Coupling between Buoyancy Forces and Electroconvective Instability near Ion-Selective Surfaces

Recent investigations have revealed that ion transport from aqueous electrolytes to ion-selective surfaces is subject to electroconvective instability that stems from coupling of hydrodynamics with electrostatic forces. These systems inherently involve fluid density variation set by salinity gradients. However, the coupling between the buoyancy effects and electroconvective instability has not yet been investigated although a wide range of electrochemical systems are naturally prone to these interplaying effects. In this study we thoroughly examine the interplay of gravitational convection and chaotic electroconvection. Our results reveal that buoyant forces can significantly influence the transport rates, otherwise set by electroconvection, when the Rayleigh number Ra of the system exceeds a value $\mathrm{Ra}\sim 1000$. We show that buoyancy forces can significantly alter the flow patterns in these systems. When the buoyancy acts in the stabilizing direction, it limits the extent of penetration of electroconvection, but without eliminating it. When the buoyancy destabilizes the flow, it alters the electroconvective patterns by introducing upward and downward fingers of respectively light and heavy fluids.

Figure 1

Aqueous monovalent salt solution between two horizontal cation-selective surfaces subject to dc electric field in a gravitationally (a) unstable and (b) stable arrangement. Surface plots show the fully developed anion-concentration fields at $t=0.2$ superimposed with flow streamlines. Here, $\mathrm{\Delta }\varphi =80V_T$, $\kappa =0.5$. The $u_{\text{rms}}$ is scaled by $D/L$.

Figure 2

Effect of magnitude and direction of the gravitational force. (a) Time averaged current density $⟨I⟩$ where the cross symbols represent $\mathrm{Ra}=0$ and the green shaded area depicts when gravitational effects are negligible. The red shaded area and the blue shaded area depict the gravitationally unstable and stable regimes, respectively. Triangles, squares, and circles represent $\mathrm{Ra}=1\times {10}^3$, $50\times {10}^3$, and $150\times {10}^3$, respectively. The black dashed line presents the one-dimensional $⟨I⟩$. (b) Instantaneous current density $I$ at $\mathrm{Ra}=0$ (green line) and $\mathrm{Ra}=150\times {10}^3$ for gravitationally unstable (red line) and stable (blue line) configurations. Here, $\mathrm{\Delta }\varphi =80V_T$. In (a) and (b), $\kappa =0.5$.

Figure 3

Time averaged current density with respect to the Ra number obtained for gravitationally unstable configuration at (a) $\mathrm{\Delta }\varphi =60V_T$ and (b) $\mathrm{\Delta }\varphi =80V_T$ for various $\kappa$. In (a) and (b), $\kappa =0.5$ (closed diamond), $\kappa =0.2$ (open diamond), $\kappa =0.1$ (square), $\kappa =0.05$ (circle), and $\kappa =0$ (downward triangle).

Figure 4

Contributions of RB and EKI induced convection to the current density in a gravitationally unstable arrangement. (a) $⟨I⟩$ data (symbols) plotted with a power law scaling $⟨I⟩\sim y_0+m{\mathrm{Ra}}^n$ (dotted lines) at a finite $\kappa =0.5$ for various $\mathrm{\Delta }\varphi$, revealing poor correlations. (b) Current density data obtained at $\kappa =0$ plotted with a power law scaling $⟨I⟩(\kappa =0)\sim {\mathrm{Ra}}^{0.3}$ for various $\mathrm{\Delta }\varphi$. (a),(b) $40V_T$, circles; $60V_T$, squares; $80V_T$, triangles; and $100V_T$, diamonds. (c) Current density $I^{*}$ suggested to be induced by the chaotic EKI vortices with respect to Ra at $\mathrm{\Delta }\varphi =80V_T$. The symbols present the DNS data obtained at $\kappa =0.5$ (closed upward triangle), $\kappa =0.2$ (open upward triangle), and $\kappa =0.1$ (open downward triangle). Lines present exponential decay fits with respect to Ra; $I^{*}\sim e^{-b\mathrm{Ra}}$, where $b\sim \mathcal{O}(10^{-6})$ for $\kappa =0.5$ (solid line), $\kappa =0.2$ (dashed line), and $\kappa =0.1$ (dotted line).