Measurement and Evaluation of Effective Mixing Diffusivity due to Chaotic Three-Dimensional Electroconvection

Numerous fluid systems exhibit mean transport effects that are largely determined by the dynamics of underlying velocity fluctuations. Examples include electroconvection in the over-limiting regime, where the mean current is significantly augmented due to chaotic vortices induced by hydrodynamic instability of the ion concentration polarization layer. Detailed numerical simulation of such systems is prohibitively expensive due to the wide range of scales present. The motivation of this work is modeling the mean transport in such system using lower dimensional models that incorporate a steady effective diffusivity, often referred to as 'eddy diffusivity.' To this end, the Micro-PIV data of three-dimensional, space-time-resolved velocity fields in a canonical electroconvection setting [Stockmeier et al., J. Membrane Science 640, 119846 (2021)] is used to drive a forced transport equation and thereby measure the effective mixing diffusivity to leading order using the IMFM framework [Mani and Park, Phys. Rev. Fluids 6, 054607 (2021)]. A posteriori analysis is performed by simulating the Poisson-Nernst-Planck equations augmented by the measured effective mixing diffusivity. The resulting current-voltage curve is compared to experiments with satisfactory agreement.