skip to main content
DOE PAGES title logo U.S. Department of Energy
Office of Scientific and Technical Information

Title: Axisymmetric oscillation modes of a double droplet system

Abstract

A double droplet system (DDS) consists of a sessile and a pendant drop that are coupled through a liquid filled cylindrical hole in a plate of thickness d. For a small hole radius R, equilibrium shapes of both drops are sections of spheres. While DDSs have a number of applications in microfluidics, a DDS oscillating about its equilibrium state can be used as a fast focusing liquid lens. Here, a DDS consisting of an isothermal, incompressible Newtonian fluid of constant density p and constant viscosity u that is surrounded by a gas is excited by oscillating in time (a) the pressure in the gas surrounding either drop (pressure excitation), (b) the plate perpendicular to its plane (axial excitation), and (c) the hole radius (radial excitation). In contrast to previous works that assumed transient drop shapes are spherical, they are determined here by simulation and used to identify the natural modes of axisymmetric oscillations from resonances observed during frequency sweeps with DDSs for which the combined volume V of the two drops is less than (4/3)πR3. Pressure and axial excitations are found to have identical responses but axial and radial excitations are shown to excite different modes. These modes are comparedmore » to those exhibited by single pendant (sessile) drop systems. Specifically, while a single pendant (sessile) drop has one additional oscillation mode compared to a free drop, a DDS is found to exhibit roughly twice as many oscillation modes as a pendant (sessile) drop. The effects of dimensionless volume V/R3, dimensionless plate thickness d/R, and Ohnesorge number Oh =μ/√ρRσ , where σ is the surface tension of the DDS-gas interface, on the resonance frequencies are also investigated.« less

Authors:
 [1];  [1]
  1. Purdue Univ., West Lafayette, IN (United States). School of Chemical Engineering.
Publication Date:
Research Org.:
Purdue Univ., West Lafayette, IN (United States). Chemical Engineering
Sponsoring Org.:
USDOE Office of Science (SC), Basic Energy Sciences (BES) (SC-22)
OSTI Identifier:
1076456
Resource Type:
Accepted Manuscript
Journal Name:
Physics of Fluids
Additional Journal Information:
Journal Volume: 22; Journal Issue: 11; Journal ID: ISSN 1070-6631
Publisher:
American Institute of Physics
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; fluid drops; free surface; free oscillations; liquid surfaces; surface tension

Citation Formats

Ramalingam, Santhosh K., and Basaran, Osman A. Axisymmetric oscillation modes of a double droplet system. United States: N. p., 2010. Web. doi:10.1063/1.3514197.
Ramalingam, Santhosh K., & Basaran, Osman A. Axisymmetric oscillation modes of a double droplet system. United States. doi:https://doi.org/10.1063/1.3514197
Ramalingam, Santhosh K., and Basaran, Osman A. Mon . "Axisymmetric oscillation modes of a double droplet system". United States. doi:https://doi.org/10.1063/1.3514197. https://www.osti.gov/servlets/purl/1076456.
@article{osti_1076456,
title = {Axisymmetric oscillation modes of a double droplet system},
author = {Ramalingam, Santhosh K. and Basaran, Osman A.},
abstractNote = {A double droplet system (DDS) consists of a sessile and a pendant drop that are coupled through a liquid filled cylindrical hole in a plate of thickness d. For a small hole radius R, equilibrium shapes of both drops are sections of spheres. While DDSs have a number of applications in microfluidics, a DDS oscillating about its equilibrium state can be used as a fast focusing liquid lens. Here, a DDS consisting of an isothermal, incompressible Newtonian fluid of constant density p and constant viscosity u that is surrounded by a gas is excited by oscillating in time (a) the pressure in the gas surrounding either drop (pressure excitation), (b) the plate perpendicular to its plane (axial excitation), and (c) the hole radius (radial excitation). In contrast to previous works that assumed transient drop shapes are spherical, they are determined here by simulation and used to identify the natural modes of axisymmetric oscillations from resonances observed during frequency sweeps with DDSs for which the combined volume V of the two drops is less than (4/3)πR3. Pressure and axial excitations are found to have identical responses but axial and radial excitations are shown to excite different modes. These modes are compared to those exhibited by single pendant (sessile) drop systems. Specifically, while a single pendant (sessile) drop has one additional oscillation mode compared to a free drop, a DDS is found to exhibit roughly twice as many oscillation modes as a pendant (sessile) drop. The effects of dimensionless volume V/R3, dimensionless plate thickness d/R, and Ohnesorge number Oh =μ/√ρRσ , where σ is the surface tension of the DDS-gas interface, on the resonance frequencies are also investigated.},
doi = {10.1063/1.3514197},
journal = {Physics of Fluids},
number = 11,
volume = 22,
place = {United States},
year = {2010},
month = {11}
}

Journal Article:
Free Publicly Available Full Text
Publisher's Version of Record

Citation Metrics:
Cited by: 13 works
Citation information provided by
Web of Science

Save / Share:

Works referenced in this record:

Low-dissipation capillary switches at small scales
journal, January 2005

  • Hirsa, Amir H.; López, Carlos A.; Laytin, Michael A.
  • Applied Physics Letters, Vol. 86, Issue 1
  • DOI: 10.1063/1.1845572

The electroosmotic droplet switch: Countering capillarity with electrokinetics
journal, August 2005

  • Vogel, M. J.; Ehrhard, P.; Steen, P. H.
  • Proceedings of the National Academy of Sciences, Vol. 102, Issue 34
  • DOI: 10.1073/pnas.0505324102

Defense by foot adhesion in a beetle (Hemisphaerota cyanea)
journal, June 2000

  • Eisner, T.; Aneshansley, D. J.
  • Proceedings of the National Academy of Sciences, Vol. 97, Issue 12
  • DOI: 10.1073/pnas.97.12.6568

Capillary dynamics of coupled spherical-cap droplets
journal, May 2007


Fast focusing using a pinned-contact oscillating liquid lens
journal, September 2008


Oscillations of a rotating liquid drop
journal, May 1984


The oscillations of a fluid droplet immersed in another fluid
journal, May 1968


Nonlinear oscillations of inviscid drops and bubbles
journal, February 1983


Oscillations of drops in zero gravity with weak viscous effects
journal, September 1988


Nonlinear oscillations of inviscid free drops
journal, December 1991


Nonlinear oscillations of viscous liquid drops
journal, August 1992


Free vibrations of a drop in partial contact with a solid support
journal, April 1984


Nonlinear oscillations of pendant drops
journal, September 1994

  • Basaran, Osman A.; DePaoli, David W.
  • Physics of Fluids, Vol. 6, Issue 9
  • DOI: 10.1063/1.868120

Behavior of a drop on an oscillating solid plate
journal, January 2006

  • Lyubimov, Dmitry V.; Lyubimova, Tatyana P.; Shklyaev, Sergey V.
  • Physics of Fluids, Vol. 18, Issue 1
  • DOI: 10.1063/1.2137358

Capillary oscillations of a constrained liquid drop
journal, March 2009

  • Bostwick, J. B.; Steen, P. H.
  • Physics of Fluids, Vol. 21, Issue 3
  • DOI: 10.1063/1.3103344

Liquid-bridge mediated droplet switch: A tristable capillary system
journal, December 2005

  • Bhandar, Anand S.; Steen, Paul H.
  • Physics of Fluids, Vol. 17, Issue 12
  • DOI: 10.1063/1.2149399

Chaotic motions of a forced droplet-droplet oscillator
journal, September 2008

  • Slater, D. M.; López, C. A.; Hirsa, A. H.
  • Physics of Fluids, Vol. 20, Issue 9
  • DOI: 10.1063/1.2982372

Forced oscillations of pendant (sessile) drops
journal, June 1997

  • Wilkes, Edward D.; Basaran, Osman A.
  • Physics of Fluids, Vol. 9, Issue 6
  • DOI: 10.1063/1.869276

Hysteretic response of supported drops during forced oscillations
journal, August 1999


A new method for significantly reducing drop radius without reducing nozzle radius in drop-on-demand drop production
journal, January 2002

  • Chen, Alvin U.; Basaran, Osman A.
  • Physics of Fluids, Vol. 14, Issue 1
  • DOI: 10.1063/1.1427441

Computational and experimental analysis of dynamics of drop formation
journal, December 1999

  • Wilkes, Edward D.; Phillips, Scott D.; Basaran, Osman A.
  • Physics of Fluids, Vol. 11, Issue 12
  • DOI: 10.1063/1.870224

Discretization of free surface flows and other moving boundary problems
journal, March 1992


Satellite drops: Unexpected dynamics and change of scaling during pinch-off
journal, March 2001

  • Notz, Patrick K.; Chen, Alvin U.; Basaran, Osman A.
  • Physics of Fluids, Vol. 13, Issue 3
  • DOI: 10.1063/1.1343906

Computational and Experimental Analysis of Pinch-Off and Scaling
journal, April 2002


Tip streaming from a liquid drop forming from a tube in a co-flowing outer fluid
journal, August 2006

  • Suryo, Ronald; Basaran, Osman A.
  • Physics of Fluids, Vol. 18, Issue 8
  • DOI: 10.1063/1.2335621

Nonlinear dynamics and breakup of compound jets
journal, August 2006

  • Suryo, Ronald; Doshi, Pankaj; Basaran, Osman A.
  • Physics of Fluids, Vol. 18, Issue 8
  • DOI: 10.1063/1.2245377

Electrohydrodynamic tip streaming and emission of charged drops from liquid cones
journal, December 2007

  • Collins, Robert T.; Jones, Jeremy J.; Harris, Michael T.
  • Nature Physics, Vol. 4, Issue 2
  • DOI: 10.1038/nphys807

Dynamics of viscoelastic liquid filaments: Low capillary number flows
journal, April 2008

  • Bhat, Pradeep P.; Basaran, Osman A.; Pasquali, Matteo
  • Journal of Non-Newtonian Fluid Mechanics, Vol. 150, Issue 2-3
  • DOI: 10.1016/j.jnnfm.2007.10.021

Hysteresis in forced oscillations of pendant drops
journal, June 1995

  • DePaoli, D. W.; Feng, J. Q.; Basaran, O. A.
  • Physics of Fluids, Vol. 7, Issue 6
  • DOI: 10.1063/1.868576

Third-order resonance effects and the nonlinear stability of drop oscillations
journal, October 1987


Micro-scale drop dynamics for heat transfer enhancement
journal, May 2002


    Works referencing / citing this record:

    Coupled oscillations of deformable spherical-cap droplets. Part 1. Inviscid motions
    journal, January 2013