Cavitation bubble dynamics in a vicinity of a thin membrane wetted by different fluids

Understanding and controlling the interaction of cavitation bubbles and nearby material is becoming essential optimization of various processes. We examined the interaction of a single bubble with a membrane with different fluids on each side of it. Significant differences in bubble behavior depending on the fluid properties were observed, while the influence of membrane properties was less pronounced. The study has important implications, such as optimization of sonoporation (targeted drug delivery) where the mechanism, by which the permeability of the membrane is increased, is still not well understood. These results show that the focus of the optimization process should, in the first place, lie on the properties of liquids, rather than the mechanical properties of the membrane itself.

www.nature.com/scientificreports/ Experimental approach. Figure 1 shows the experimental setup. A Nd:YAG laser. Beam is expanded and then tightly focused with a lens, NA of the optical system is 0.2 in water. Optical breakdown occurred in the focal area, followed by bubble formation. The conversion efficiency was approximately 20% for an unbounded bubble (calculated as the fraction of potential energy of the maximal achievable bubble size R b = 1.1 mm ( E = p at V b ) and the laser energy delivered to the breakdown spot (already considering the losses in optical system and absorption in water-roughly 45% of the initial laser energy of 6 mJ)). In the presented experiments we used lower laser energy, what resulted in a bubble with R≈0.9 mm. This is comparable to the setups of other researchers 22,23 . No significant differences in efficiency due to the changes in liquids or membranes is expected-all energy is deposited at breakdown, when membrane is far enough to not to be in direct contact with plasma. The evolution of the cavitation bubble was recorded by a high-speed camera Photron Fastcam SA-Z with a frame rate of 210,000 fps. The whole region of interest was 10 × 4 mm big and resolved by 384 × 160 pixels, leading to the pixel size of approximately 25 μm. LED light source Ryobi One + (50,000 lm) served as a backlight illumination source.
To determine the influence of the membrane properties, two very different materials were selected. Both foils were 10 μm thick. The measured elastic modulus of aluminum one was E Al ≈35 GPa. the elastic modulus of the plasticized PVC was several orders of magnitude lower-E PVC ≈50 MPa.
Membrane was fixed to a plastic cuvette filled by air, water or oil. To fix the foil, special attention was given, not to pre-stretch it. A thin layer of glue (cyanoacrylate) was first applied to cuvette sides. A larger sheet of foil was positioned on a flat surface and pressed against the cuvette. The excess of the foil was removed once glue set in place. Distilled water was used both inside the cuvette as well as in the water container to decrease the amount of impurities. Vegetable oil with viscosity 50 cP and density 915 g/cm 3 was used.
Cuvette with membrane was oriented with membrane down and fixed to a 3-D positioning stage to allow precise manipulation of its position. As shown in Fig. 2, laser is incident parallel to the membrane.

Results
Several exemplary cases are shown first. These all correspond to same dimensionless ratio of bubble-interface distance h and maximum bubble radius R max : γ = h R max = 0.7 (except the case of a bubble in an "infinity", top sequence in Fig. 2). The time and size scales are the same in all figures. The first frame that is shown occurs 10 μs after the optical breakdown, the time difference between the frames is always 33 μs. Figure 2 shows the bubble dynamics for the case where there is no physical boundary placed between the two fluids (for the water-water case, this is of course a situation of an unbounded bubble).
For the case of unbounded bubble (H 2 O-No-H 2 O) the growth and the collapse are of course symmetrical. The size of the rebounded bubble is small compared to the maximum bubble radius. This points to the fact that the majority of the energy, which was released at the instant of collapse transferred into the shock wave emission.
When the plasma discharge is positioned near an oil interface (H 2 O-No-Oil), the growth phase is not significantly influenced-the maximum radius is the same. The collapse is obviously asymmetrical, a jet pointing away from the interface forms. Splitting of the bubble at the rebound is witnessed-a very small bubble moves toward the interface, while a much larger one follows the jet.
For the case of bubble evolution near a free surface (H 2 O-No-Air) the most obvious feature is a very large bubble rebound. The jet, which is penetrating the bubble has a large diameter (almost the size of the rebounded bubble) and is very slow-most of the energy is transferred to the building of the liquid cone on the free surface.
In Fig. 3 a 10 μm PVC membrane is separating the fluids. Placing a thin membrane to separate the fluids completely changes the bubble evolution. For the case of H 2 O-PVC-H 2 O, the rebound shows separation of initial volume into two bubbles of comparable size. The rebounded volume is also much larger than in the case of unbounded bubble (Fig. 3, top).
In the case of H 2 O-PVC-Oil similar dynamics is observed-at rebound the bubble splits into two equal parts. Unlike in the case of no membrane where jet is directed away from the oil, here significant portion of energy is directed towards the membrane. Jet resulting from breakdown is occasionally even sufficient to penetrate the membrane.
Interestingly, the H 2 O-PVC-Aircase is very similar to the case, where no membrane separated the fluids (Fig. 3, bottom). This is a result of very low inertia, which is offered by air (and the PVC membrane). Finally examples of case at γ = 0.7 with a 10 μm aluminum membrane separating the fluids is shown in Fig. 4. Aluminum membrane is stiffer than the PVC one. Hence, one would expect significant influence on the bubble evolution. However, this is not really the case. In the case of H 2 O-Al-Air, the stiffer aluminum membrane still does not change the volume or the jet formation-although the rebounded bubble is somewhat more elongated than in the case of PVC or no membrane, also it exhibits a "mushroom shape" during primary bubble collapse.  Influence of fluids and membranes was explored for different γ. Two parameters can be assessed simply and accurately: the cumulative volume of the rebound bubble(s) and their displacement. The volume was calculated by firstly measuring the area the bubble occupies and then assuming the rotational symmetry along the axis through the centre of the bubble in the direction perpendicular to the foil/interface. The displacement is determined by measuring the distance between the initial centre of gravity of the bubble and the one at the rebound (at the moment of maximum rebounded size of the bubble). Figure 5 shows ratio of cumulative volume of the rebounded bubble(s) nondimensionalised against the maximum volume of the bubble for different γ values.
The first obvious observation is that there is no significant influence of the nondimensional distance of the bubble form the interface. This is expected in the investigated range of γ, where the bubble collapse is severely asymmetrical. At larger distances, for example in the case of H 2 O-No-Oil at γ = 1.5, the bubble collapse deviates less from its initial spherical shape, hence its rebound is smaller. This can, of course, be extrapolated to the ideal, unbounded case ( The volume of the rebound is influenced only by the neighboring fluid. The type of membrane is not important at all, despite significant difference in their stiffness. The volume of the rebound decreases from approximately 30% for the case of air to about 7% for the case of water. In an ideal case (H 2 O-No-H 2 O) the ratio of volumes is only 2%. The closer the densities of neighboring fluids lie, the larger is ratio of the energy which is transferred to the shock wave and the smaller is the bubble rebound. Another effect could lie in the difference in the fluids viscosity, however in our preliminary study 24 on bubble dynamics near a water-oil interface we found that the differences in the behaviours of the bubble dynamics is insignificant, when oils with similar density and different viscosity are used. Figure 6 shows displacement of the rebounded bubble(s) together with their radius (given by the size of the circle) nondimensionalized against the maximum radius of the bubble. Since the bubble is not perfectly symmetrical, the radius is considered as one that would form a sphere of the same volume as the real volume of the bubble. Distance at maximum rebound is used. Positive values of displacement mark movement away from the interface and negative values towards the interface.
Air, due to its negligible inertia, offers little resistance, hence the bubble is not stretched and does not split, regardless of the presence of the membrane. Also, the radius of the rebounded bubble is in the range of 60-70% of the maximal radius (volume ratio of approximately 30%, Fig. 5). www.nature.com/scientificreports/ If either oil or water is wetting the membrane, in a certain range of γ the bubble splits, regardless of the membrane type. Three regimes can be observed. After the collapse the rebounded bubble remains attached to the membrane at approximately γ < 0.5, in a range of 0.5 < γ < 1 the bubble splits into two rebounded bubbles and when γ > 1 the bubble does not move or split at the rebound.
The rebounded bubble, which moves towards the interface is larger if membrane is present. This may be due to the wettability of the membranes used in the present experiment-both are hydrophilic and attract the bubble. Only in the case of H 2 O-No-Oil the bubble closer to the membrane is much smaller than the one displaced away from the interface.
One, not so obvious difference is that the density of the neighboring fluid influences the size of the rebounded bubbles. In the case of air, we cannot observe bubble splitting-all of the energy that went into rebound manifests in the bubble, which moves away from the interface. For the case of oil the energy is shared-more of it goes into the bubble, which is closer to the interface, but the opposing bubble (which moved away from the interface) still has significant size. The trend is continued for the case of water, where only very small bubble (even no bubble for the case of Al membrane) can be observed to move away from the interface, while a larger one remains in contact with the membrane.
Interestingly, the results presented here also fit well with the past study by Orthaber et al. 25 , where bubble collapse near a membrane wetted by water from both sides was observed. The elastic modulus of the polyethylene membrane was 0.24 GPa-an order of magnitude stiffer than the PVC one and an order of magnitude more elastic than the Al one used in the present experiment. An in-depth analysis was not performed in the work by Orthaber et al. 25

Conclusions
The present study opens a new look into the interaction between a bubble and a membrane. It shows that the stiffness of the membrane has a small influence on the bubble dynamics. The topology of the bubble collapse is predominantly dependent on the properties (density) of the fluid that wets the opposite side of the membrane. Also, the density of the fluid that wets the opposite side of the membrane determines the portion of the energy which is transferred into the shock wave emission and the portion that is transferred into the rebound.
This understanding is essential, for example, for optimization of sonoporation process, where one wants to create aggressive bubbles, which collapse in the vicinity of the membrane, transfer the majority of the energy into shockwaves or to a jet oriented towards the membrane in order to make it more permeable for drug delivery.
One of the possible paths for further exploration is scaling down the present experiment. This is essential for developing more exact methodologies for optimisation of sonication technologies, where the bubbles are several orders of magnitude smaller than the ones used in the present study.