Convection. Wiley.Google Scholar
Gershuni, G.Z., Nepomnyashchy, A.A. & Velarde, M.G. 1992 On dynamic excitation of Marangoni instability. Phys. Fluids A 4, 2394.CrossRefGoogle Scholar
Huth, R., Jachalski, S., Kitavtsev, G. & Peschka, D. 2015 Gradient flow perspective on thin-film bilayer flows. J. Engng Maths 94, 43–61.CrossRefGoogle Scholar
Ju, G., Yang, X., Li, L., Cheng, M. & Shi, F. 2019 Removal of oil spills through a self-propelled smart device. Chem.-Asian J. 14, 2435–2439.CrossRefGoogle ScholarPubMed
Kriegsmann, J.J. & Miksis, M.J. 2003 Steady motion of a drop along a liquid interface. SIAM J. Appl. Maths 64, 18–40.CrossRefGoogle Scholar
Labanieh, L., Nguyen, T.N., Zhao, W.A. & Kang, D.K. 2015 Floating droplet array: an ultrahigh-throughput device for droplet trapping, real time analysis and recovery. Micromachines 60, 1469–1482.CrossRefGoogle Scholar
Manga, M. & Stone, H.A. 1995 Low Reynolds number motion of bubbles, drops and rigid spheres through fluid-fluid interfaces. J. Fluid Mech. 287, 279–298.CrossRefGoogle Scholar
Nepomnyashchy, A. & Simanovskii, I. 2010 Effect of gravity on the dynamics of non-isothermic ultra-thin two-layer films. J. Fluid Mech. 661, 1–31.CrossRefGoogle Scholar
Nepomnyashchy, A. & Simanovskii, I. 2012 Nonlinear Marangoni waves in a two-layer film in the presence of gravity. Phys. Fluids 24, 032101.CrossRefGoogle Scholar
Nepomnyashchy, A. & Simanovskii, I. 2020 Synchronization of Marangoni waves by temporal modulation of interfacial heat consumption. Phys. Rev. Fluids 5, 094007.CrossRefGoogle Scholar
Nepomnyashchy, A. & Simanovskii, I. 2021 Droplets on the liquid substrate: thermocapillary oscillatory instability. Phys. Rev. Fluids 6, 034001.CrossRefGoogle Scholar
Nepomnyashchy, A., Simanovskii, I. & Legros, J.C. 2012 Interfacial Convection in Multilayer Systems, 2nd edn. Springer.CrossRefGoogle Scholar
Nepomnyashchy, A.A. & Simanovskii, I.B. 2007 Marangoni instability in ultrathin two-layer films. Phys. Fluids 19, 122103.CrossRefGoogle Scholar
Nepomnyashchy, A.A. & Simanovskii, I.B. 2015 Generation of nonlinear Marangoni waves in a two-layer film by heating modulation. J. Fluid Mech. 771, 159–192.CrossRefGoogle Scholar
Or, A.C. & Kelly, R.E. 2002 The effects of thermal modulation upon the onset of Marangoni-Bénard convection. J. Fluid Mech. 456, 161–182.CrossRefGoogle Scholar
Oron, A., Davis, S.H. & Bankoff, S.G. 1997 Long-scale evolution of thin liquid films. Rev. Mod. Phys. 69, 931.CrossRefGoogle Scholar
Pearson, J.R.A. 1958 On convection cells induced by surface tension. J. Fluid Mech. 4, 489–500.CrossRefGoogle Scholar
Pototsky, A., Bestehorn, M., Merkt, D. & Thiele, U. 2005 Morphology changes in the evolution of liquid two-layer films. J. Chem. Phys. 122, 224711.CrossRefGoogle ScholarPubMed
Pototsky, A., Oron, A. & Bestehorn, M. 2019 Vibration-induced flotation of a heavy liquid drop on a lighter liquid film. Phys. Fluids 31, 087101.CrossRefGoogle Scholar
Princen, H.M. 1969 Shape of interfaces, drops, and bubbles. In Surface and Colloid Science, 1st edn (ed. E. Matijevic), vol. 2. Wiley.Google Scholar
Rybalko, S., Magome, N. & Yoshikawa, K. 2004 Forward and backward laser-guided motion of an oil droplet. Phys. Rev. E 70, 046301.CrossRefGoogle ScholarPubMed
Scardovelli, R. & Zaleski, S. 1999 Direct numerical simulation of free surface and interfacial flow. Annu. Rev. Fluid Mech. 31, 567–603.CrossRefGoogle Scholar
Shimazaki, Y., Shiratori, A., Harada, K., Nakagawa, T., Tanaka, J. & Uematsu, C. 2021 Dense array of floating water droplets aligned to an assembly of tubular wells. Japan J. Appl. Phys. 60, 037002.CrossRefGoogle Scholar
Smith, K.A. 1966 On convection instability induced by surface tension gradient. J. Fluid Mech. 24, 401–414.CrossRefGoogle Scholar
Smith, K.A., Ottino, J.M. & de la Cruz, M.O. 2004 Dynamics of a drop at a fluid interface under shear. Phys. Rev. E 69, 046302.CrossRefGoogle Scholar
Smorodin, B.L., Mikishev, A.B., Nepomnyashchy, A.A. & Myznikova, B.I. 2009 Thermocapillary instability of a liquid layer under heat flux modulation. Phys. Fluids 21, 062102.CrossRefGoogle Scholar
Song, C., Moon, J.K., Lee, K., Kim, K. & Pak, H.K. 2014 Breathing, crawling, budding, and splitting of a liquid droplet under laser heating. Soft Matt. 10, 2679–2684.CrossRefGoogle ScholarPubMed
Sternling, C.V. & Scriven, L.E. 1964 On cellular convection driven by surface tension gradients: effects of mean surface tension and surface viscosity. J. Fluid Mech. 19, 321–340.Google Scholar
Yamini, Y., Rezazadeh, M. & Seidi, S. 2019 Liquid-phase microextraction - the different principles and configurations. TRAC-Trend. Anal. Chem. 112, 264–272.CrossRefGoogle Scholar