A perturbation solution to the full Poisson–Nernst–Planck equations yields an asymmetric rectified electric field

Abstract

<p>We derive a perturbation solution to the one-dimensional Poisson–Nernst–Planck (PNP) equations between parallel electrodes under oscillatory polarization for arbitrary ionic mobilities and valences.</p>

Dielectrophoretic Colloidal Levitation by Electrode Polarization in Oscillating Electric Fields

“…The last, but not least, mechanism is based on the so-called AREF (Figure S15b). In brief, the AREF mechanism states that electrode polarization in an AC electric field leads to a time-averaged, steady electric field (⟨ E ⟩ t ). ,,− An electrically charged colloidal particle therefore levitates by electrophoresis to a height where the electrophoretic lift balances gravity. The AREF mechanism has two key requirements: an electrolyte of δ ≠ 1 and particles that carry substantial surface charges.…”

Asymmetric rectified electric and concentration fields in multicomponent electrolytes with surface reactions

“…At first order in ϕ D , we directly apply the analytical results of Hashemi et al 17 Note that their derivation is only valid for binary electrolytes, and as such is used exclusively to compare with results for binary electrolytes. To match the formulation used in their work, we definewhere ion 1 is the cation and ion 2 is the anion.…”

“…Eqn (2) are subjected to the following boundary and initial conditions. The sinusoidal potential boundary conditions are given as Φ (± L , τ ) = ± Φ D sin( Ωτ ).The above equation ignores any native zeta potential of the electrodes, similar to Hashemi et al 17 We consider a surface reactive flux condition ( i.e. , non-ideally blocking) at the two electrodes N i (± L , τ ) = N i 0 sin( Ωτ ).We note that the flux amplitude N i 0 may not be identical at the two electrodes, 37 but is assumed to be the same and time-independent for simplicity.…”

“…bvp4c deploys an adaptive grid meshing in the spatial dimension. We benchmark these numerical results with the results from Hashemi et al 17 for a binary electrolyte with no reactions and asymmetric diffusivities.…”

Propulsion of Homonuclear Colloidal Chains Based on Orientation Control under Combined Electric and Magnetic Fields

“…The long-range steady field generated within the liquid could potentially create an electro-osmotic flow on the particle surface, which is ignored in our numerical model. However, the AREF effect is typically strong when the ions have a significant difference in mobilities, such as acidic or basic electrolytes (vs DI water used here), and when the frequency is lower than 100 Hz , (vs ∼1000 Hz in our experiments). Therefore, its quantitative impact on chain propulsion remains elusive and will be subject to a detailed study in the future.…”