Extreme Levitation of Colloidal Particles in Response to Oscillatory Electric Fields

Abstract

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.

pH-Mediated Aggregation-to-Separation Transition for Colloids Near Electrodes in Oscillatory Electric Fields

“…Indeed, increases in particle height with decreasing frequency were observed in this study ( cf . Figure c) and in several prior reports and have been attributed to AREF-induced electrophoretic lift forces. ,,, The EHD fluid flow magnitude is sensitive to particle height, with a prior scaling argument predicting the EHD flow magnitude to vary with particle height ( h ) as U EHD ∼ h –4 . Confocal microscopy measurements showed the particle height increased 2-fold when decreasing the frequency from 1 kHz to 100 Hz, which would result in a 16-fold decrease in the EHD flow magnitude.…”

“…The ion mobility mismatch is quantified by , where D – and D + are the anion and cation diffusivities . Prior work has investigated AREF in electrolytes with a permanent mismatch in ion diffusivity, e.g ., aqueous NaOH and KOH. , In the present experiments, electroreduction of BQ at the cathode consumes protons and increases the local hydroxyl ion concentration due to water dissociation, which creates a local ion diffusivity mismatch. The increased hydroxyl ion concentration at the bottom electrode leads to δ > 1 due to the larger diffusion coefficient of hydroxyl ions compared to potassium ions , resulting in an AREF that is oriented toward the bottom electrode where the colloids are located.…”

“…Micron-scale dielectric colloids in dilute aqueous electrolytes (10 –5 to 10 –2 M) are widely known to assemble into planar aggregates near charged electrodes in low-frequency (<1 kHz) oscillatory electric fields. − The formation of planar aggregates is attributed to attractive hydrodynamic drag forces created by electrohydrodynamic (EHD) fluid flow around each particle, which occurs due to perturbation of the otherwise spatially uniform electric field by the particles, creating a rectified electric field directed along the electrode surface that drives the EHD flow. , In basic (NaOH) or acidic (HCl) electrolytes that induce large ζ-potentials on particles (|ζ p | ∼ 100 mV), colloids do not aggregate and in some cases separate. ,− A large survey study found that the aggregation rate of colloids was correlated with colloid ζ-potential and electric field amplitude across 26 unique particle–electrolyte pairs . Recent theoretical and experimental work has shown that colloid ζ-potential, surface conductivity, , and cation/anion diffusivity mismatch , play roles in whether colloids aggregate or separate in a given electrolyte. Ma et al showed that colloids with large ζ-potential and surface conductivity generated extensile fluid flows in oscillatory fields .…”

“…Separation and aggregation of colloids in various electrolytes has previously been explained by competition between multiple extensile and contractile electrokinetic flows. , Previous work has shown that steady electric fields induce particle aggregation or separation due to electroosmotic (EO) flow along the particle surface, which creates either extensile or contractile flow around each particle depending on the sign of the steady potential and particle ζ-potential. ,,, Motion of particles normal to the electrode surface also plays an important role in determining whether colloids aggregate or separate in oscillatory electric fields. , The phase angle between the oscillatory electrophoretic motion of colloids and the electric field magnitude correlates with whether particles will aggregate or separate. ,,,, Prior work by the Prieve group has demonstrated changes in particle height upon application of electrochemical potentials that drive water electrolysis . In these experiments, vertical motion of the particle was effected by faradaic current density passing through the electrochemical cell. , Colloids in electrolytes where the cations and anions have different mobilities, e.g ., NaOH, have been shown to separate and levitate tens of microns above the electrode surface in low-frequency oscillatory fields. ,, Colloid levitation was explained by the recently identified asymmetric rectified electric field (AREF), which is induced by the action of an oscillatory potential on an electrolyte with different cation and anion diffusivities . The disparate electrophoretic motion of ions creates free charge density outside the diffuse layer near the electrode, which partially rectifies the oscillatory current to create the AREF .…”

Discovering dynamic laws from observations: the case of self-propelled, interacting colloids

“…Thanks to these changes, we correctly extract the forces present in simulations of systems of thousands of active particles. After validating our approach, we use our model to extract both active and two-body forces in experiments of electrophoretic Janus particles [64,65]. This system is composed of asymmetric particles that self-propel due to the energy injected by an external electric field, see Fig.…”