Hostname: page-component-586b7cd67f-t7czq Total loading time: 0 Render date: 2024-11-26T19:42:46.632Z Has data issue: false hasContentIssue false
  • English
  • Français

Marangoni instabilities of droplets on the liquid substrate under the action of a spatial temperature modulation

Published online by Cambridge University Press:  11 February 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]
Get access Rights & Permissions [Opens in a new window]

Abstract

The dynamics of a droplet on an inhomogeneously cooled liquid substrate is investigated numerically. The longwave approximation is applied. It is shown that spatial temperature modulation leads to the droplet's motion towards the region of lower temperature, which is accompanied by the change of the droplet shape. An intensive cooling from below can lead to periodic or quasiperiodic oscillations or the droplet's decomposition. A spatial temperature modulation can suppress the oscillatory instability.

JFM classification

Instability: Nonlinear instability Drops and Bubbles: Thermocapillarity Convection: Marangoni convection
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 936 , 10 April 2022 , A26
Check for updates
Copyright
© The Author(s), 2022. 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

REFERENCES

Bacri, L., Debrégeas, G. & Brochard-Wyart, F. 1996 Experimental study of the spreading of a viscous droplet on a nonviscous liquid. Langmuir 12, 6708–6711.CrossRefGoogle Scholar
Brochard Wyart, F., Martin, P. & Redon, C. 1993 Liquid/liquid dewetting. Langmuir 9, 3682–3690.CrossRefGoogle Scholar
Buffone, C. 2019 Formation, stability and hydrothermal waves in evaporating liquid lenses. Soft Matt. 15, 1970.CrossRefGoogle ScholarPubMed
Burton, J.C., Huisman, F.M., Alison, P., Rogerson, D. & Taborek, P. 2010 Experimental and numerical investigation of the equilibrium geometry of liquid lenses. Langmuir 26, 15316–15324.CrossRefGoogle ScholarPubMed
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
de Gennes, P.G. 1985 Wetting: statics and dynamics. Rev. Mod. Phys. 57, 827.CrossRefGoogle Scholar
de Gennes, P.G., Brochard-Wyart, F. & Quéré, D. 2004 Capillarity and Wetting Phenomena: Drops, Bubbles, Pearls, Waves. Springer.CrossRefGoogle Scholar
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
Greco, E.F. & Grigoriev, R.O. 2009 Thermocapillary migration of interfacial droplets. Phys. Fluids 21, 042105.CrossRefGoogle Scholar
Haut, B. & Colinet, P. 2005 Surface-tension-driven instabilities of a pure liquid layer evaporating into an inert gas. J. Colloid Interface Sci. 285, 296–305.CrossRefGoogle ScholarPubMed
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
Jachalski, S., Huth, R., Kitavtsev, G., Peschka, D. & Wagner, B. 2013 Stationary solutions of liquid two-layer thin-film models. SIAM J. Appl. Maths 73, 1183.CrossRefGoogle Scholar
Joanny, J.F. 1987 Wetting of a liquid substrate. Physicochem. Hydrol. 9, 183.Google Scholar
Keiser, L., Bense, H., Colinet, P., Bico, J. & Reyssat, E. 2017 Marangoni bursting: evaporation induced emulsification of binary mixtures on a liquid layer. Phys. Rev. Lett. 118, 074504.CrossRefGoogle ScholarPubMed
Knobloch, E. 1990 Pattern selection in long-wavelength convection. Physica D 41, 450–479.CrossRefGoogle Scholar
Kriegsmann, J.J. 1999 Spreading on a liquid interface. PhD thesis, Northwestern University, Evanston, IL.Google Scholar
Kriegsmann, J.J. & Miksis, M.J. 2003 Steady motion of a drop along a liquid interface. SIAM J. Appl. Maths 64 (1), 18–40.CrossRefGoogle Scholar
Langmuir, I. 1933 Oil lenses on water and the nature of monomolecular expanded films. J. Chem. Phys. 1, 756.CrossRefGoogle Scholar
Nepomnyashchy, A.A. & Simanovskii, I.B. 2006 Decomposition of a two-layer thin liquid film flowing under the action of Marangoni stresses. Phys. Fluids 18, 112101.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. 2009 Dynamics of ultra-thin two-layer films under the action of inclined temperature gradients. J. Fluid Mech. 31, 165–197.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.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
Nepomnyashchy, A. & Simanovskii, I. 2016 Marangoni waves in two-layer films under the action of spatial temperature modulation. J. Fluid Mech. 805, 322–354.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
Neumann, F. 1894 Vorlesungen über die Theorie der Capillarität. Teubner.Google Scholar
Oron, A., Davis, S.H. & Bankoff, S.G. 1997 Long-scale evolution of thin liquid films. Rev. Mod. Phys. 69, 931.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 (ed. E. Matijevic), vol. 2, p. 1. 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
Scriven, L.E. & Sternling, C.V. 1964 On cellular convection driven by surface-tension gradients: effects of mean surface tension and surface viscosity. J. Fluid Mech. 19, 321–340.CrossRefGoogle Scholar
Simanovskii, I.B. & Nepomnyashchy, A.A. 1993 Convective Instabilities in Systems with Interface. Gordon and Breach.Google Scholar
Sivashinsky, G.I. 1982 Large cells in nonlinear Marangoni convection. Physica D 4, 227–235.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.CrossRefGoogle ScholarPubMed
Suciu, D.G., Smigelschi, O. & Ruckenstein, E. 1970 The spreading of liquids on liquids. J. Colloid Interface Sci. 33, 520–528.CrossRefGoogle Scholar
Yakshi-Tafti, E., Cho, H.J. & Kumar, R. 2010 Droplet actuation on a liquid layer due to thermocapillary motion: shape effect. Appl. Phys. Lett. 96, 264101.CrossRefGoogle Scholar