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Microstreaming induced by an acoustically excited gas
bubble - experiments and comparison to theory
Sarah Cleve, Gabriel Regnault, Alexander Doinikov, Cyril Mauger, Philippe
Blanc-Benon, Claude Inserra
To cite this version:
Sarah Cleve, Gabriel Regnault, Alexander Doinikov, Cyril Mauger, Philippe Blanc-Benon, et al.. Microstreaming induced by an acoustically excited gas bubble - experiments and comparison to theory. Acoustofluidics2020, Aug 2020, San Diego, United States. �hal-02924139�
Microstreaming induced by an acoustically excited gas bubble
– experiments and comparison to theory
Sarah Cleve1,∗, Gabrielle Regnault1, Alexander A. Doinikov1, Cyril Mauger1, Philippe Blanc-Benon1, Claude Inserra2
1Univ Lyon, ´Ecole Centrale de Lyon, INSA de Lyon, CNRS, LMFA UMR 5509, F-69134 ´Ecully
CEDEX, Lyon, FRANCE
2Univ Lyon, Universit´e Lyon 1, INSERM, LabTAU, F-69003, LYON, France, Lyon, FRANCE ∗now at: Physics of Fluids group, MESA+ Institute for Nanotechnology and Technical Medical
(TechMed) Center, University of Twente, P.O. Box 217, 7500 AE, Enschede, THE NETHERLANDS E-mail: s.cleve@utwente.nl
Introduction
Microbubbles are used in a large number of medical ultrasound applications. If these acoustically excited bubbles oscillate nonspherically or translationally, they are known to induce a relatively slow steady flow in the vicinity of the bubble. This flow, called microstreaming, goes along with shear stresses which can be exploited in medical treatment, e.g. by so-called sonoporation [1]. The detailed mechanisms of such treatments are however not yet fully understood. Our study therefore aims to provide a fundamental understanding on the exact nature of microstreaming induced by acoustically excited, nonspherically oscillating microbubbles. Experimentally, we show a large variety of streaming patterns which depend mainly on the dominant mode of oscillations, but also on more subtle details in the bubble dynamics [2]. Theoretically, a newly developed theory confirms the variety of patterns and succeeds in a so far qualitative comparison to the experiments.
Methods
For the experiments, gas bubbles are created by short, focused laser pulses (Nd:YAG pulsed laser, λ = 532 nm). The bubbles under consideration range between 40µm and 80 µm in radius and are trapped in a cubic water tank (width 8 cm) in an acoustic standing field. The driving frequency of the transducer is fixed to 31.25 kHz and the acoustic pressure at the bubble position is varied between 5 kPa and 25 kPa. Through variation of the bubble size and of the acoustic pressure the nature of the bubble oscillations can be controlled: they will either show pure radial oscillations or exhibit surface oscillations [3], in our case the modes 2, 3 or 4. The bubble dynamics is captured with backlightning and a high speed camera (Phantom V12.1) at 180 kfps. In order to visualize the microstreaming flow around the bubble, fluorescent tracer particles (Thermofisher, 0.71µm diameter) are added to water and illuminated by a thin laser sheet. The acquisition rate for the microstreaming is 600 Hz.
The theoretical model [4] for the microstreaming induced by a nonspherically oscillating bubble assumes the bubble dynamics (bubble size, complex modal amplitudes, oscillating frequency) to be known and takes these as input parameters. No restrictions are imposed on the ratio of the bubble radius to the viscous penetration depth, that means no restrictions on the bubble size and on the fluid viscosity. According to the model, microstreaming is generated due to the interaction of two nonspherical modes, n and m, oscillating at the same frequency. The general set of equations has been derived and then applied to specific cases: the interaction of the radial mode 0 with an arbitrary surface mode (case n − 0), the interaction of the translational mode 1 with an arbitrary surface mode (case n − 1), the self-interacting mode n (case n − n) and the interaction of two arbitrary modes n and m (case n − m, with n > m ≥ 2). All cases together cover the full range of possible interactions. Results
The dynamics of the bubble surface is axisymmetric and can be expressed as a sum of different zonal modes. Mathematically, this means in spherical coordinates (r, θ, ϕ) that the bubble contour rs can
be decomposed over a sum of Legendre Polynoms Pn:
rs= R0+ ∞
X
n=0
(a1) (a2) 0 mode number n2 4 6 8 0 5 10 15 ˆan [µ m] (a3) -4 -2 0 2 4 z=R0 -4 -2 0 2 4 x = R0 interaction 2!2 theory: streaming from interaction 2-2 (b1) (b2) 0 mode number n2 4 6 8 0 5 10 15 ˆan [µ m] (b3) -4 -2 0 2 4 z=R0 -4 -2 0 2 4 x = R0 interaction 0!4 theory: streaming from interaction 0-4
Figure 1: Two example streaming patterns (a1,b1) together with the corresponding bubble dynamics (absolute
value of modal amplitudes ˆan) (a2,b2) and a theoretical result giving the same type of pattern (a3,b3).
where an are the complex modal amplitudes of the mode n oscillating at the frequency fn and R0 is
the radius at rest of the bubble. Practically, we can reduce the infinite sum to a few relevant modes. In Fig.1(a2) for instance, only the radial mode 0 and the mode 2 appear in the bubble dynamics. The corresponding, experimentally observed streaming pattern is shown in Fig.1(a2). It shows a cross-like shape with two small pairs of recirculation zones close to the bubble. As the two modes 0 and 2 are oscillating at different frequencies (due to parametric excitation of the mode 2), we do not expect a streaming pattern due to the interaction of the two modes. Furthermore, the mode 0 alone does not lead to microstreaming. Consequently, the only interaction expected to lead to streaming is the self-interacting mode 2. Indeed, we obtain the same type of pattern when considering the self-self-interacting mode 2 in the theoretical model, see Fig. 1(a3). A second example is shown in Fig. 1(b). Here, the bubble dynamics reveals components of the modes 0, 2 and 4. Consequently, a several interactions will contribute to the total streaming pattern. A first qualitative comparison to theory suggests however that the dominant interaction is the interaction between the modes 0 and 4, which leads to the pattern of eight lobes around the bubble.
Conclusion
We have experimentally shown a large variety of streaming patterns linked to the bubble dynamics of nonspherically oscillating microbubbles. These patterns are due to nonlinear effects, which can be described by an analytical model. The qualitative comparison between experiments and theory reveal very satisfying results, a more quantitative evaluation including the effect of several simultaneous interactions is under way.
Acknoledgement
This work was supported by the LABEX CeLyA (ANR-10-LABX-0060) of Universit´e de Lyon, within the program “Investissements d’Avenir” (ANR-16-IDEX-0005) operated by the French National Re-search Agency (ANR). A.A.D. gratefully acknowledges the financial support from Institut National des Sciences Appliqu´es de Lyon (INSA de Lyon).
References
[1] I. Lentacker, I. De Cock, R. Deckers, S. De Smedt and C. Moonen. Advanced drug delivery reviews 72, 49-64 (2014).
[2] S. Cleve, M. Gu´edra, C. Mauger, C. Inserra, P. Blanc-Benon. Journal of fluid mechanics, 875, 597-621
(2018).
[3] M. P. Brenner, D. Lohse and T. F. Dupont. Physical Review Letters, 75.5, 954 (1995).
[4] A.A. Doinikov, S. Cleve, G. Regnault, C. Mauger, C. Inserra. Physical Review E, 100(3), 033105 (2019); and 100(3), 033104 (2019); and 101(1), 013111 (2020).
