(a) Experimental setup consisting of a power supply where a 5500 μF capacitor is charged to 60 V via a 1 kΩ resistor. The spark bubble is created in a water tank at the location of two crossed electrodes when the discharge circuit is activated with a switch. The bubble dynamics are captured using a Photron SA 1.1 high speed camera; (b) A photograph showing the bubble “trapping” mechanism using silicone oil; (c) Definition of D (distance between the center of the two bubbles), R s (radius of the initial stationary bubble), and R o,max (the maximum radius of the oscillating bubble).
Interaction between a stationary bubble (initial radius, R s = 0.84 mm) and a spark-generated nonequilibrium bubble (maximum radius, R o ,max = 5.15 mm) with center-to-center distance, D = 3.43 mm, hence R′ = 0.16 and D′ = 0.67. Scale bars of 5 mm are shown in the first frames. Time, t is shown in the bottom right hand corner of every frame. (a) Experimental observations occupy the upper half of the figure. The first frame at t = 0 μs shows a stationary bubble trapped within a droplet of silicone oil and at t = 50 μs and beyond, a jet noticeably emerges through the wall of the stationary bubble in a direction away from the spark bubble (which expands until its maximum at t = 750 μs and collapses at 1150 μs); (b) Corresponding numerical results are shown at the lower half of the figure. While the spark bubble expands initially, a budding jet is formed within the stationary bubble. It is predicted that this jet strikes the wall of the stationary bubble att = 27 μs; (c) This insert shows the enlarged view of the stationary bubble jet from the frame at t = 27 μs from the numerical results.
Interaction between a stationary bubble (initial radius, R s = 0.96 mm) and a spark-generated nonequilibrium bubble (maximum radius, R o ,max = 4.81 mm) with center-to-center distance, D = 10.01 mm, hence R′ = 0.20 and D′ = 2.08. 5 mm scale bars are shown in the first frames. Time, t is shown in the bottom right hand corner of every frame. (a) Experimental results. The first frame at t = 0 μs shows a stationary bubble held within a droplet of silicone oil. At t = 250 to 750 μs, the stationary bubble appears to have an internal jet forming while the spark bubble expands to its maximum. Some protrusions can be seen at the left hand side of the stationary bubble at t = 900 μs. During the collapse of the spark bubble, the stationary bubble flattens, starts to disintegrate and is even slightly attracted toward the spark bubble. Both bubbles breakup into numerous small bubbles (t = 3100 μs); (b) Corresponding numerical results. At t = 250 μs, we notice that the budding jet stops halfway within the stationary bubble (which contracts until t = 550 μs). The protrusion observed earlier is also predicted here at t = 750 μs and t = 900 μs and is clearly not a jet penetrating the bubble. This protrusion disappears again at t = 950 μs and instead a jet toward the spark bubble appears.
Jet velocity as a function of the dimensionless interbubble distance D′ for various dimensionless initial stationary bubble sizes R’ s [Eqs. (1) and (2)].
Expansion and collapse of an oscillating bubble (maximum radius, R o ,max = 4.10 mm) beneath two nearby (initially) stationary bubbles (initial radii, R s = 1.00 mm) at center to center distance of D = 2.20 and 2.10 mm for the left and right bubble, respectively. The stationary bubble centers are separated 2.00 mm initially and they are captured by a silicone oil droplet to keep them in place. D′ for the left and right stationary bubbles are found to be 0.53 and 0.51, respectively while R′s = 0.24 for them both. As the spark bubble expands, it causes the other bubbles to collapse and form outward directed jets (300 and 400 μs). After reaching its maximum radius at 400 μs, the spark bubble collapses (600 and 700 μs). Remnants of the oil droplet aid in the flow visualization. Time, t in μs is given on the top right corner of each frame.
The interaction between a spark-generated bubble and two initially stationary bubbles placed in a line. The stationary bubbles (initial radii of R s = 0.65 mm) have center-to-center distances from the spark bubble (maximum radius, R o ,max = 3.40 mm) at D = 7.10 and 5.80mm for the left and right bubble, respectively. The stationary bubble centers are initially separated 1.30 mm apart. As the spark bubble expands, the right most stationary bubble collapses (frame 350 μs) and seems to generate a jet that penetrates the other stationary bubble. The spark bubble expands to its maximum radius at t = 500 μs and collapses from t = 750 to 850 μs. The jet can be visualized as a thin stream of liquid on the left of the stationary bubble from t = 750 μs onward. Time is given on the left bottom corner of each frame.
Typical interaction of a spark bubble near a free surface. Initially the center of the bubble is 5.76 mm away from the free surface. It expands to its maximum radius 5.03 mm at t = 0.201 ms. A water jet, going through the collapsing bubble away from the interface, is visible at t = 0.268 and 0.335 ms. The bubble then collapses (t = 0.268 to 0.402 ms). At the same time, a water plume with small horizontally directed micro jets is seen to have developed on the free surface. Then a “crown” shaped water plume appears between t = 0.804 to 2.41 ms. The “crown” moves up and eventually breaks into droplets (t = 3.89 to 6.23 ms). After which the water plume continues to rise (t = 7.91 to 12.9). A scale-bar of 10 mm is indicated in the first frame (time is indicated in each frame).
Interaction of a spark bubble located very near to a free surface. The initial distance of the center of the bubble to the free surface is 1.17 mm. The bubble’s maximum radius is estimated from the frame at t = 1.07 ms to be 3.64 mm. When the spark bubble is formed, a spray is observed on top of the water plume (frames 0.000, 0.134, and 0.268 ms). The water plume breaks up as the bubble collapses with a jet away from the free boundary (t = 2.14 to 5.83 ms). A scale bar of 5 mm is indicated in the first frame. The time for each frame is given on top.
Interaction of a stationary bubble (upper) and a spark bubble (lower) near a free surface. The distance between the centers of the two bubbles is 2.80 mm; the distance between the center of the spark bubble and free surface is 5.80 mm. The initial radius of the stationary bubble is 1.50 mm; and the maximum radius of the spark bubble (taken at frame 0.40 ms) is 3.50 mm. After 0.15 ms, the growing spark bubble has caused a strong deformation of the stationary bubble toward the free surface. A jet is formed in this bubble toward the free interface (t = 0.25 ms) and continues to develop from 0.40 to 1.95 ms. Meanwhile the spark bubble expands to its maximum size and then collapses with a jet away from the free surface. Time for each frame is indicated in milliseconds.
Interaction of two side-by-side stationary bubbles located between a free surface (black horizontal line) and a spark bubble. The stationary bubbles have radii of 1.00 mm (left) and 0.80 mm (right) and the initial distance between their centers is 1.60 mm. The initial centers of the left and right stationary bubbles are separated from the spark point at 2.80 and 2.40 mm respectively. The distance between the center of the spark bubble and the free surface is 6.20 mm. As the spark bubble expands (t = 0.10 ms), the stationary bubbles start to deform in the upward direction resulting in jets directing toward the free surface (t = 0.2 ms), yet with a different angle for each bubble. The spark bubble continues to grow, and reaches its maximum radius of 3.10 mm at t = 0.4 ms. It then collapses and reaches its minimum size at 0.75 ms, after which the spark bubble re-expands and moves away from the free surface with a downward directed jet (t = 0.95 to 1.75 ms).
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