Evolution of the Plasma Bubble in a Narrow Gap

We investigate the evolution of the plasma bubble in a narrow gap. According to the morphological changes, we further show that there are three phases during the evolution for spherical fluctuating, radial fingering, and dense branching plasma bubbles, which are similar to the radial fingering pattern in a Hele-Shaw cell. The dependences of the wavelength of the fingering boundary are experimentally discussed. The dense branching plasma bubble is found with a fractal dimension of $D_f=1.74$. The reduced surface tension pressure from the local heatings due to the filamentary discharges is suspected of being responsible for the growth of the radial fingering and the dense branching plasma bubbles.

Figure 1

The evolution of a plasma bubble at $V=7.3{\mathrm{kV}}_{pp}$, $d=85\mu \mathrm{m}$, and $\mu =50{\mathrm{mm}}^2/\mathrm{s}$. (a) Original gas bubble before ignition. (b)–(f) According to the morphological changes of the plasma bubble, there are three phases in the evolution process for spherical fluctuating, radial fingering, and dense branching plasma bubbles. The evolving time (the plasma bubble is ignited at time zero) is labeled in each image. (g) Changes of the area ratio of the plasma bubble and gas bubble at different applied voltages. The upper inset shows that the shrinking of the plasma bubble is stronger at a larger driving voltage. The lower inset shows the current and voltage profiles, which suggest that the plasma bubble is operated at the filamentary discharge mode.

Figure 2

Measurements of the characteristics of the radial fingering plasma bubble. (a) A typical mode number analysis of the fingering boundary. The inset shows the corresponding radial fingering plasma bubble. (b) The wavelength $\lambda$ is constant for different sizes of the initial gas bubble. $\lambda \sim 0.7\mathrm{mm}$ for $d=85\mu \mathrm{m}$, $V=7.3{\mathrm{kV}}_{pp}$, and $\mu =50{\mathrm{mm}}^2/\mathrm{s}$. (c),(d) show $\lambda \propto d{\mu }^{-0.5}$.

Figure 3

Measurements of the characteristics of the dense branching plasma bubble. (a) The skeleton distribution of a typical branching plasma bubble in polar coordinates. (b) The fractal dimension analysis of the morphology of the branching plasma bubble by the sandbox method suggests a fractal dimension of $D_f=1.74$.

Figure 4

Microbubble ejection near the protruding boundary of a plasma bubble at (a) the radial fingering phase and (b) the branching phase. There are some bright spots observed near the tips of the protruding boundary.

Figure 5

Schlieren observation of the plasma bubble. (a) Clear boundary of the initial gas bubble is observed. (b)–(f) The boundary of the plasma bubble starts fluctuating right after the ignition. A hot gas layer is observed next to it. The regions near the outward tips and inward boundary are found with different thicknesses of the hot gas layer. (g) Surface tension would try to suppress the fluctuation and smooth a typical fluctuating gas-oil interface. (h) Local heatings on the boundary of the protruding boundary would enhance the fluctuation of the boundary due to the reduced surface tension pressure.