Induction of Microstreaming by Nonspherical Bubble Oscillations in an Acoustic Levitation System

The presented procedure consists of using bubble coalescence in order to trigger steady-state, symmetry-controlled bubble shape oscillations, allowing the study of the long-term fluid flow induced by these oscillations. The main challenge in the technique is the control of nonspherical oscillations for a bubble being trapped, far from any boundaries.

Most of the existing techniques proposed in the literature focused on substrate-attached bubbles^7,16, as the absence of motion of the bubble center makes the capture of its interface at the acoustic timescale (up to hundreds of kHz) easier. While exceeding the pressure threshold necessary to trigger shape modes is an easy task in this case, the control of shape oscillations is complicated due to the break of symmetry induced by the substrate. A wall-attached bubble is contacting the substrate with a particular contact angle, leading to the triggering of asymmetric surface modes²¹. In addition to the complexity of interpreting the three-dimensional, asymmetric modes with only a single camera view, abrupt transition to a chaotic surface oscillation regime arises³³. Therefore, the main challenge consists in capturing shape oscillations of a single, trapped bubble far from any boundaries in order to obtain axisymmetric nonspherical oscillations. Such conditions enable comparison between experiments and the large variety of analytical studies available in literature. The main experimental difficulty lies in the positional stability of the microbubble. To overcome this problem, optical tweezers have been used to control bubble trapping³⁴, and amplitude-modulated ultrasound fields are used to trap and drive bubble oscillations²⁹. In both cases, a single bubble is trapped and nonspherical modes are triggered. Also, in the case of the amplitude-modulated driving field, the shape modes only exist for a small period of time as they periodically onset and disappear. In addition, the orientation of bubble shape oscillations is not controlled and leads to a bias in the analysis of the interface motion.

The alternative we propose is the use of a pulsed laser to nucleate a single bubble, later trapped at a pressure antinode of a resonance levitation chamber. By nucleating successive bubbles over time, each nucleated bubble moves towards its trapping location which is already occupied by another bubble. Coalescence occurs and induces an initially-deformed bubble interface. If the driving pressure is sufficiently strong, the shape oscillations are sustained. Laser-nucleation has been preferred to other nucleation techniques, such as electrolysis for instance, as it allows fast and reliable bubble generation. As illustrated in Figure 9, the axis of symmetry of shape oscillations is given by the axis of bubble approach prior to coalescence. However, this major result requires a relatively long time for setting the experimental setup as it is required that the bubbles stay inside the focal plane of the camera during the approach phase of coalescence (in order to orient the axis of symmetry in this plane). To do so, slight changes of the bubble nucleation site are made in order to optimize the path along which the bubbles move and encounter each other. The change into bubble-nucleation site requires fine modification of the tank location relatively to the laser path, and is performed with a three-directions stage with micrometric accuracy. In addition, fine tuning of the laser energy is performed in order to optimize the nucleated bubble size. Bubbles that are too large will immediately generate shape modes with high mode number and approach the volumetric bubble resonance. This leads to high positional instability of the bubble center. Bubbles that are too small will require a large number of coalescence processes before reaching the appropriate size for triggering shape modes.

The main advantage of the proposed technique is the establishment of a steady-state regime for symmetry-controlled shape oscillations. As the interface motion is sustained for a relatively long time (from seconds to minutes), capturing the bubble-induced fluid flow is possible by switching the experimental setup to the tracking of fluorescent nanoparticles seeded into the liquid medium. It is worth noting that no experimental studies of microstreaming induced by a bubble in an infinite liquid exist so far in the literature. Also, even when cavitation microstreaming is investigated for substrate-attached bubble, the analysis is limited to qualitative observations without considering the link to the bubble dynamics¹⁶. The measurement of particle motion is performed in a thin laser sheet provided by a continuous wave laser. Because it is necessary to perform quasi-simultaneously (i) the laser-nucleation by pulsed laser, (ii) the particle tracking with a laser sheet and (iii) the recording by the high-speed camera, particular attention has to be paid to the potential obstruction of materials surrounding the water tank. This leads to a compact setup with many restrictions on the devices disposition, as shown in Figure 5. When capturing a microstreaming pattern induced by a shape-oscillating bubble, it is necessary to alternatively track the bubble interface dynamics, as mentioned in step 4.2. Indeed, switching between alternative sequences of bubble dynamics and fluid flow visualization allow safely associating the microstreaming pattern to a given shape oscillation. This alternative procedure is mandatory as (i) shape oscillations may turn off, (ii) bubble stability may abruptly increase leading to the positional instability of the bubble, (iii) bubble may fragment when large deformations occur. Even if these events are rare, it is important to verify that the bubble dynamics stays the same by recording it both before and after filming the microstreaming pattern. (In this way it can be assured that the bubble motion and the pattern are really correlated).

Is it evidenced that a bubble oscillating predominantly on a given mode number leads to a particular microstreaming pattern, as shown in Figure 12. The pattern is unique and depends on the modal content of the interface motion. As illustrated in Figure 13, the same predominant mode number may induce large- or small-distance vortices depending on the number, amplitude, and phase of the secondary modes that are excited.

These observations may have practical use in medical applications such as targeted and localized ultrasound-mediated drug delivery, for instance. Bubbles are known to act as vectors for permeabilizing tight junctions between cells, and even the cell membrane itself, leading to sonoporation¹. In case of stably oscillating microbubbles, this phenomenon may be induced by the shear stress or shear stress gradients³⁵ induced by bubble oscillations, through the generation of microstreaming flows. We recall that microstreaming is a nonlinear, second-order phenomenon. At first, scaling the observed streaming patterns to the one obtained for therapeutic, shelled, microbubbles with smaller sizes (~3 µm radius) is not straightforward. We already evidenced in the introduction how nonspherical dynamics of free or coated bubbles of one order of magnitude size difference may be scaled: the eigenfrequency ω_n of a given mode n is related to the bubble size as ²⁵. In Dollet et al.²⁷, shape modes of order 4 have been captured for coated micrometric bubbles excited at 1.7 MHz, similarly to the observed shape mode number in our experiment. Also, the applied pressure strongly differs, as pressure up to 200kPa are required to trigger shape modes on ultrasound contrast agent microbubbles²⁷. In the proposed setup, the maximum applied pressure does not exceed 25 kPa. The strong difference in applied pressure results from the triggering of surface instabilities, as shape modes appear above a certain pressure threshold. For the experimental conditions at 1.7 MHz given in Dollet et al. ²⁷, it has been shown that the pressure threshold leading to shape instability is around 150 kPa for a mode 4³⁶. For a 30 kHz driving frequency, only a 10 kPa driving field amplitude is required to trigger shape instability on a ~50 µm bubble. Once triggered, the shape instability develops after a few acoustic cycles, and demonstrates a plateau saturation of the mode amplitude. Amplitude saturation was observed for both free bubbles^24,29 and coated bubbles²⁷. It indicates the possibility of reaching steady-state shape oscillations for free or coated bubbles, with shape oscillations as large as 25 to 50% of the radial mode amplitude^27,37. Using our experimental approach, we reach extreme shape deformations in the configuration, (where a_n is the shape mode amplitude), as illustrated in Figure 13.

To summarize, the proposed experimental setup allows scaling the main features of nonspherical oscillations of microbubbles, even for sizes varying with almost one order of magnitude. Concerning the microstreaming flow, the scaling of flow velocity may be investigating for bubbles exhibiting both lateral and radial oscillations⁷, or a nonspherical mode that is self-interacting³². In both cases the streaming velocities scale as v ~ ωR₀a_ia_j, where i, j denotes the considered mode amplitudes normalized by the bubble radius. For similar values of the nonspherical expansion parameter a_i, identical streaming velocities are obtained when ωR₀ ~ Constant. Comparing our experimental conditions to the one used for therapeutic shelled microbubbles²⁷, theoretical predictions of streaming velocities differ only from a factor 2.5. Measurements of streaming velocities by particle tracking velocimetry led to estimations of the velocity magnitude of 1mm/s in the here presented setup. This value is similar to the one obtained when investigating microstreaming induced by ultrasound contrast agents¹⁹. Concerning the spatial organization of the streaming pattern, the angular distribution of the flow vortices around the bubble interface is independent of the bubble radius³¹. Only the radial expansion of the streaming field is impacted by the bubble size modification. This radial expansion scales as , where is a coefficient linked to the investigated mode number. It is clear that the overall shape of the streaming pattern is conserved, as the radial expansion is ruled by the bubble radius R₀. However, as illustrated in Figure 13, the streaming pattern can significantly differ even when considering the same shape mode number. Figure 13 highlights the huge impact of the bubble interface dynamics on the streaming pattern, and particularly on the spatial rate of change in the velocity field. The spatial distribution of shear stress, or shear stress gradient, has been indicated as an appropriate indicator of sonoporation efficiency³⁵. In our proposed experimental setup, only the shear stress in the bulk fluid may be assessed at this stage. Further extension to the wall shear stress would require the addition of a nearby surface close to the bubble. It is predictable that a surface in the bubble vicinity will disturb the bubble positional stability by locally modifying the standing wave field. Ensuring bubble stability at a close distance from a wall is still a challenge that may be partly solved by adding a secondary ultrasound field dedicated to bubble trapping with a wavelength identical to the bubble-wall distance. Such a dual-frequency acoustic levitation chamber was already designed for investigating bubble pair dynamics and interaction forces³⁸. Unfortunately, the large size difference between the bubbles investigated here and biological cells (typical radius ~10µm) makes the direct use of this experimental setup impossible for biological investigations. However, we expect that our experimental results in combination with the most recent theoretical developments on bubble-induced microstreaming will help improve such modeling, as well as provide confidence in the theoretical prediction of bubble-induced shear stress or shear stress gradients in the vicinity of a cell membrane.