Electrophoresis of solid particles at large Peclet numbers

Mishchuk, N. A.; Dukhin, S. S.

doi:10.1002/1522-2683(200207)23:13<2012::aid-elps2012>3.0.co;2-y

Cited by 43 publications

(90 citation statements)

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“…Since the thickness of the diffusion layer scales as δ ∼ (xD/v) 0.5 (assuming high Peclet number) [12], with the convective flow velocity v ∼ E 2 (x: characteristic length of the system), one can conclude δ ∼ 1/E and the limiting current i' = 2FDC o /δ ∼ E. The result complies with the experimental observation we have in Fig. 2(c).…”

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confidence: 90%

Concentration Polarization and Nonlinear Electrokinetic Flow near a Nanofluidic Channel

et al. 2007

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A perm-selective nanochannel could initiate concentration polarization near the nanochannel, significantly decreasing (increasing) the ion concentration in the anodic (cathodic) end of the nanochannel. Such strong concentration polarization can be induced even at moderate buffer concentrations because of local ion depletion (therefore thicker local Debye layer) near the nanochannel. In addition, fast fluid vortices were generated at the anodic side of the nanochannel due to the nonequilibrium electro-osmotic flow (EOF), which was at least ∼10X faster than predicted from any equilibrium EOF. This result corroborates the relation among induced EOF, concentration polarization, and limiting-current behavior.Recently, science and engineering of molecular transport within nanofluidic channels, with critical dimensions of 10-100 nm, have drawn a lot of attention with the advances in microand nanofabrication techniques [1]. In addition to various applications [2,3], nanofluidic channels can be an ideal, well-controlled experimental platform to study nanoscale molecular, fluidic, or ionic transport properties. Recent experiments strongly suggest that nanochannels thinner than ∼50 nm demonstrate unique ion-perm selectivity at low ionic strengths, due to the fact that the Debye layer thickness (λ D ) is non-negligible compared with the channel thickness in these nanochannels [4]. Often, these phenomena are explained as Debye layer overlap, with the ratio between (equilibrium) Debye length and the channel dimension as the critical parameter. While proper in explaining near-equilibrium diffusion process through the nanochannels, this reasoning becomes invalid when the (local) ionic concentrations within the system start to change significantly, which is often the case in electrokinetic driving of nanochannels. More comprehensive models that can account for the change of (local) Debye length are yet to be developed. One of the characteristic behaviors that accompany strong concentration polarization is that local electrokinetic responses can be greatly amplified, especially in the ion-depleted anodic region. The result is typically a circulating, vortexlike flow pattern with a flow speed much higher than typical (equilibrium) electro-osmotic flow (EOF). Such an "induced" or "second-kind" EOF pattern, either in front of electrodes [5] or charge gel [6], has been experimentally observed. Recently, Rubinstein and co-workers suggested that similar nonlinear electrokinetic flow in front of perm-selective membrane is the main factor behind the overlimiting current at high dc bias [7]. However, more detailed study

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confidence: 90%

Concentration Polarization and Nonlinear Electrokinetic Flow near a Nanofluidic Channel

et al. 2007

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“…[29][30][31] Unlike the present analysis, these were not based upon a macroscale model. Moreover, while the present study allows for an arbitrary field magnitude, these papers appear to focus upon the respective limits of weak and strong fields.…”

Section: B Nonlinear Macroscale Modelmentioning

confidence: 83%

“…The derivation of the SY model allows for the possibility of a highly charged surface, where σ is comparable to δ −1 . This is explicit in the appearance of the dimensionless group [see (30)]…”

Section: Thin-double-layer Limit: Macroscale Formulationmentioning

confidence: 99%

“…obtained by substitution of (38) into (30). In addition, c 1 decays at large distances from the particle [see (27)]…”

Section: Polarization Due To Surface Conduction At O(du)mentioning

confidence: 99%

“…30 Equations (48)- (50) imply a solution of the form c 1 = E f (x; Pe). Since Pe itself depends on E, the polarization is, in general, nonlinear in the applied field.…”

Section: Polarization Due To Surface Conduction At O(du)mentioning

confidence: 99%

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Nonlinear electrophoresis at arbitrary field strengths: small-Dukhin-number analysis

Schnitzer

Yariv

2014

Physics of Fluids

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Smoluchowski's formula for thin-double-layer electrophoresis does not apply for highly charged particles, where surface conduction modifies the electrokinetic transport in the electro-neutral bulk. To date, systematic studies of this nonzero Dukhinnumber effect have been limited to weak fields. Employing our recent macroscale model [O. Schnitzer and E. Yariv, "Macroscale description of electrokinetic flows at large zeta potentials: Nonlinear surface conduction," Phys. Rev. E 86, 021503 (2012)], valid for arbitrary Dukhin numbers, we analyze herein particle electrophoresis at small (but finite) Dukhin numbers; valid for arbitrary fields, this asymptotic limit essentially captures the practical range of parameters quantifying typical colloidal systems. Perturbing about the irrotational zero-Dukhin-number flow, we derive a linear scheme for calculating the small-Dukhin-number correction to Smoluchowski's velocity. This scheme essentially amounts to the solution of a linear diffusion-advection problem governing the salt distribution in the electro-neutral bulk. Using eigenfunction expansions, we obtain a semi-analytic solution for this problem. It is supplemented by asymptotic approximations in the respective limits of weak fields, small ions, and strong fields; in the latter singular limit, salt polarization is confined to a diffusive boundary layer. With the salt-transport problem solved, the velocity correction is readily obtained by evaluating three quadratures, corresponding to the contributions of (i) electro-and diffuso-osmotic slip due to polarization of both the Debye layer and the bulk; (ii) a net Maxwell force on the electrical double layer; and (iii) Coulomb body forces acting on the space charge in the "electro-neutral" bulk. The velocity correction calculated based upon the semi-analytic solution exhibits a transition from the familiar retardation at weak fields to velocity enhancement at moderate fields; this transition is analytically captured by the small-ion approximation. At stronger fields, the velocity correction approaches a closed-form asymptotic approximation which follows from an analytic solution of the diffusive boundary-layer problem. In this régime, the correction varies as the 3/2-power of the applied field. Our smallDukhin-number scheme, valid at arbitrary field strengths, naturally lends itself to a tractable analysis of nonlinear surface-conduction effects in numerous electrokinetic problems. C 2014 AIP Publishing LLC. [http://dx

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Aperiodic capillary electrophoresis method using an alternating current electric field for separation of macromolecules

Dukhin

2005

Electrophoresis

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Switching from direct current (DC) to alternating current (AC) electric fields has provided substantial improvements in various instrument techniques that use electric fields for manipulating with various liquid-based systems. For example, AC fields are now used in both light scattering and electroacoustic instruments for measuring xi-potential, largely replacing more traditional microelectrophoresis techniques that use DC fields. In this paper, we suggest a novel way to make a similar transition in the area of separation techniques, capillary electrophoresis (CE) in particular. Dielectrophoresis is one well-known separation effect in which a drifting motion of particles is produced in a "spatially nonhomogeneous" AC electric field. However, there is another field effect that also causes a similar drift of particles. Instead of a "spatially nonhomogeneous" field, this method relies on a "temporally nonhomogeneous" field, normally referred to as "aperiodic electrophoresis". Despite a number of recently published experimental and theoretical papers describing this effect, it is less well-known than dielectrophoresis. We present a short overview of some of the relevant papers. We point out for the first time the idea that "aperiodic electrophoresis" might be useful for separation of macromolecules. We suggest several new mechanisms that could induce this effect in a sufficiently strong AC electric field. This effect can be used as a basis for a new separation method having several important advantages over traditional CE. We present a simple scheme as an example illustrating this new method.

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Electrophoresis of solid particles at large Peclet numbers

Cited by 43 publications

References 1 publication

Concentration Polarization and Nonlinear Electrokinetic Flow near a Nanofluidic Channel

Concentration Polarization and Nonlinear Electrokinetic Flow near a Nanofluidic Channel

Nonlinear electrophoresis at arbitrary field strengths: small-Dukhin-number analysis

Aperiodic capillary electrophoresis method using an alternating current electric field for separation of macromolecules

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