Saffman-Taylor–like instability in a narrow gap induced by dielectric barrier discharge

This work is inspired by the expansion of the plasma bubble in a narrow gap reported by Chu and Lee [Phys. Rev. Lett. 107, 225001 (2011)]. We report the unstable phenomena of the plasma-liquid interface with different curvature in a Hele-Shaw cell. Dielectric barrier discharge is produced in the cell at atmospheric pressure which is partially filled with silicone oil. We show that the Saffman-Taylor-like instability is observed on the bubble-type, channel-type, and drop-type interfaces. The Schlieren observation of the plasma-drop interaction reveals that there is a vapor layer around the drop and the particle image velocimetry shows the liquid flow inside the drop. We propose that the thermal Marangoni effect induced by the plasma heating is responsible for the unstable phenomena of the plasma-liquid interaction. The fluctuation of the interface is shown consistently with the Saffman-Taylor instability modified by the temperature-dependent velocity and surface tension.

Figure 1

Schematic diagram of the experimental setup.

Figure 2

Observations of the unstable phenomena in various environments. Experiments were conducted at $d=100 \mu \text{m}, \nu =50{\text{mm}}^2/\text{s}, V_{\text{pp}}=8.3$ kV. (a)–(c) Discharge in the bubble-type background (gas bubble surrounded by liquid oil). (d)–(f) Discharge in the channel-type background (left: gas region; right: liquid region). (g)–(i) Discharge in the drop-type background (liquid drop surrounded by gas). The time of the sequential acquisition is labeled on the corner of the image. The periodic fluctuations and the dense branching stages of the liquid were observed in various setups.

Figure 3

Characteristics of the periodic fluctuation in the drop-type environment. (a) The wavelength $\lambda$ of the fluctuation is found linearly proportional to the gap size $d$ at $\nu =50{\text{mm}}^2/\text{s}$ and $V_{\text{pp}}=8.3$ kV. (b) The wavelength $\lambda$ of the fluctuation is found linearly proportional to $1/\sqrt{\nu }$ at $d=100 \mu \text{m}$ and $V_{\text{pp}}=8.3$ kV.

Figure 4

(a)–(d) Schlieren observation on the interface of the drop. The time of the sequential frame is denoted at the corner of the image. A gas layer is observed after the ignition of the discharge. (e)–(h) Particle image velocimetry analysis of the flow in the drop. The averaged velocity in each frame is labeled in the same scale. The time of the sequential frame for measuring velocity is labeled in the corner of the image. The PIV result shows that the protrusions of the liquid fingers are driven by the liquid flow in the indented regions. Experiments were both conducted at $d=100 \mu \text{m}, \nu =50{\text{mm}}^2/\text{s}, V_{\mathrm{pp}}=8.3$ kV.

Figure 5

The wavelengths of the fluctuation in the channel-type environment and in the drop-type environment are shown by blue squares and red circles. The simulation of the proposed model (gray curve) shows consistent results that confirm the effects of the temperature-mediated velocity and surface tension. Inset: the initial velocity is fitted by $v=v_0(1+C\mathrm{\Delta }{V}_{\text{pp}})$. It is found that $C=1.016$ 1/kV at $\nu =50{\text{mm}}^2/\text{s}$ and $d=100 \mu \text{m}$.

Figure 6

Demonstration of the plasma-liquid interaction in a ring-shaped bubble. The interfacial instability is observed at both interfaces.