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.
In this paper we present calculations of levitation forces between a cylindrical permanent magnet and a cylindrical superconductor using a commercial finite element program. Force limits for zero field cooled and field cooled processes have been obtained using the Meissner effect and the perfect pinning hypothesis, respectively. Comparison of the experimentally determined forces with respect to these limits provides a simple estimation of the sample quality. The hysteretical behavior of the forces has been reproduced assuming a critical state model for the superconductor. Results are compared with experimental data. Excellent agreement has been found for forces measured after zero field cooled process thus allowing us to estimate the critical current of the samples. As a further exploitation of the software capabilities we have investigated the effects of the superconducting sample geometry and the effects of different strategies of flux conditioning to optimize the levitation forces.
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