Three-dimensional coherent structures of electrokinetic instability

Abstract

A direct numerical simulation of the three-dimensional elektrokinetic instability near a charge-selective surface (electric membrane, electrode, or system of micro- or nanochannels) has been carried out and analyzed. A special finite-difference method has been used for the space discretization along with a semi-implicit 31/3-step Runge-Kutta scheme for the integration in time. The calculations employ parallel computing. Three characteristic patterns, which correspond to the overlimiting currents, are observed: (a) two-dimensional electroconvective rolls, (b) three-dimensional regular hexagonal structures, and (c) three-dimensional structures of spatiotemporal chaos, which are a combination of unsteady hexagons, quadrangles, and triangles. The transition from (b) to (c) is accompanied by the generation of interacting two-dimensional solitary pulses.

Helical vortex formation in three-dimensional electrochemical systems with ion-selective membranes

“…In order to limit excessive grid refinement near membrane surfaces, the equations were solved with a dimensionless Debye length, λ = 10 −3 , far larger than a physically realistic value (i.e., ∼10 −4 ). Other studies [6,7,[15][16][17][18] employ similar dimensionless Debye length values, and as shown below, the simulation results are clearly qualitatively similar to the realistic phenomenon observed in the experiment.…”

Spatial distribution of mechanical forces and ionic flux in electro-kinetic instability near a permselective membrane

“…However, the cationic streamlines must bypass the counter-rotating vortices located in the middle of the domain (x ∼ 0.25 and z ∼ 0.5) where the two components of the flux are close to zero. The cationic flux is mainly located in the outer boundary of the domain (z ∼ 0) as shown in the work of Demekhin et al 33 so that at the membrane surface half of the total cationic flux is located in the region z < 0. In the region x > 0.6, the cationic rolls form a barrier for the cationic transfer to the membrane so that the flux is displaced to the outer boundary of the domain and they push the transversal concentration gradient to the region x > 0.3 [ Fig.…”

“…Even if these theoretical studies shed a new light on electro-convective instability in membrane systems, it is necessary to solve the fluid and ionic transport equations in order to reach all the details of the electro-convective instability and to expand the domain of validity of the investigation. In this aim, Demekhin research group [29][30][31][32][33] studied the temporal evolution of the instability expansion (self-similarity and ESC layer deformation), the instability mode interaction in the presence of rugosity, the instability regimes (from the bifurcation analysis for steady instability to the chaotic motion), the 3D electro-convective pattern in the function of the potential drop. In the same spirit, Pham et al 34,35 analyzed the current hysteresis at the transition limiting/over-limiting regime and helical hydrodynamic motion.…”

“…However, these results describe the instability evolution in the transient and chaotic mode and also under pressure driven flow. To my knowledge, results dealing with marginal instability computed by direct numerical simulations are published by Pham et al 34 and Demekhin et al 31,33 only. So, the goal of the present work is to describe, in more detail and in the simplest bi-dimensional situation, the contribution of each term of the transport of momentum and ionic species at steady-state.…”

Controllable pH Manipulations in Micro/Nanofluidic Device Using Nanoscale Electrokinetics

“…This is because CP system usually has length scale greater than 100 µm and ICP system has one below 10 µm. In such circumstances, even the driving mechanism of overlimiting current is different: electrokinetic instability in CP system [5][6][7][8][9][10][11], surface conduction and electroosmotic flow in ICP system [12][13][14][15][16][17][18][19][20]. Since the ion depletion zone in ICP acts as an electrical filter together with zero-Reynolds number characteristics, it has been actively utilized for low abundance biomolecular separation / accumulation device [21][22][23].…”