Direct Observation of a Nonequilibrium Electro-Osmotic Instability

We present a visualization of the predicted instability in ionic conduction from a binary electrolyte into a charge selective solid. This instability develops when a voltage greater than critical is applied to a thin layer of copper sulfate flanked by a copper anode and a cation selective membrane. The current-voltage dependence exhibits a saturation at the limiting current. With a further increase of voltage, the current increases, marking the transition to the overlimiting conductance. This transition is mediated by the appearing vortical flow that increases with the applied voltage.

Figure 1

A schematic view of the experimental system. (a) A horizontal transparent PMMA cell is sealed by a massive, polished copper anode and a CEM at the bottom and top, respectively. Above the membrane, a large compartment is sealed by a massive copper cathode. The voltage bias, $V$, is applied directly to the cell in series with a $330\Omega$ resistor over which the current response, $I$, is measured. The electrolyte solution is seeded with $1\mu \mathrm{m}$ polystyrene tracer particles. A typical enlarged view is shown on the left. The dashed line illustrates the CP profile at the limiting current. (b) A typical $I\mathrm{\text{−}}V$ curve measured by continuously increasing $V$ at an average rate of $3\mathrm{mV}/\sec$ is shown. Three regimes are highlighted: the Ohmic underlimiting, limiting, and overlimiting regime.

Figure 2

Variations in the current relaxation dynamics. (a) A time series of the current (blue) passing through the membrane. Voltage (black line) is increased in discrete jumps of 0.1 V once every minute. Three regions are highlighted, as in Fig. 1. Above $10\mu \mathrm{A}$, an increase in voltage is followed by a rapid rise in current and then a slower relaxation. Three relaxation events within the limiting region are highlighted by dashed rectangles. These correspond, from left to right, to (b),(c), and (d), respectively. (b) ED relaxation of concentration to a new linear steady-state profile leads to an exponential decay. (c) Movement toward the establishment of limiting regime relaxation is characterized by quasilogarithmic decay. (d) At the developed limiting regime, the time decay changes from an exponential to a power-law with a measured exponent of $-1/2$. Continuous lines in (b)–(d) follow from time-dependent 1D ED simulations.

Figure 3

(a) Time-lapse snapshots of the experimental cell seeded with tracer particles showing ‘quasi-steady-state’ streamlines. The membrane is situated at the top boundary of each image, and for each snapshot the applied voltage (Volts) is indicated. (b) Corresponding current-voltage curve (c) The measured (dotted line) and numerically computed (solid line) average size (height) of the vortical structures increases approximately linearly with the value of the bias voltage. Their appearance coincides with the shoulder of the curve in (b).

Figure 4

Numerical simulation of EC for dimensionless Debye length ${10}^{-6}$ showing hysteresis: black line is shown on the way up, and blue line is shown on the way down. (a) Current-voltage dependence. (Inset: Laterally averaged concentration profiles for two voltages corresponding to the limiting (1) and overlimiting (2) currents); (b) the flow streamlines’ pattern; (c) voltage dependence of the absolute value of the dimensionless linear flow velocity averaged over the DL; (d) the current’s relaxation in the overlimiting regime.