Electro - osmotic instability and chaos : membranes , polarizable surfaces , and cross - flow

Despite century-old developments in the fields of electrokinetics and electrochemistry, the fundamental phenomenon of ionic transport above the diffusion-limited current across a charge-selective surface in aqueous electrolytes is still not fully understood (Nikonenko et al. 2010). Charge-selective surfaces include ion-selective membranes (Druzgalski et al. 2013), electrodes (Newman & Thomas-Alyea 2004), and nanochannels (Zangle et al. 2010), and are used in applications such as electrodialysis/desalination (Strathmann 2010), flow batteries (Weber et al. 2011), electrodeposition (Newman & Thomas-Alyea 2004), lab-on-a-chip bioanalysis (Wang et al. 2005), fuel cells, and the production of chemicals (Pourcelly et al. 2012). Levich recognized that the transport at large voltages becomes rate-limited by diffusion from a well-stirred bulk to an ion-depleted charge-selective surface (see Figure 1a) (Levich & Spalding 1962). For currents above the diffusion-limit, several theories for possible mechanisms have been proposed including electro-osmotic instability (EOI) (Rubinstein & Zaltzman 2000; Zaltzman & Rubinstein 2007), water splitting (Simons 1979), and current-induced membrane discharge (Andersen et al. 2012). Accumulating experimental evidence has made it clear that EOI mixes the diffusion layer and enhances the transport in the overlimiting regime (Maletzki et al. 1992; Chang et al. 2012). EOI develops due to electrostatic body forces in a charged boundary layer, the socalled extended space charge (ESC), that forms when voltages larger than a few times the thermal voltage O(25 mV) are applied across the system. The ESC is one of several electrochemical boundary layers and it emerges between the electric double layer (EDL) and the diffusion layer (DL). For a more thorough exposition of EOI, we refer the reader to our recent publication (Druzgalski et al. 2013). In this brief, after introducing the governing equations in Section 2, we explain our recent research on EOI in three different settings. In Section 3, we study overlimiting transport in a well-stirred stationary reservoir at a flat ion-selective surface (see Figure 1a). This study demonstrates for the first time that EOI transitions into fully chaotic flow. In Section 4, we extend our first analysis by considering the transport at a cylindrical and inert metallic electrode (see Figure 4) and show for the first time the development of EOI and chaotic flow in this type of system. In Section 5, we do a linear stability analysis of an electrodialysis system where we account for the cross-flow (see Figure 1b) and show that it has a stabilizing effect on the EOI.