Application of an oscillatory electric field is known to alter the separation distance between micron-scale colloidal particles and an adjacent electrode. This behavior is believed to be partially due to a lift force caused by electrohydrodynamic flow generated around each particle, with previous work focused on identifying a single steady-state "height" of the individual particles over the electrode. Here, we report the existence of a pronounced bifurcation in the particle height in response to low-frequency electric fields. Optical and confocal microscopy observations reveal that application of a ∼100 Hz field induces some of the particles to rapidly move several particle diameters up from the electrode, while the others move closer to the electrode. Statistics compiled from repeated trials demonstrate that the likelihood for a particle to move up follows a binomial distribution, indicating that the height bifurcation is random and does not result from membership in some distinct subpopulation of particles. The fraction of particles that move up increases with increased applied potential and decreased frequency, in a fashion qualitatively consistent with an energy landscape predicated on competition between electrohydrodynamic flow, colloidal interactions, and gravitational forces. Taken together, the results provide evidence for the existence of a deep tertiary minimum in the effective electrode-particle interaction potential at a surprisingly large distance from the electrode.

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.

Micrometer-scale particles suspended in NaCl solutions aggregate laterally near the electrode upon application of a low-frequency (∼100 Hz) field, but the same particles suspended in NaOH solutions are instead observed to separate laterally. The underlying mechanism for the electrolyte dependence remains obscure. Recent work by Woehl et al. (PRX, 2015) revealed that, contrary to previous reports, particles suspended in NaOH solutions indeed aggregate under some conditions while simultaneously exhibiting a distinct bifurcation in average height above the electrode. Here we elaborate on this observation by demonstrating the existence of a critical frequency (∼25 Hz) below which particles in NaOH aggregate laterally and above which they separate. The results indicate that the current demarcation of electrolytes as either aggregating or separating is misleading and that the key role of the electrolyte instead is to set the magnitude of a critical frequency at which particles transition between the two behaviors.

Micron-scale colloidal particles suspended in electrolyte solutions have been shown to exhibit a distinct bifurcation in their average height above the electrode in response to oscillatory electric fields. Recent work by Hashemi Amrei et al. (Phys. Rev. Lett., 2018, 121, 185504) revealed that a steady, long-range asymmetric rectified electric field (AREF) is formed when an oscillatory potential is applied to an electrolyte with unequal ionic mobilities. In this work, we use confocal microscopy to test the hypothesis that a force balance between gravity and an AREF-induced electrophoretic force is responsible for the particle height bifurcation observed in some electrolytes. We demonstrate that at sufficiently low frequencies, particles suspended in electrolytes with large ionic mobility mismatches exhibit extreme levitation away from the electrode surface (up to 50 particle diameters). This levitation height scales approximately as the inverse square root of the frequency for both NaOH and KOH solutions. Moreover, larger particles levitate smaller distances, while the magnitude of the applied field has little effect above a threshold voltage. A force balance between the AREF-induced electrophoresis and gravity reveals saddle node bifurcations in the levitation height with respect to the frequency, voltage, and particle size, yielding stable fixed points above the electrode that accord with the experimental observations. These results point toward a low-energy, non-fouling method for concentrating colloids at specific locations far from the electrodes.