Microstreaming patterns induced by shape modes of acoustically trappedbubbles
Sarah CLEVE(1) , Gabriel REGNAULT(2) , Cyril MAUGER(3) , Claude INSERRA(4) , Philippe BLANC-BENON(5)(1) Univ Lyon, École Centrale de Lyon, INSA de Lyon, CNRS, LMFA UMR 5509, Écully, France, sarah.cleve@ec-lyon.fr(2) Univ Lyon, École Centrale de Lyon, INSA de Lyon, CNRS, LMFA UMR 5509, Écully, France, gabriel.regnault@insa-lyon.fr(3) Univ Lyon, INSA de Lyon, École Centrale de Lyon, CNRS, LMFA UMR 5509, Villeurbanne, France,cyril.mauger@insa-lyon.fr(4) Univ Lyon, Université Lyon 1, Centre Léon Bérard, INSERM, LabTAU, Lyon, France, claude.inserra@inserm.fr(5) Univ Lyon, École Centrale de Lyon, INSA de Lyon, CNRS, LMFA UMR 5509, Écully, France,philippe.blanc-benon@ec-lyon.fr

Abstract
The combination of volumic, translational and nonspherical bubble oscillations induces a relatively slow mean
flow, called microstreaming, in the vicinity of the bubble. It is well known that microstreaming and its resultingshear stresses play an important role in medical applications such as sonoporation (permeabilization of a cellmembrane). The exact mechanisms occuring between bubbles, fluid and biological matter are however not fully
understood. Only few studies have tried to correlate the relatively slow streaming to the fast temporal bubble
dynamics. In the present work, we visualize for the first time microstreaming around an acoustically trappedbubble that is oscillating with axisymmetric shape modes. Different types of streaming patterns can be observed.
Correlation to the temporal bubble dynamics allows us to identify several important parameters that define thepatterns of microstreaming. As might be expected the mode number plays an important role, nevertheless it is
not sufficient to define a streaming pattern. Phase differences between several modal components as well as thebubble size with respect to the resonance frequency have to be taken into account as well.
Keywords: Microstreaming, bubble, nonspherical oscillations

1

INTRODUCTION

Micrometer sized bubbles find use in diagnostic and therapeutic medical applications. One of those applications
is sonoporation, the permeabilization of a cell membrane. Amongst possible mechanisms that may lead tosonoporation, bubble-induced microstreaming and its related shear stress are supposed to play a key role. Thiswas evidenced by Wu et al. [1] and Marmottant et al. [2] who respectively produce streaming around a Mason
horn tip or generated by microbubbles. Investigations of microstreaming commonly refer to bubbles attached toa wall [3] allowing the identification of the different pattern types [4]. However, there are no detailed studies
on microstreaming induced by a single bubble far from any boundary. Furthermore, most existing studies on
microstreaming do not correlate the streaming to its cause, that means to the bubble dynamics. While extensive
microstreaming observations and modelling have been performed for bubbles combining radial oscillations andtranslational motions, few studies are dedicated to the combination of spherical and surface oscillations, thathave been evidenced to lead to large amplitudes of bubble interface motion [5].
In the present study, we aim to characterize microstreaming induced by such a single bubble far from any
boundary and to correlate it to the bubble dynamics. We are in particular interested in the effect of surface
modes on the streaming pattern.

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Bubble coalescence and dynamics
ultra-fastcameraVisualization of microstreaming
ultra-fastcamerawater tank
US transducer

CW laserfluorescentparticles

water tank
US transducer

CW laserpulsed laser

pulsed laser
laser sheet

LED source

collimating/focusinglens set

LED source

Figure 1. Schematic representation of the experimental setup; left: creation of bubbles by short laser pulses,
trapping in the acoustic field and triggering of surface modes via bubble coalescence. The camera and lightsource allow the visualization of the bubble dynamics; right: visualization of microstreaming with fluorescent
tracer particles and a laser sheet.

2EXPERIMENTAL SETUP AND PROCEDURE

The experiments consist of two steps. In a first step surface modes are triggered, in a second step bubbledynamics and microstreaming are recorded.
2.1 Experimental setup
The experimental setup, see figure 1, consists of a 8 cm cubic water tank filled with non-degassed water. Singlebubbles are nucleated by short laser pulses (λ = 532 nm, second harmonic of a Nd:YAG pulsed laser, NewWave Solo III, 6 ns pulse duration). An ultrasonic plane transducer (SinapTec R , diameter of the active area35 mm) is attached to the bottom of the tank and driven at 31.25 kHz. All bubbles are smaller than resonant
size and are hence attracted to the pressure antinodes of the standing acoustic field. Experiments are captured
with a CMOS camera (Vision Research R V12.1) equipped with a 12× objective lens (Navitar R equipped withan additional 1.5× lense). For the visualization of the bubble dynamics, backlight imaging with a LED lightsource is used. For the visualization of streaming, a continuous wave laser source (λ = 532 nm, DPSS, CNI
MLL-FN, 400 mW) is used and a thin laser sheet is formed. Red fluorescent polymer microspheres (diameter,0.71 µm, Duke Scientific) are added to the water as flow tracers.
2.2 Triggering of surface modes
In order to obtain surface modes, we use bubble coalescence. The method is explained in detail elsewhere [6],the main idea is the following. Performing controlled experiments on microstreaming lead to two requirements
for the surface modes, (1) controlled orientation of the bubble symmetry and (2) steady-state oscillations of
the bubble. Both requirements are fulfilled with the method of bubble coalescence. It is worth noting that themode number can be predicted through the choice of the parameters bubble radius R0 , acoustic pressure pa anddriving frequency fac [7].
An example bubble coalescence is shown in figure 2. The approach is followed by film rupture between thebubbles, leading to an initial shape-deformed bubble. Being acoustically driven this bubble will exhibit transient642

steady-state regime →coalescencea2 [µm]

R [µm]

approach7065
150a3 [µm]−15150

−15
0.0

0.5

1.0time [ms]

1.5

2.0 0

T

2T

ac. period T

Figure 2. Example snapshot of bubble coalescence (frame size 220 × 220 µm). After the approach, the twobubbles coalesce at the time defined as t = 0 ms. After a relatively short time, the steady-state regime is reached.
The plot shows the modal decomposition for the radial mode R and the modes 2 and 3. As can be seen on
the snapshots, the modals amplitude a2 becomes negligible while the maximum modal amplitude a3 reaches asteady state value. Note that the experimental values (black line) are superposed with a numerical simulation(green line) according to the coupled-mode theory of volumic and nonspherical oscillation [8].
nonspherical oscillations, and after a sufficient number of acoustic cycles a steady-state regime is reached. As
a result, we dispose of one bubble oscillating on a surface mode (here mode 3) in the steady-state regime anda controlled axis of symmetry (which equals the axis along which the two bubbles approach each other justbefore coalescence).
2.3 Visualization of microstreaming and bubble dynamics
Once a surface mode is triggered, quickly alternating recordings of the bubble dynamics, figure 1 left, andmicrostreaming, figure 1 right, are made. The bubble dynamics is recorded at a frame rate of 180 kfps andimage analysis is done to extract the information on the bubble dynamics. Microstreaming is a relatively slow
phenomenon compared to the fast bubble dynamics. Recordings are done at about 500 fps. The videos areanalysed by two methods. The first method is the so called streak photography, where all obtained snapshots
are superposed and only minimum values for every pixel are kept. The result, see figure 3 on the left, reveals
the trajectories of the tracer particles. The second method is particle image velocimetry (PIV). Figure 3 shows
the corresponding result to the streak photography on the left.

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-0.4z [mm]

-0.2
00.2
0.4
-0.600-0.4-0.2-0.200x [mm]0.50.5

0.2
0.2

10.4
0.4

1

[mm s−1 ]Figure 3. Microstreaming around a bubble oscillating on a mode 3. On the streak image (left), six lobes arevisible. The PIV result reveals maximum velocities of the order of 1 mms−1 .

3

RESULTS AND DISCUSSION

In the following is detailed a study on microstreaming induced by an acoustically trapped bubble that is oscillating with surface modes.
Intuitively, the streaming patterns induced by a bubble will depend on the predominant mode n of the bubble
oscillations and more specifically one might expect a streaming pattern with 2n lobes. However, this assumption
is a too large simplification and does not correspond to the complete results. Four example patterns, that
underline this statement, are shown in figure 4. It is true that we do observe 2n lobes, here 6 lobes for themode 3 in the upper right example and 8 lobes for the mode 4 in the lower right one. On the left side we see
however two examples for a mode 3 and 4 respectively, which lead to larger cross-like patterns.
Through classification of the different examples we found that the bubble size plays an important role in thedistinction between the two cases. For the mode 3, the example on the upper left of figure 4 showing a large
cross-like pattern corresponds to a bubble with a radius of ≈ 65 µm, which is smaller than the resonant size ofthe mode 3 (≈ 67 µm). The example on the upper right of figure 4 showing a pattern with six lobes aroundthe bubble corresponds to a bubble with a radius of ≈ 70 µm, which is larger than the resonant size of themode 3. The same observation can be made for mode 4 oscillations: smaller bubbles show large cross-likepatterns (lower left example of figure 4) and larger bubbles show lobes confined around the bubble (lower rightexample of figure 4).
Possible reasons for this separation are the following. First of all, the modal content is not the same below andabove the resonant size Rres,n [9]. Furthermore, the equations of the surface dynamics reveal that different phaselags may occur on either side of Rres,n .
The control of such streaming patterns might find application in different small-scale applications. For micromixing with acoustically excited bubbles it is helpful to understand the extent of the streaming, a relatively
small lobe-shaped pattern and a large cross-like one obviously not leading to the same effects on the surrounding. Further applications can be found in medical field, where streaming may result for instance in thepermeabilization of a cell membrane (sonoporation). Controlling the extent of the streaming pattern can help tolocalize the therapeutic effect.

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800 µmmode 3mode 4

R0 < Rres,nR0 > Rres,nFigure 4. Four examples of microstreaming patterns. The upper row shows two examples for a mode 3, thelower row two examples for a mode 4 (see snapshots of the respective dynamics in the respective inlets). Twotypes of patterns are observed: the examples on the left are large cross-like patterns for bubbles that are smaller
than the respective resonant size (Rres,3 ≈ 54 µm and Rres,4 ≈ 67 µm), the examples on the right are confined
lobes patterns for bubbles that are larger than the respective resonant size. The radii are in the upper left caseR0 ≈ 65 µm, in the upper right R0 ≈ 70 µm, in the lower left R0 ≈ 53 µm, and in the lower right R0 ≈ 55 µm.

4CONCLUSION

In the present work we show microstreaming around an acoustically trapped bubble. A large number of patterns
can be observed. A classification into two groups is possible, large mostly cross-like patterns and smaller
patterns with confined lobes. For modes 3 and 4 we observed that a distinction is obtained when classing themaccording to the respective bubble size.
The finding of this work are expected to play a role in small-scale applications such as micromixing and medical
applications such as sonoporation.

ACKNOWLEDGEMENTS
This work was performed within the framework of the Labex CeLyA of the Université de Lyon, within the programme ‘Investissements d’Avenir’ (ANR-10-LABX-0060/ANR-16-IDEX-0005) operated by the French National
Research Agency (ANR).

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