Deionization shock driven by electroconvection in a circular channel

In a circular channel passing overlimiting current (faster than diffusion), transient vortices of bulk electroconvection are observed in a salt-depleted region within the horizontal plane. The spatiotemporal evolution of the salt concentration is directly visualized, revealing the propagation of a deionization shock wave driven by bulk electroconvection up to millimeter scales. This mechanism leads to quantitatively similar dynamics as for deionization shocks in charged porous media, which are driven instead by surface conduction and electro-osmotic flow at micron to nanometer scales. The remarkable generality of deionization shocks under overlimiting current could be used to manipulate ion transport in complex geometries for desalination and water treatment.

Figure 1

(a) Sketch of a circular channel. The positive voltage bias for $\tilde{\varphi }\left(1\right)>\tilde{\varphi }\left(\chi \right),\tilde{I}<0$. (b) OLC dependent on ${\tilde{c}}_d$, (c) concentration distribution, and (d) profile of the electric field ($\tilde{\varphi }=35,{\tilde{c}}_d=0.1,R_d={\tilde{r}}_d{R}_2$).

Figure 2

Vortex observation from a top-down view. (a) Sketch of the PDMS device ($2R_2=6$ mm, $H\approx 35\mu \mathrm{m}, \chi =1/30$, and $\mathrm{\Phi }>0$ for the positive voltage bias). (b) The $I-V$ curve showing $I_{\mathrm{pos}}\approx 0.14\mu \mathrm{A}$. (c)–(e) Under an applied current at $2\mu \mathrm{A}$ in the overlimiting current regime, the time-lapse snapshot at $t=60$ s with an exposure time of 5 s for (c), and with an exposure time of 100 ms for (d); (e) PIV images with a short exposure time of 40 ms at $t=20$ s when the first vortex pair occurs. (f) Voltage and vortex size increase with time. (g) The number of vortex decreases with the applied current, while the size of vortex increases with the applied current when the vortex occurs. Scale bar in (c)–(e) for $200\mu \mathrm{m}$.

Figure 3

Spatiotemporal evolution of concentration ($R_1=100\mu \mathrm{m}$). (a) Snapshots of fluorescent signals at $20\mu \mathrm{A}$, red circular contours for the propagation front. Saturated white color in the center due to the extra liquids around the copper wire. (b) Radial profiles of fluorescent intensity at $t=0$, 20, 40, and 60 s; $R_d$ is marked by the red dash line at the steep jump of fluorescent intensity due to the concentration depletion. $R_d$ has a 1/2 power law under various currents (c) and voltages (e), while $D_{\mathrm{eff}}$ is proportional to the currents (d) and voltages (f) from Eqs. (3) and (4). Error bars in (d) and (f) for the standard deviations from six measurements.

Figure 4

Model for DS propagation. The experiment data under a constant voltage at 20 V are fitted well by Eq. (7). The power law of 1/2 is recovered for a smaller radius $R_1=100\mu \mathrm{m}$ ($\chi =1/30$), while deviation from 1/2 power law occurs for a larger radius $R_1=1$ mm ($\chi =1/3$). The lower bound of $R_d$ is limited by the extra liquids around the wire, and the upper bound of $R_d$ is $R_2$ (3 mm). The experimental data were reproduced by three times.

Figure 5

Measured $I-V$ curves for 10 mM aqueous ${\mathrm{CuSO}}_4$ solution showing (a) $I_{\mathrm{pos}}\approx 0.4\mu \mathrm{A}$ for the positive voltage bias and (b) $I_{\mathrm{neg}}\approx 2.25\mu \mathrm{A}$ for the negative voltage bias ($\chi =1/30$). (c) $\tilde{I}$ agreeing well with Eq. (A4) and error bars for the standard deviations from four measurements.

Figure 6

Observed DS and vortices under the negative voltage bias ($\chi =1/30$). (a) Snapshot of fluorescent signals at 60 s under an applied current at $10\mu \mathrm{A}$; red line for the front position of DS. (b) An array of observed vortices near cathode side at 60 s under an applied current at $5\mu \mathrm{A}$.