Electrostatic Debye layer formed at a plasma-liquid interface

We construct an analytic model for the electrostatic Debye layer formed at a plasma-liquid interface by combining the Gouy-Chapman theory for the liquid with a simple parabolic band model for the plasma sheath. The model predicts a nonlinear scaling between the plasma current density and the solution ionic strength, and we confirmed this behavior with measurements using a liquid-anode plasma. Plots of the measured current density as a function of ionic strength collapse the data and curve fits yield a plasma electron density of $\sim {10}^{19}{\mathrm{m}}^{-3}$ and an electric field of $\sim {10}^4\mathrm{V}/\mathrm{m}$ on the liquid side of the interface. Because our theory is based firmly on fundamental physics, we believe it can be widely applied to many emerging technologies involving the interaction of low-temperature, nonequilibrium plasma with aqueous media, including plasma medicine and various plasma chemical synthesis techniques.

Figure 1

A sketch of the theoretical distribution of (a) charged species, (b) net space charge, and (c) resultant electrostatic potential profile plotted as a function of distance normal to the interface.

Figure 2

(a) A schematic of the experimental setup showing the plasma electrochemical cell and camera. Not shown is the microscope and kinematic mounts used for positioning the cathode above the solution surface. (b) Photographs (100 ms exposure) illustrating how the plasma visibly contracts with increasing ionic strength at a fixed plasma current of 10 mA. (c) The optical emission intensity profile at the interface for a $250\mathrm{m}M \mathrm{NaCl}{\mathrm{O}}_4$ solution extracted from a digital photograph (25 ms exposure).

Figure 3

Current-voltage relations for the discharge for $200\mathrm{m}M$ solutions of $\mathrm{NaCl}{\mathrm{O}}_4$ and $\mathrm{MgS}{\mathrm{O}}_4$ with gap distances of 1 and 2 mm.

Figure 4

A photo of the liquid-anode discharge using (a) $200\mathrm{m}M \mathrm{NaCl}{\mathrm{O}}_4$ solution containing $p\mathrm{H}$ sensitive dye, which turns dark green due to the production of NaOH, and (b) $200\mathrm{m}M \mathrm{MgS}{\mathrm{O}}_4$ solution, which develops a white precipitate due to the production of $\mathrm{Mg}{\left(\mathrm{OH}\right)}_2$.

Figure 5

The measured current density is plotted as a function of ionic strength for monovalent solutions of $\mathrm{NaCl}{\mathrm{O}}_4$ and divalent solutions of $\mathrm{MgS}{\mathrm{O}}_4$ at gap sizes of (a) 1 mm and (b) 2 mm. Solid black lines represent a curve fit using Eq. (15).

Figure 6

The electric field just beneath the liquid surface is plotted as a function of ionic strength, using the extrapolated voltage drop of $V_L=30\mu \mathrm{V}$ and $33\mu \mathrm{V}$ across the liquid side of the interface for 1- and 2-mm gaps, respectively.