Skip to main content
SpringerLink
Log in

The Forced Oscillations of an Oblate Drop Sandwiched Between Different Inhomogeneous Surfaces under AC Vibrational Force

  • Original Article
  • Published:
Microgravity Science and Technology Aims and scope Submit manuscript

Abstract

The dynamics of an incompressible fluid drop under the action of non-uniform electric field are considered. The drop is bounded axially by two parallel solid planes, which in the examined case are considered to be heterogeneous. The external electric field acts as an external force which causes motion of the contact line. In equilibrium, the drop has the form of a circular cylinder. The equilibrium contact angle is \(0.5\pi\). In order to describe the motion of the contact line the modified Hocking boundary condition is applied: the velocity of the contact line is proportional to the deviation of the contact angle and the rate of fast relaxation process, the frequency of which is proportional to twice the frequency of the electric field. The Hocking parameter depends on the polar angle \(\alpha\), i.e. the coefficient of the interaction between the plate and the fluid (the contact line) is a function of the plane coordinates. The focus of this study is on a special case, in which this function is proportional to \(|\cos (\alpha )|\).

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8

Similar content being viewed by others

References

  • Alabuzhev, A.A.: Axisymmetric oscillations of a cylindrical droplet with a moving contact line. Appl. Mech. Tech. Phys. 53, 9–19 (2016)

    Article  MathSciNet  Google Scholar 

  • Alabuzhev, A.A.: Influence of heterogeneous plates on the axisymmetrical oscillations of a cylindrical drop. Microgravity Sci. Technol. 30(1–2), 25–32 (2018)

    Article  Google Scholar 

  • Alabuzhev, A.A., Kashina, M.A.: The oscillations of cylindrical drop under the influence of a nonuniform alternating electric field. J. Phys. Conf. Ser. 681, 012042 (2016)

  • Alabuzhev, A.A., Kashina, M.A.: The oscillations of oblate drop under the influence of a alternating electric field. J. Phys. Conf. Ser. 929, 012107 (2017)

  • Alabuzhev, A.A., Kashina, M.A.: Influence of surface properties on axisymmetric oscillations of an oblate drop in an alternating electric field. Radiophys. Quantum Electron. 61(8–9), 589–602 (2019)

    Article  Google Scholar 

  • Alabuzhev, A.A., Kaysina, M.I.: The translational oscillations of a cylindrical bubble in a bounded volume of a liquid with free deformable interface. J. Phys. Conf. Ser. 681, 012043 (2016)

  • Alabuzhev, A.A., Lyubimov, D.V.: Effect of the contact-line dynamics on the natural oscillations of a cylindrical droplet. J. Appl. Mech. Tech. Phys. 48, 686–693 (2007)

    Article  Google Scholar 

  • Antonov, D.V., Piskunov, M.V., Strizhak, P.A.: Characteristics of the child-droplets emerged by micro-explosion of the heterogeneous droplets exposed to conductive, convective and radiative heating. Microgravity Sci. Technol. 1–15 (2019)

  • Berge, B.: Electrocapillarity and wetting of insulator films by water. Comptes Rendus de l’Académie des Sciences Serie II 317(2), 157–163 (1993)

    Google Scholar 

  • Borkar, A., Tsamopoulus, J.: Boundary-layer analysis of dynamics of axisymmetric capillary bridges. Phys. Fluids A. 3, 2866–2874 (1991)

    Article  Google Scholar 

  • Chen, L., Bonaccurso, E.: Electrowetting - From statics to dynamics. Adv. Colloid Interface Sci. 210, 2–12 (2014)

    Article  Google Scholar 

  • Chevalliot, S., Kuiper, S., Heikenfeld, J.: Experimental validation of the invariance of electrowetting contact angle saturation. J. Adhes. Sci. Technol. 26, 1909–1930 (2012)

    Article  Google Scholar 

  • Chung, S.K., Rhee, K., Cho, S.K.: Bubble actuation by electrowetting-on-dielectric (EWOD) and its applications: A review. Int. J. Precis. Eng. Manuf. 11, 991–1006 (2010)

    Article  Google Scholar 

  • Demin, V.A.: Problem of the free oscillations of a capillary bridge. Fluid Dyn. 43, 524–532 (2008)

    Article  MathSciNet  Google Scholar 

  • Dolmatova, A.V., Goldobin, D.S.: Interface wave dynamics in a two-layer system of inviscid liquids subject to horizontal vibrations. Bulletin of Perm University. Physics 4, 38–45 (2018)

    Article  Google Scholar 

  • Fayzrakhmanova, I.S., Straube, A.V.: Stick-slip dynamics of an oscillated sessile drop. Phys. Fluids 21, 072104 (2009)

    Article  Google Scholar 

  • Fayzrakhmanova, I.S., Straube, A.V., Shklyaev, S.: Bubble dynamics atop an oscillating substrate: Interplay of compressibility and contact angle hysteresis. Phys. Fluids 23, 102105 (2011)

    Article  Google Scholar 

  • Ferrera, C., Montanero, J.M.: Experimental study of small-amplitude lateral vibrations of an axisymmetric liquid bridge. Phys. Fluids 19, 118103 (2007)

    Article  Google Scholar 

  • De Gennes, P.G.: Wetting: statics and dynamics. Rev. Mod. Phys. 57, 827–863 (1985)

    Article  MathSciNet  Google Scholar 

  • Goldobin, D.S.: Existence of the passage to the limit of an inviscid fluid. Eur. Phys. J. E 40(11), 103 (2017)

    Article  Google Scholar 

  • Hayat, T., Shaheen, U., Shafiq, F., et al.: Marangoni mixed convection flow with Joule heating and nonlinear radiation. AIP Adv 5, 077140 (2015)

    Article  Google Scholar 

  • Hayes, R.A., Feenstra, B.J.: Video-speed electronic paper based on electrowetting. Nature 425, 383–385 (2003)

    Article  Google Scholar 

  • Hocking, L.M.: The damping of capillary-gravity waves at a rigid boundary. J. Fluid Mech. 179, 253–266 (1987)

    Article  Google Scholar 

  • Hocking, L.M.: Waves produced by a vertically oscillating plate. J. Fluid Mech. 179, 267–281 (1987)

    Article  Google Scholar 

  • Hua, Z., Rouse, J.L., Eckhardt, A.E., et al.: Multiplexed real-time polymerase chain reaction on a digital microfluidic platform. Anal. Chem. 82, 2310–2316 (2010)

    Article  Google Scholar 

  • Il’in, V.A., Kartavykh, N.N.: Model of electrothermal convection of a poorly conducting liquid in a horizontal capacitor. Surf. Eng. Appl. Electrochem. 54, 379–384 (2018)

    Article  Google Scholar 

  • Kartavykh, N.N., Smorodin, B.L., Il’in, V.A.: Parametric electroconvection in a weakly conducting fluid in a horizontal parallel-plate capacitor. J. Exp. Theor. Phys. 121(1), 155–165 (2015)

    Article  Google Scholar 

  • Kashina, M.A., Alabuzhev, A.A.: Oscillations of oblate drop between heterogeneous plates under uniform electric field. J. Phys. Conf. Ser. 955, 012016 (2018a)

  • Kashina, M.A., Alabuzhev, A.A.: The dynamics of oblate drop between heterogeneous plates under alternating electric field: Non-uniform field. Microgravity Sci. Technol. 30, 11–17 (2018b)

    Article  Google Scholar 

  • Kashina M.A., Alabuzhev, A.A.: Effect of a contact line dynamics on oscillations of oblate bubble in a non-uniform electric field. J. Phys. Conf. Ser. 1135, 012084 (2018c)

  • Kashina, M.A., Alabuzhev, A.A.: The influence of difference in the surface properties on the axisymmetric vibrations of an oblate drop in an AC field. J. Phys.: Conf. Ser. 1163, 012017 (2019)

  • Klimenko, L.S., Lyubimov, D.V.: Generation of an average flow by a pulsating stream near a curved free surface. Fluid Dynamics 47(1), 26–36 (2012)

    Article  MathSciNet  Google Scholar 

  • Klimenko, L., Lyubimov, D.: Surfactant effect on the average flow generation near curved interface. Microgravity Sci. Technol. 30, 77–84 (2018)

    Article  Google Scholar 

  • Kuiper, S., Hendriks, B.H.W.: Variable-focus liquid lens for miniature cameras. Appl. Phys. Lett. 85, 1128–1130 (2004)

    Article  Google Scholar 

  • Li, C., Jiang, H.: Fabrication and characterization of flexible electrowetting. Micromachines 5, 432–441 (2014)

    Article  Google Scholar 

  • Li, J., Wang, Y., Chen, H., Wan, J.: Electrowetting-on-dielectrics for manipulation of oil drops and gas bubbles in aqueous-shell compound drops. Lab Chip 14, 4334–37 (2014)

    Article  Google Scholar 

  • Mampallil, D., Eral, H.B., Staicu, A., Mugele, F., van den Ende, D.: Electrowetting-driven oscillating drops sandwiched between two substrates. Phys. Rev. E 88, 053015 (2013)

    Article  Google Scholar 

  • Miles, J.W.: The capillary boundary layer for standing waves. J. Fluid Mech. 222, 197–205 (1991)

    Article  MathSciNet  Google Scholar 

  • Mugele, F., Baret, J.-C.: Electrowetting: from basics to applications. J. Phys. Condens. Matter. 17, 705–774 (2005)

  • Nelson, W.C., Kim, C.-J.: Droplet actuation by electrowetting-on-dielectric (EWOD): a review. J. Adhes. Sci. Technol. 26, 1747–1771 (2012)

    Article  Google Scholar 

  • Quilliet, C., Berge, B.: Electrowetting: a recent outbreak. Curr. Opin. Colloid Interface Sci. 6, 34–39 (2001)

    Article  Google Scholar 

  • Roques-Carmes, T., Hayes, R.A., Feenstra, B.J., Schlangen, L.J.M.: Liquid behavior inside a reflective display pixel based on electrowetting. J. Appl. Phys. 95, 4389–4396 (2004)

    Article  Google Scholar 

  • Samoilova, A.E., Lobov, N.I.: On the oscillatory Marangoni instability in a thin film heated from below. Phys. Fluids 26(6), 064101 (2014)

    Article  Google Scholar 

  • Samoilova, A.E., Shklyaev, S.: Oscillatory Marangoni convection in a liquid-gas system heated from below. Eur. Phys. J. Special Topics. 224(2), 241–248 (2015)

    Article  Google Scholar 

  • Shklyaev, S., Straube, A.V.: Linear oscillations of a hemispherical bubble on a solid substrate. Phys. Fluids 20, 052102 (2008)

    Article  Google Scholar 

  • Wang, T., Li, H.-X., Zhao, J.-F., Guo, K.-K.: Numerical simulation of quasi-static bubble formation from a submerged orifice by the axisymmetric VOSET method. Microgravity Sci. Technol. 1–14 (2019)

  • Zhao, Y.-P., Wang, Y.: Fundamentals and applications of electrowetting: a critical review. Rev. Adhesion Adhesives 1, 114–174 (2013)

    Article  Google Scholar 

Download references

Acknowledgements

This work was supported by the Russian Science Foundation (project 19-42-04120).

Author information

Authors and Affiliations

  1. Perm State University, Bukireva St, 15., Perm, 614990, Russia

    A. A. Alabuzhev

  2. Institute of Continuous Media Mechanics UB RAS, Academika Koroleva St, 1., Perm, 614013, Russia

    M. A. Kashina & A. A. Alabuzhev

Authors
  1. M. A. Kashina
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. A. A. Alabuzhev
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to A. A. Alabuzhev.

Additional information

Publisher’s Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Kashina, M.A., Alabuzhev, A.A. The Forced Oscillations of an Oblate Drop Sandwiched Between Different Inhomogeneous Surfaces under AC Vibrational Force. Microgravity Sci. Technol. 33, 35 (2021). https://doi.org/10.1007/s12217-021-09886-4

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s12217-021-09886-4

Keywords

Search

Navigation