An approximate model for the velocity due to electrohydrodynamic flow of electrolyte in the vicinity of a dielectric sphere near an electrode is described. The model considers the interaction of a lateral electric field, caused by the presence of the sphere, with free charge produced in the diffusion layer near an electrode when alternating current is passed through it. An equation based on the model predicts that adjacent dielectric particles aggregate or separate depending on the relative magnitude of the individual ionic conductivities and the frequency of oscillation in the case of a binary electrolyte. If the anion reacts and its conductance exceeds the cation conductance, the particles repel each other; the particles aggregate if the reverse is true. The equation also predicts that separation or aggregation depends on frequency of oscillation of the current. The model accounts for observed effects of frequency and particle size found in the literature. Finally, a dimensionless group that places a constraint on the frequency at which electroneutrality remains a good assumption for calculating electrohydrodynamic flow in oscillating systems is derived.

No abstract

A rectified electroosmotic flow mechanism and its expression in a quantitative model account for the net lateral motion of colloidal particles above a uniform planar electrode in an alternating electric field that drives a faradaic reaction on the electrode surface. Specific comparison to published particle doublet trajectories at 100 Hz in sodium hydroxide and sodium bicarbonate electrolytes demonstrates that the model quantitatively agrees with the experimental doublet trajectories when only independently measurable parameters are employed. This model reproduces the experimental signatures of the published particle pair motion at 100 Hertz: dependence of the direction of motion on the electrolyte, order of magnitude of the interparticle velocity, invariance of the lateral motion to changes in the particle zeta potential, and observed steady separation between particles that otherwise tend to aggregate. The model is expected to apply up to approximately 1 kHz, at which essentially all of the alternating current flows through the double-layer capacitance and not the faradaic reaction.

Total internal reflection microscopy was used to monitor the elevation of 4-7.5 mum diameter particles near an electrode in response to an oscillating electric field with amplitude up to 8.5 kV/m. The media were 0.15 mM electrolyte solutions of HNO(3), NaHCO(3), and KOH, and the frequency band was 40 Hz to 10 kHz. Polystyrene-sulfonate particles were used in bicarbonate and KOH solutions, while polystyrene-amine particles were used in nitric acid. At frequencies less than 500 Hz, large oscillations in elevation at the driving frequency with small superimposed Brownian excursions were observed. At frequencies above 1 kHz, deterministic oscillations in elevation were negligible compared to Brownian fluctuations, which allowed transformation of histograms of elevations into potential energy profiles. The ac field drew the particle closer on average to the electrode in KOH solutions (compared to the no-field average elevation) and the field pushed the particle farther from the electrode in NaHCO(3). In HNO(3) a reversal of average height was observed at a frequency of 300 Hz at 1.7 kV/m with the particle being drawn closer to the electrode at low frequencies and being pushed away at higher frequencies. The reversal reflects two different electrohydrodynamic mechanisms. Analysis of the data at a high frequency (10 kHz) revealed a net force that was attractive in KOH and repulsive in HNO(3). This net force scaled with E(2)omega(-)(1), where E is the amplitude and omega is the frequency.

Electroosmotic flow in the vicinity of a colloidal particle suspended over an electrode accounts for observed changes in the average height of the particle when the electrode passes alternating current at 100 Hz. The main findings are (1) electroosmotic flow provides sufficient force to move the particle and (2) a phase shift between the purely electrical force on the particle and the particle's motion provides evidence of an E2 force acting on the particle. The electroosmotic force in this case arises from the boundary condition applied when faradaic reactions occur on the electrode. The presence of a potential-dependent electrode reaction moves the likely distribution of electrical current at the electrode surface toward uniform current density around the particle. In the presence of a particle the uniform current density is associated with a nonuniform potential; thus, the electric field around the particle has a nonzero radial component along the electrode surface, which interacts with unbalanced charge in the diffuse double layer on the electrode to create a flow pattern and impose an electroosmotic-flow-based force on the particle. Numerical solutions are presented for these additional height-dependent forces on the particle as a function of the current distribution on the electrode and for the time-dependent probability density of a charged colloidal particle near a planar electrode with a nonuniform electrical potential boundary condition. The electrical potential distribution on the electrode, combined with a phase difference between the electric field in solution and the electrode potential, can account for the experimentally observed motion of particles in ac electric fields in the frequency range from approximately 10 to 200 Hz.

The relative motion between two colloidal particles loosely deposited on an electrode passing alternating current was investigated. Parameters such as zeta potential, electrolyte composition, electrolyte concentration, and frequency were varied. At a low frequency (100 Hz), the particles aggregated in both sodium bicarbonate and sodium chloride solutions but separated in sodium hydroxide solutions. At 1000 Hz, the particles separated in both bicarbonate and hydroxide solutions, and the rate of separation was slower than at 100 Hz for the hydroxide solutions. The effect of zeta potential was negligible, indicating a convective mechanism causing the relative motion between the particles. Electrolyte concentration had no appreciable effect on the motion. These results are qualitatively consistent with predictions of a theory based on electrohydrodynamic flow induced by the interaction between a space charge in the liquid adjacent to the electrode's surface, generated by concentration gradients of the ions, and an electric field tangent to the electrode which is caused by deflection of current around each particle. The interparticle separation velocity in hydroxide solutions predicted from the theory without adjustable parameters is comparable to the experimental values.

A numerical solution of the equations describing electrohydrodynamic flow around a single particle next to an electrode during passage of alternating current is presented. The Stokes equations, the diffusion equation, and Laplace's equation are solved simultaneously. The results confirm earlier approximate calculations showing that electrohydrodynamic flow is a significant factor in aggregative and deaggregative behavior of colloidal particles near electrodes. Both electrode kinetics and the ratio of particle size to diffusion layer thickness affect not only the strength of the flow around the particle but also its direction. Sluggish electrode kinetics causes the lateral flow around a particle in KOH solution to move away from it at 100 Hz, but fast electrode kinetics causes the flow to reverse at the same frequency. Increasing the frequency can cause flow reversal, which might explain experimental observations of the existence of a critical frequency above which particles separate and below which they aggregate in alkaline solution. The critical frequency is inversely proportional to the square of the particle radius.

A model incorporating a phase angle between an applied electric field and the motion of particles driven by it explains electrolyte-dependent pairwise particle motion near electrodes. The model, predicting that two particles aggregate when this phase angle is greater than 90 degrees but separate when the phase angle is less than 90 degrees , was based largely on contrasting behavior in two electrolytes (KOH and NaHCO3) used with indium tin oxide (ITO) electrodes. The present contribution expands the experimental evidence for this model to KOH, NaHCO3, NaOH, NH4OH, KCl, and H2CO3 solutions with Pt, as well as ITO electrodes. The phase angle correlation was verified in all cases. Comparisons of the model predictions to experimental data show that the sign and order of magnitude of rates of change in the separation distances between particle pairs are correctly predicted.