Session L23: Electrokinetics: Transient Phenomena

Oscillating Electric Fields in Liquids Create a Long-Range Steady Field

We demonstrate that application of an oscillatory electric field to a liquid yields a long-range steady field, provided the ions present have unequal mobilities. The main physics are illustrated by a two-ion harmonic oscillator, yielding an asymmetric rectified field whose time average scales as the square of the applied field strength. Computations of the fully nonlinear electrokinetic model corroborate the two-ion model and further demonstrate that steady fields extend over large distances between two electrodes. Experimental measurements of the levitation height of micron-scale colloids versus applied frequency accord with the numerical predictions. The heretofore unsuspected existence of a long-range steady field helps explain several longstanding questions regarding the behavior of particles and electrically-induced fluid flows in response to oscillatory potentials.    

Transition of AC electroosmotic flow to chaos nearby electric double layer by frequency-dependent routes

So far, most of the investigations on the velocity fluctuations of electroosmotic flow driven by periodic electric field (PEOF) are by theoretical and numerical analysis, which are based on conventional understanding, such as commonly used apparent viscosity, linear and 1D electric double layer (EDL) and linearized fluid dynamics. Although the influence of nonlinear and nonuniform electric field on electroosmotic flows has been developed for several years, due to the lack of experimental supports, our understanding of ACEO flows or even the most fundamental DC electroosmotic flows is far from complete. In present, based on the measurement using laser induced fluorescent photobleaching anemometer with ultrahigh spatial and temporal resolutions, the nonlinear velocity response of ACEO flow has been observed and experimentally investigated around electric double layer. Beside the influence of electric field intensity, it is also found that the transition of periodic flow to chaotic flow is frequency dependent. The frequency of AC electric field is also a control parameter of flow state and determines the routes to chaos.   

Extended self-similarity and abnormal intermittency factor of hierarchical velocity structures in micro electrokinetic turbulence

Experimental investigations on electrokinetic turbulence (EKT) that generated by high-intensity AC electric field have been done in a 240μm high, 130μm wide and 5mm long microchannel, by laser induced fluorescence photobleaching anemometer. Under low bulk flow Re (~0.4), the velocity structure functions (VSF) of the highly random flow exhibit apparent extended self-similarity (ESS). An inertial subrange with scaling exponent of 2/3 has been observed. Further investigations indicate, the scaling exponents of high-order VSF in ESS model are relatively smaller than that predicted by Kolmogorov 1941 law and the experimental results in homogeneous and isotropic (HI) turbulence (Benzi et al., Physica D, 1996, 96, 162). This indicates the inertial subrange of EKT has stronger intermittency, which is further related to an abnormal curled-up of the exponential tail in the probability density function of velocity gradient. The intermittency of the inertial subrange of EKT is further investigated by the intermittency factor (β) of SL94 law (She and Leveque, Phys. Rev. Lett., 1994, 72, 336), where 0<β<1. However, in the EKT, β is around 1.1 to 1.2, which is beyond the limits of β in SL94 law. The abnormal β may imply an inverse energy cascade in the inertial subrange of EK turbulent flow.   

Electroconvective Instability in annular geometry

Electroconvective instability associated with concentration polarization near a charge selective interface in the overlimiting current, has been extensively studied in the past years. These theoretical studies mainly rely on the parallel electrodes geometry where the concentration profile of electrolyte is linear in the electro-neutral bulk region. But less has been explored in an annular geometry (inner electrode at R₁ and outer one at R₂), in which the concentration profile is logarithmic in the electro-neutral bulk. Consequently, the limiting current depends on both the direction of electric field and the radius ratio R₁/R₂. When the inner electrode radius R₁ is much larger than the Debye length ε, the electro-osmotic slip at a charge selective interface is similar to the one in parallel electrodes geometry. By employing the slip formula and Nernst-Plank equations, we perform a linear stability analysis of the quiescent electric conduction in annular geometry.   

Numerical analysis of electrohydrodynamic instability with and without crossflow

The study focuses on the electrohydrodynamic (EHD) instability problem with and without cross-flow. Lattice Boltzmann Method (LBM) with two-relaxation time (TRT) model is used for 3-dimensional numerical simulation. In the absence of cross-flow, the base-state of the problem is hydrostatic and the electric field is one-dimensional. The base-state is an unstable equilibrium under strong charge injection and high electric Rayleigh number. Perturbed by different perturbation patterns (rolling pattern, square pattern and hexagon pattern), the flow would develop according to the most unstable mode. The growth rate and the unstable modes can be obtained by performing dynamic mode decomposition (DMD) on the transient numerical solutions. The steady-state flow patterns depend on the patterns used to perturb the flow. Once the steady-state solution is reached, a Couette-type and/or Poiseuille-type cross-flow is applied to the steady-state solution. The flow patterns will change according to the direction and strength of the cross-flow. When the cross-flow velocity is greater than a threshold value, the instability flow patterns would develop into 2-dimensional rolling patterns with vortices in the direction of the cross-flow.
  

Analysis of electroconvective instability of aqueous electrolytes under oscillatory voltages

It was reported that electroconvective instability (ECI) can be generated in aqueous electrolytes near flat electrodes under AC voltages (Kim, Davidson and Mani 2017). Similar to ECI under DC electric fields, strong nonlinearity and enhanced mixing by large-scale vortices characterize ECI under AC voltages. In this study, a series of statistical and spectral analysis are conducted to understand the underlying physics of ECI. Solutions of direct numerical simulation of the Poisson--Nernst--Planck and Stokes equations are analyzed. The critical voltage above which ECI is amplified is a strong function of oscillation frequency. At frequencies higher than the intrinsic RC frequency, the critical voltage is higher than 200 thermal volts. Above the critical voltage, ion depletion outside the Debye layer and the transverse instability of extended space charge layers are intensified, with velocity fluctuations two to three orders of magnitude higher than the diffusion velocity. As frequency is lowered to 1/16 of the RC frequency, an optimal response in terms of velocity and current density is obtained. The bulk electrolyte loses equilibrium, and its salt concentration fluctuates at the oscillation frequency. The maximum current density is doubled compared with the corresponding 1D setup.