Title: Numerically study the combined effect of electrophoresis and electroosmosis in the nonpolar system

Abstract:

Electrophoresis (EP) is the movement of the charged particles relative to a stationary liquid induced by an applied electric field. Electroosmosis (EO), on the other hand, is the movement of a liquid relative to a stationary charged surface caused by an external electric field. In nonpolar systems, charges are generated in the form of charged inverse micelles (CIMs). The addition of surfactants helps disperse particles in nonpolar systems and makes it possible for EP and EO to take place. The novelty of this work is in using numerical ways to uncover the physics behind the experimental fluid motion and particle trajectories in nonpolar systems, which may help people understand, control, and optimize the switching ability of microfluidic devices, especially electronic paper displays based on micro or nano-particles. A detailed 2D model is proposed to numerically study the combination of EP and EO in nonpolar solvents. In this model, the electroosmotic boundary condition is utilized to investigate the influence of the zeta potential. What’s more, to fully uncover the physics and chemistry in nonpolar systems, the surface reaction, which describes how IMs generate at the liquid-solid interface, is implemented. The interdigitated electrodes are shown (see Fig 1). In this model, the Navier-Stokes equation, Nernst-Planck equation, and Poisson equation are coupled together to solve the fluid motion and particle trajectories. The results of the simulation and experiment are firstly compared to validate the numerical model (see Fig 2), the analytic particle velocity is calculated by adding the fluid velocity produced by the numerical model to the electrophoretic particle velocity. Comparable results between simulations and experiments imply the accuracy of this model. To compare the particle trajectories, 50 particles are released in the numerical model, feeling the electric force and drag force, and move from random positions to the positive electrode (particles are negatively charged). The experimental and simulated particle trajectories are similar (see Fig 3a and b) which proves that the EP and EO contribute to the particle motion at the same time. To further validate this hypothesis, we separate the influence of EP and EO in a simple model, in which pure EP is implemented only. Particle trajectories follow the electric field lines (see Fig 3c). Comparing that with the experimental particle trajectories makes it easy to distinguish the importance of EO. What’s more, a model without taking zeta potential into account is built to investigate the role of the zeta potential. The result (see Fig 3d) shows that particle velocities in the area between two electrodes are very small. This means EO near the glass surface (glass substrates are negatively charged) generated due to the zeta potential can explain why particles in experiments move against the field lines near the edge of the positive electrode as well (see Fig 2a). The comparison between experimental and numerical results implies that the practical particle motion is dominated by both EP and EO. The numerical results of pure EP and the model without zeta potential further prove that both electric field and fluid motion influence the particle trajectories, which emphasizes the important role of the zeta potential as well. This work may benefit the fundamental study of EP and EO in nonpolar systems and help develop fast-switching electrokinetic displays as well.