Electrostatic and dispersion forces have long been known to dictate the behavior of colloidal particles adjacent to surfaces. The summation of the forces determines the potential energy landscape between the particles and the surface, often giving rise to the well-known “primary” and “secondary” minima that govern colloidal stability. This classical situation, however, is drastically changed when an external oscillatory electric field is applied normal to the surface, and the changes are still not well understood. Even though the field is applied perpendicular to the electrode, particles are sometimes observed to move toward one another, parallel to the electrode, ultimately creating crystalline aggregates. In other cases, the particles are observed to separate instead. Previous reports have focused on identification of a single equilibrium particle height in response to an oscillatory electric field. We report a surprising bifurcation in the colloidal particle height for micron-scale particles in sufficiently low applied frequency fields ($<400\mathrm{Hz}$).

We focus on polystyrene particles $2\mu \mathrm{m}$ in diameter, suspended in water. We apply oscillatory electric fields with frequencies ranging from 50 to 500 Hz and potentials ranging from 0.5 to 10 V. The fluorescent intensities of the particles are used as proxies for the particle height above the electrode. When the electric field is applied, some of the particles levitate many microns away from the electrode; the rest move closer to the electrode. Our confocal microscopy observations indicate that the particles choose randomly which equilibrium height to occupy and that they reside at the chosen height essentially indefinitely. Taken together, our experiments and scaling analysis suggest the existence of a previously unsuspected “tertiary” minimum in the potential energy landscape, at a surprisingly large distance from the electrode (several particle diameters). The particle behavior is believed to result from various types of electrically induced fluid flows generated around each particle, which in turn depend on the particle position relative to the electrode, i.e., its “height.” The particle height is known to be modulated by the oscillating electric field, but the details of the force balance controlling the height remain unknown.

Our results shed light on the underlying flow mechanisms giving rise to lateral aggregation and separation of colloidal particles near electrodes, and they provide a new tool for externally controlling the positioning of particles for lab-on-a-chip and other applications.