Electrodiffusiophoresis of a large-zeta-potential particle in weak fields

Abstract

The electrodiffusiophoresis of a large-zeta-potential (ζ) particle in weak fields is investigated. In this large-ζ regime, Debye-layer kinetics determines O(1) perturbations to the electric- and concentration fields in the surrounding electroneutral solution. Taking these effects into account, the expressions of the slip-flow coefficient and the effective surface boundary-conditions for the electric- and concentration fields are derived. For binary and symmetric electrolyte where only one ion species carries the current in the electroneutral domain, the far-field salt gradient as related to the electric field is determined. The electrodiffusiophoretic mobility is obtained for three particle geometries: sphere, cylinder and spheroid arbitrarily oriented with respect to the externally applied field. Strong departure from Smoluchowskian behavior is found. If co-ion is the current carrier, the mobility is independent of ζ, regardless of the body shape. Also, the hydrodynamic flow-field is irrotational. If counter-ion is the current carrier, the problem formulated in terms of a properly-defined scalar field (Ω), which embodies both the electric potential (Ψ) and the salt concentration, becomes formally identical to the one addressed in our previous work, concerning the small-ζ regime, with negligible salt gradients. Then, all the results obtained in that study are extended and applied even to the large-ζ regime considered here, provided the new expressions now derived for the surface boundary conditions and the slip-flow coefficient are employed and Ω is used in place of Ψ. The present results are discussed also in comparison with the classical studies of Dukhin et al and O'Brien et al concerning electrophoresis of highly charged particles with no salt gradient at infinity, and with recent studies of electrodiffusiophoresis, which, however, neglected the fields perturbations caused by Debye-layer kinetics. It is found that the effects addressed and incorporated in the present study determine remarkably different mobility-versus-ζ behaviour as compared to those previous theories.

Controlled Levitation of Colloids through Direct Current Electric Fields

“…The theory of electrodiffusiophoresis (EDP) can predict levitation. ,, Specifically, the theory predicts a sign reversal in particle velocity across an electrochemical cell that depends on the relative magnitudes of the purely electrophoretic and diffusiophoretic contributions (the latter itself being the result of electrophoretic and chemiphoretic contributions). The purely electrophoretic contribution is a linear function of current density and particle surface charge (or zeta potential), whereas the diffusiophoretic contribution depends on the diffusion coefficients ( D ) of ions and the ion concentration gradient.…”

Visualization of Concentration Gradients and Colloidal Dynamics under Electrodiffusiophoresis

“…The experimental results demonstrate that measurable gradients in pH induce motion that balance and counteract traditional electrophoretic motion. Except for the seminal work of Dukhin, 26,36 and a few recent-theoretical 24,25,37,62,63 as well as experimental 46,47 -studies, most treatments of colloidal electrokinetics ignore the effects of electrochemically induced gradients. Therefore, by providing the means to simultaneously map concentration gradients and the ensuing colloidal dynamics, this work provides tools to further the understanding of charged particles under electric fields, especially near electrodes.…”

“…Out of the three electrokinetic phenomena (EP, 31,32 DP, 18,19,[33][34][35] and EDP), EDP has been the least studied since the seminal work of Dukhin and collaborators. [24][25][26]36,37 In this sense and given significant advances in imaging, particle synthesis, surface modification and microfluidics since the early 80's, the study of EDP offers opportunities not only in fundamental research, but also in applied areas such as in the directed transport of colloids, fabrication of reconfigurable materials, and environmental remediation. For example, the closely related phenomenon of ion-concentration polarization (ICP) is used in microfluidics to focus, sort, and concentrate synthetic colloids [38][39][40][41][42] as well as biomolecules, such as DNA and proteins.…”

“…43,44 Similarly, ICP can be used in the desalination of water. 45 Although existing theories describe EDP for single particles with small or large zeta potentials, [24][25][26]37 possibilities for fundamental contributions exist in the context of dynamic assembly and manipulation of colloids near electrodes. 46 For example, pH gradients generated in the vicinity of planar electrodes led to the patterning of particles.…”

Colloidal Suspensions Displaying Anomalous Phoretic Behavior: Field and Mobility Reversal

“…They also showed that these effects become important only for “logarithmically” large zeta potentials, namely, for a binary and symmetric electrolyte: e ze |ζ|/2 k B T ≫ 1 ( k B , T , z , and e denoting the Boltzmann constant, absolute temperature, anion/cation valence, and elementary charge, respectively). Building on those theories, Tricoli and Orsini 23 have addressed more recently the electrodiffusiophoresis of a highly charged particle under simultaneously acting salt gradient and electric field—a situation encountered in various technical applications (here, highly charged is used to refer to particles possessing logarithmically large zeta potential). Similar to Dukhin’s and O’Brien’s theories, strong departure from Smoluchowski behavior was predicted due to excess surface transport in the highly charged DDL.…”