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Physics of Fluids / Volume 21 / Issue 9 / ARTICLES / Micro- and Nanofluid Mechanics

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Phys. Fluids 21, 092003 (2009); http://dx.doi.org/10.1063/1.3227903 (7 pages)

History force on coated microbubbles propelled by ultrasound

Valeria Garbin1, Benjamin Dollet1, Marlies Overvelde1, Dan Cojoc2, Enzo Di Fabrizio2, Leen van Wijngaarden1, Andrea Prosperetti1, Nico de Jong1, Detlef Lohse1, and Michel Versluis1

1Physics of Fluids Group and Research Institute for Biomedical Technology BMTI, University of Twente, 7500 AE Enschede, The Netherlands
2CNR-INFM, Laboratorio Nazionale TASC, 34149 Trieste, Italy

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(Received 10 June 2009; accepted 18 August 2009; published online 21 September 2009)

In this paper the unsteady translation of coated microbubbles propelled by acoustic radiation force is studied experimentally. A system of two pulsating microbubbles of the type used as contrast agent in ultrasound medical imaging is considered, which attract each other as a result of the secondary Bjerknes force. Optical tweezers are used to isolate the bubble pair from neighboring boundaries so that it can be regarded as if in an unbounded fluid and the hydrodynamic forces acting on the system can be identified unambiguously. The radial and translational dynamics, excited by a 2.25 MHz ultrasound wave, is recorded with an ultrahigh speed camera at 15×106 frames/s. The time-resolved measurements reveal a quasisteady component of the translational velocity, at an average translational Reynolds number 〈Ret〉 ≈ 0.5, and an oscillatory component at the same frequency as the radial pulsations, as predicted by existing models. Since the coating enforces a no-slip boundary condition, an increased viscous dissipation is expected due to the oscillatory component, similar to the case of an oscillating rigid sphere that was first described by Stokes [“On the effect of the internal friction of fluids on the motion of pendulums,” Trans. Cambridge Philos. Soc. 9, 8 (1851) ]. A history force term is therefore included in the force balance, in the form originally proposed by Basset and extended to the case of time-dependent radius by Takemura and Magnaudet [“The history force on a rapidly shrinking bubble rising at finite Reynolds number,” Phys. Fluids 16, 3247 (2004) ]. The instantaneous values of the hydrodynamic forces extracted from the experimental data confirm that the history force accounts for the largest part of the viscous force. The trajectories of the bubbles predicted by numerically solving the equations of motion are in very good agreement with the experiment.

© 2009 American Institute of Physics

Article Outline

  1. INTRODUCTION
  2. EFFECT OF CONFINING GEOMETRY: MICROMANIPULATION OF BUBBLES
  3. EXPERIMENTAL PROCEDURE
  4. HYDRODYNAMIC MODEL
  5. RESULTS AND DISCUSSION
  6. SUMMARY AND CONCLUSIONS

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KEYWORDS and PACS

Keywords

acoustic streaming, bubbles, ultrasonic effects

PACS

  • 47.55.dd

    Bubble dynamics

  • 43.35.Bf

    Ultrasonic velocity, dispersion, scattering, diffraction, and attenuation in liquids, liquid crystals, suspensions, and emulsions

  • 43.25.Qp

    Radiation pressure

  • 43.25.Nm

    Acoustic streaming

ARTICLE DATA

Digital Object Identifier
http://dx.doi.org/10.1063/1.3227903

PUBLICATION DATA

ISSN

1070-6631 (print)  
1089-7666 (online)

Publisher

$abstract.society.value is a Member of CrossRef American Institute of Physics

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Figures (click on thumbnails to view enlargements)

FIG.1
Observations of the dynamics of two coated bubbles in ultrasound. (a) Layout of the experiment (side view). A microscope objective is used to focus the laser traps (optical tweezers) and for transmission imaging. The direction of incidence of the ultrasound beam is orthogonal to the line of centers x. (b) Frames from an ultrahigh speed time series of bubble dynamics (top view). The recording is taken at 13.4×106 frames/s, corresponding to an interframe time of 70 ns. Here only every second frame is shown. The black crosses in the first and last frames indicate the initial positions of the bubble centers. The distance between the bubbles decreases due to the secondary Bjerknes force. White scale bar: 5 μm (enhanced online).[URL: http://dx.doi.org/10.1063/1.3227903.1 ]

FIG.1 Download High Resolution Image (.zip file) | Export Figure to PowerPoint

FIG.2
System of coordinates. Ri (i = 1,2) is the radius of bubble i and xi is its position on the line of centers x. ri denotes the position of a fluid element relative to bubble i.

FIG.2 Download High Resolution Image (.zip file) | Export Figure to PowerPoint

FIG.3
(a) Time evolution of the radii obtained by image tracking. The solid symbols represent experimental data points and the lines represent the resampled and filtered radius-time curves. The bubbles oscillate in phase and have relative radial excursions ΔR/R0 ∼ 0.3. (b) Time evolution of the distance between the centers, d = x2−x1. The solid symbols represent experimental data points and the line represents the resampled and filtered distance-time curve. [(c) and (d)] Time evolution of the Reynolds numbers computed from the experimental radial and translational dynamics. Only the values for bubble 1 are plotted for clarity. The radial Reynolds number Rer = R|math|/ν is below 25 with a time average 〈Rer〉 ≈ 3. The translational Reynolds number Ret = R|U|/ν is below 5 with a time average 〈Ret〉 ≈ 0.5.

FIG.3 Download High Resolution Image (.zip file) | Export Figure to PowerPoint

FIG.4
Comparison of models for the viscous force. The values are computed for one bubble from the experimental values of the radius and position and their derivatives. Dashed line: experimental value from the force balance −(FA+FG). The solid symbols show the values corresponding to the experimental data points. Solid line: model including quasisteady drag and history force FQS+FH. Dashed-dotted line: a model including only quasisteady drag FQS, neglecting history force, largely underestimates viscous dissipation.

FIG.4 Download High Resolution Image (.zip file) | Export Figure to PowerPoint

FIG.5
Time evolution of the distance between the centers of the bubbles. Dashed line: experimental value (after resampling and filtering). The solid symbols are the measured data points. Solid line: prediction using the model including history force and quasisteady drag, FQS+FH. The shaded area represents the tolerance (±5%) on the prediction due to the systematic experimental uncertainty on the resting radius of a bubble. Inset: comparison of the model including only the quasisteady drag FQS (dashed-dotted line) with the model including history force, FQS+FH (solid line).

FIG.5 Download High Resolution Image (.zip file) | Export Figure to PowerPoint



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