Assessment of a reduced-order model for electroconvective flows and applications in optimization

Electroconvection (EC) is a hydrodynamic instability that arises in a wide range of electrochemical applications involving voltage-driven transport of ions through an ion-selective surface. In most applications, such as desalination, EC leads to enhanced transport rate and faster product throughput. Simulation of EC requires direct numerical solution (DNS) of the coupled Poisson-Nernst-Planck and Navier-Stokes equations, which can be extremely expensive since most practical regimes demand high spatial and temporal resolutions. We present the assessment of a reduced-order model for EC flows in which the velocity field is constrained to have a prescribed, smooth, periodic profile, and the charge transport is modeled via quasi-electroneutral approximation. Instead of as a solution to the Navier-Stokes equation, the velocity magnitude is determined by a balance between input mechanical power from the local electrostatic forces and viscous dissipation. We present results from this model and discuss its application in estimating bounds of opportunity for optimization of EC flows.