Scaling of velocity and scalar structure functions in ac electrokinetic turbulence

Scaling Effects of the Weissenberg Number in Electrokinetic Oldroyd-B Fluid Flow Within a Microchannel

This study attempts to extend previous research on electrokinetic turbulence (EKT) in Oldroyd-B fluid by investigating the relationship between the Weissenberg number (W i $Wi$ ) and the second-order velocity structure function (S v 2 $S_v^2$ ) under applied electric fields. Inspired by Sasmal's demonstration in Sasmal (2022) of how heterogeneous zeta potentials induce turbulence above a criticalW i $Wi$ , we develop a mathematical framework linkingW i $Wi$ to turbulent phenomena. Our analysis incorporates recent findings on AC (Zhao & Wang, 2017) and DC (Zhao & Wang 2019) EKT, which have defined scaling laws for velocity and scalar structure functions in the forced cascade region. Our finding shows thatS v 2 ( l ) ∼ λ 1 4 / 5 l 2 / 5 $S_v^2(l) \sim \lambda _1^{4/5} l^{2/5}$ andS σ 2 ( l ) ∼ λ 1 - 2 / 5 l 4 / 5 $S_\sigma ^2(l) \sim \lambda _1^{-2/5} l^{4/5}$ , for a length scale l $l$ , andW i = λ 1 u l l $Wi = \frac{\lambda _1 u_l}{l}$ , whereu l = S u 2 ( l ) $u_l = \sqrt {S_u^2(l)}$ is a velocity fluctuations quantity andλ 1 $\lambda _1$ denotes the time relaxation parameter. This work establishes a positive correlation betweenλ 1 $\lambda _1$ and turbulent flow phenomena through a rigorous analysis of velocity structure functions, thereby offering a mathematical foundation for building the design and optimization of EKT-based microfluidic devices.

Transition Routes of Electrokinetic Flow in a Divergent Microchannel with Bending Walls

Electrokinetic flow can be generated as a highly coupled phenomenon among velocity fields, electric conductivity fields, and electric fields. It can exhibit different responses to AC electric fields in different frequency regimes, according to different instability/receptivity mechanisms. In this investigation, by both flow visualization and single-point laser-induced fluorescence (LIF) method, the response of AC electrokinetic flow and the transition routes towards chaos and turbulence have been experimentally investigated. It is found, when the AC frequency ff>30 Hz, the interface responds at both the neutral frequency of the basic flow and the AC frequency. However, when ff≥30 Hz, the interface responds only at the neutral frequency of the basic flow. Both periodic doubling and subcritical bifurcations have been observed in the transition of AC electrokinetic flow. We hope the current investigation can promote our current understanding of the ultrafast transition process of electrokinetic flow from laminar state to turbulence.

Mixing and Flow Transition in an Optimized Electrokinetic Turbulent Micromixer

Micromixer is a key element in a lab on a chip for broad applications in the analysis and measurement of chemistry and engineering. Previous investigations reported that electrokinetic (EK) turbulence could be realized in a "Y" type micromixer with a cross-sectional dimension of 100 μm order. Although the ultrafast turbulent mixing can be generated at a bulk flow Reynolds number on the order of unity, the micromixer has not been optimized. In this investigation, we systematically investigated the influence of electric field intensity, AC frequency, electric conductivity ratio, and channel width at the entrance on the mixing effect and transition electric Rayleigh number in the "Y" type electrokinetic turbulent micromixer. It is found that the optimal mixing is realized in a 350 μm wide micromixer, under 100 kHz and 1.14 × 10⁵ V/m AC electric field, with an electric conductivity ratio of 1:3000. Under these conditions, a degree of mixedness of 0.93 can be achieved at 84 μm from the entrance and 100 ms. A further investigation of the critical electric field and the critical electric Rayleigh number indicates that the most unstable condition of EK flow instability is inconsistent with that of the optimal mixing in EK turbulence. To predict the evolution of EK flow under high Ra_σ and guide the design of EK turbulent micromixers, it is necessary to apply a computational turbulence model instead of linear instability analysis.

Rapid AC Electrokinetic Micromixer with Electrically Conductive Sidewalls

We report a quasi T-channel electrokinetics-based micromixer with electrically conductive sidewalls, where the electric field is in the transverse direction of the flow and parallel to the conductivity gradient at the interface between two fluids to be mixed. Mixing results are first compared with another widely studied micromixer configuration, where electrodes are located at the inlet and outlet of the channel with electric field parallel to bulk flow direction but orthogonal to the conductivity gradient at the interface between the two fluids to be mixed. Faster mixing is achieved in the micromixer with conductive sidewalls. Effects of Re numbers, applied AC voltage and frequency, and conductivity ratio of the two fluids to be mixed on mixing results were investigated. The results reveal that the mixing length becomes shorter with low Re number and mixing with increased voltage and decreased frequency. Higher conductivity ratio leads to stronger mixing result. It was also found that, under low conductivity ratio, compared with the case where electrodes are located at the end of the channel, the conductive sidewalls can generate fast mixing at much lower voltage, higher frequency, and lower conductivity ratio. The study of this micromixer could broaden our understanding of electrokinetic phenomena and provide new tools for sample preparation in applications such as organ-on-a-chip where fast mixing is required.

Numerical Simulation of the Photobleaching Process in Laser-Induced Fluorescence Photobleaching Anemometer

At present, a novel flow diagnostic technique for micro/nanofluidics velocity measurement-laser-induced fluorescence photobleaching anemometer (LIFPA)-has been developed and successfully applied in broad areas, e.g., electrokinetic turbulence in micromixers and AC electroosmotic flow. Nevertheless, in previous investigations, to qualitatively reveal the dynamics of the photobleaching process of LIFPA, an approximation of uniform laser distribution was applied. This is different from the actual condition where the laser power density distribution is normally Gaussian. In this investigation, we numerically studied the photobleaching process of fluorescent dye in the laser focus region, according to the convection-diffusion reaction equation. The profiles of effective dye concentration and fluorescence were elucidated. The relationship between the commonly used photobleaching time constant obtained by experiments and the photochemical reaction coefficient is revealed. With the established model, we further discuss the effective spatial resolution of LIFPA and study the influence of the detection region of fluorescence on the performance of the LIFPA system. It is found that at sufficiently high excitation laser power density, LIFPA can even achieve a super-resolution that breaks the limit of optical diffraction. We hope the current investigation can reveal the photobleaching process of fluorescent dye under high laser power density illumination, to enhance our understanding of fluorescent dynamics and photochemistry and develop more powerful photobleaching-related flow diagnostic techniques.