Abstract
Forced oscillations of a cylindrical droplet of an inviscid liquid surrounded by another liquid and bounded in the axial direction by rigid planes are investigated. The system is affected by vibrations whose force is directed parallel to the axis of symmetry of the droplet. The velocity of motion of the contact line is proportional to the deviation of the contact angle from the value at which the droplet is in equilibrium. Linear and nonlinear oscillations are considered. The conditions of the occurrence of resonance are determined.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
D. V. Lyubimov, T. P. Lyubimova, and S. V. Shklyaev, “Axisymmetric Oscillations of a Hemispherical Droplet” Izv. Ross. Akad. Nauk, Mekh. Zhidk. Gaza, No. 6, 8–20 (2004).
D. V. Lyubimov, T. P. Lyubimova, and S. V. Shklyaev, “Behavior of a Drop on an Oscillating Solid Plate” Phys. Fluids 18, 012101 (2006).
F. Mugele and J.-C. Baret, “Electrowetting: From Basics to Applications” J. Phys., Condens. Matter. 17, 705–774 (2005).
A. E. Korenchenko and V. P. Beskachko, “Oscillations of a Sessile Droplet in Open Air” Phys. Fluids 25, 112106 (2013).
K. John and U. Thiele, “Self-Ratcheting Stokes Drops Driven by Oblique Vibrations” Phys. Rev. Lett. 104, 107801 (2010).
A. Borkar and J. Tsamopoulos, “Boundary Layer Analysis of the Dynamics of Axisymmetric Capillary Bridges” Phys. Fluids A 3, 2866–2874 (1991).
A. A. Alabuzhev and D. V. Lyubimov, “Behavior of a Cylindrical Drop under Multi-Frequency Vibrations” Izv. Ross. Akad. Nauk, Mekh. Zhidk. Gaza, No. 2, 18–28 (2005).
O. V. Voinov, “Wetting Hydrodynamics” Izv. Akad. Nauk SSSR, Mekh. Zhidk. Gaza 5, 76–84 (1976).
O. V. Voinov, “Dynamic Edge Angles of Wetting upon Spreading of a Drop over a Solid Surface” Prikl. Mekh. Tekh. Fiz. 40 (1), 101–107 (1999) [J. Appl. Mech. Tech. Phys. 40 (1), 86–92 (1999)].
H. B. van Lengerichal and P. H. Steen, “Energy Dissipation and the Contact-Line Region of a Spreading Bridge” J. Fluid Mech. 709, 111–141 (2012).
L. M. Hocking, “The Damping of Capillary-Gravity Waves at a Rigid Boundary” J. Fluid Mech. 179, 253–266 (1987).
L. Zhang and D. B. Thiessen, “Capillary-Wave Scattering from an Infinitesimal Barrier and Dissipation at Dynamic Contact Lines” J. Fluid Mech. 719, 295–313 (2013).
A. A. Alabuzhev and D. B. Lyubimov, “Effect of the Contact-Line Dynamics on the Natural Oscillations of a Cylindrical Droplet” Prikl. Mekh. Tekh. Fiz. 48 (5), 78–86 (2007) [J. Appl. Mech. Tech. Phys. 48 (5), 686–693 (2007)].
A. A. Alabuzhev and D. B. Lyubimov, “Effect of the Contact-Line Dynamics on the Oscillations of a Compressed Droplet” Prikl. Mekh. Tekh. Fiz. 53 (1), 12–24 (2012) [J. Appl. Mech. Tech. Phys. 53 (1), 9–19 (2012)].
A. A. Alabuzhev, “Behavior of a Cylindrical Bubble under Vibrations” Vychisl. Mekh. Sploshn. Sred. 7 (2), 151–161 (2014).
Author information
Authors and Affiliations
Corresponding author
Additional information
Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 57, No. 6, pp. 53–63, November–December, 2016.
Rights and permissions
About this article
Cite this article
Alabuzhev, A.A. Axisymmetric oscillations of a cylindrical droplet with a moving contact line. J Appl Mech Tech Phy 57, 1006–1015 (2016). https://doi.org/10.1134/S0021894416060079
Received:
Revised:
Published:
Issue Date:
DOI: https://doi.org/10.1134/S0021894416060079