Critical selection of shear sheltering in electroconvective flow from chaotic to steady state

Abstract

Ion and water are transported by electroconvection near permselective membranes, resulting in complex phenomena associated with the flow–fines interaction. Sheltering the flow chaos by the shear flow is a common strategy in plasma fluids and has recently been successfully applied to control ionic fluids. The paper herein reveals the critical selection of shear velocity regarding the fluid from a chaotic to a steady state through numerical and theoretical analyses. For the shear sheltering, the dimensionless Debye length ${\lambda _D}$ with varying channel height is introduced to achieve a comprehensive discussion of the factors and laws affecting the shear vortex state. Based on an analysis of the vortex driving mechanism, the scaling of the slip velocity ${u_s}\sim {(\lambda _D^{ - 1}\Delta {\phi ^4})^{1/3}}$ is recommended as the critical selection factor for the steady and chaotic state under a fixed shear flow velocity, which involves the dimensionless Debye length ${\lambda _D}$ and voltage difference $\Delta \phi $ . Furthermore, for ionic fluid control by shear flow, a critical shear velocity ${U_{HPC}}$ is proposed to distinguish the electroconvective flow from a chaotic state to a steady state. When the shear flow velocity ${U_{HP}} > {U_{HPC}}$ , the shear flow shelters chaos, and the scaling law is also recommended for the regulation of the critical shear flow velocity ${U_{HPC}}$ jointly by ${\lambda _D}$ and $\Delta \phi $ . The analysis is confirmed by direct numerical simulation and existing experimental data (J. Fluid Mech, vol. 813, 2017, pp. 799–823). This work provides a more comprehensive physical insight for shear sheltering and affects the design of electromembrane microfluidics.

Interplay between Forced Convection and Electroconvection during the Overlimiting Ion Transport through Anion-Exchange Membranes: A Fourier Transform Analysis of Membrane Voltage Drops

“…As compared to the conditions without stirring, the thinning of the diffusion boundary layer and the growth of the electroconvection zone takes place simultaneously, and this is translated into an overlapping between both phenomena. Liu et al also observed via numerical simulations that increasing shear flow velocity can shelter chaotic electroconvection, while increasing the voltage increases it [ 42 ]. However, increasing the stirring rate up to 600 rpm implies a further decrease in n , demonstrating that vortices can be swept by the fluid flow.…”

Ion Transport in Electromembrane Systems under the Passage of Direct Current: 1D Modelling Approaches

“…Therefore, following Rubinshtein and Shtilman [19], we set the concentration of counterions c 1m under the boundary conditions, and consider it as a parameter. Note that this boundary condition is intensively used in studies of electromembrane systems by Pham et al [38], Mani et al [20], Demekhin et al [39], Shi et al [40], and others.…”

Time-Dependent Two-Dimensional Model of Overlimiting Mass Transfer in Electromembrane Systems Based on the Nernst–Planck, Displacement Current and Navier–Stokes Equations

“…Numerical modeling of overlimiting mass transfer based on the NPP-NS equations made it possible to obtain detailed information on the development of electroconvection in systems with ion-exchange membranes: the influence of forced flow on the height [21,30], speed [31] and state [32][33][34] of the electroconvective vortex; the calculation of the CVC of the flow-through electrodialysis membrane cells, taking into account overlimiting mass transfer caused by electroconvection [20]; the influence of the potential drop on the mode of electrokinetic instability [35]; statistical analysis of electroconvective flow [36]; the calculation of the trajectory of particles that visualize the dynamics of electroconvective flow [37]; development of electroconvection during pulsed electric field electrodialysis [38]; the study of the coupling between buoyancy forces and electroconvective instability [39]; and many others results.…”

“…The electrical mode in membrane systems can be determined either by setting the current density (galvanodynamic mode) or by setting the potential drop (potentiodynamic mode). When modeling the potentiodynamic mode, to solve the Poisson equation, the potential drop is set at the boundaries of the region under consideration (parallel to the membrane surface), which are assumed to be equipotential [18][19][20][21][30][31][32][33][34][35][36][37][38][39][40][41][42]. When modeling the galvanodynamic mode, one of these boundaries is assumed to be equipotential (usually a zero potential is fixed on it), and on the other, a boundary condition is set that relates the normal derivative (to the membrane surface) of the potential and the given current density [28,[43][44][45][46][47][48][49][50].…”