Bulletin of the American Physical Society
64th Annual Meeting of the APS Division of Fluid Dynamics
Volume 56, Number 18
Sunday–Tuesday, November 20–22, 2011; Baltimore, Maryland
Session G26: Minisymposium: Electrokinetic Flows about Ion-Selective Surfaces |
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Chair: Udi Yariv, Technion - Israel Institute of Technology Room: 329 |
Monday, November 21, 2011 8:00AM - 8:26AM |
G26.00001: Phoretic motion of ion exchangers Invited Speaker: One-dimensional ionic conduction normal to an ion-exchange surface is a two-scale problem, with a charged Debye layer adjacent to the surface and an electro-neutral bulk outside it. Due to ion selectivity, the bulk salt concentration must vary linearly with distance. When the ion-exchange surface is curved, the electric field tangential to the surface results in an accompanying flow. Specifically, a freely suspended ion- exchange particle would move under the action of an external field. This problem is described in a systematic microscale model, wherein the boundary conditions on the highly-conducting particle surface represent ion-exchange kinetics. For thin Debye layers, an equivalent macroscale model is extracted, wherein boundary conditions reflect asymptotic matching with the Debye layer. Thus, the equi-potential condition on the literal particle surface is transformed to a nonuniform Dirichlet condition, accounting for Debye layer voltage (zeta potential). The latter is not a surface property, but rather depends upon surface kinetics. As in the one-dimensional problem, microscale ion selectivity on the particle surface results in a macroscale salt concentration polarization (on the particle scale), whereby the electric potential is rendered non-harmonic. Accordingly, the macroscale model is significantly more complicated than the comparable one for inert particles. Even in the weak-field limit, the effects of salt polarization and electric field on particle motion are comparable: Smoluchowski's formula does not apply. Open problems in the context of strong fields and self-propulsion will also be described. [Preview Abstract] |
Monday, November 21, 2011 8:26AM - 8:52AM |
G26.00002: Deionization shocks in cross flows Invited Speaker: Recent experimental and theoretical studies have shown that surface conduction in supported electrolytes, such as in micro/nanochannels or porous media, can lead to nonlinear modes of transport and formation of sharp concentration fronts analogous to shock waves in gas dynamics. Propagation of these shocks leaves behind a region of ultra pure fluid, acting to deionize the bulk solution. In this work we present the analysis of salt transport in a porous medium next to a membrane with an electric field applied normal to the interface and cross flow in tangential direction. We show that two distinct boundary layers grow near the membrane: an inner (shocked) region with almost deionized solution dominated by surface conduction, and an outer layer with diffuse dynamics. Under certain conditions both regions collapse into a similarity solution with the same scaling. We will discuss advantages of such systems for desalination and water purification. [Preview Abstract] |
Monday, November 21, 2011 8:52AM - 9:18AM |
G26.00003: Rectification Phenomena Across an Asymmetric Nanofluidic Channel Invited Speaker: We review our recent experimental and theoretical studies of nanofluidic diodes. A continuum theory is developed to show that the literature and our rectification data can be generically classified into two regimes: a low-voltage regime dominated by intra- channel ionic strength (Donnan potential) gradient and a high-voltage regime dominated by external ion depletion. The two regimes drive different anomalous phenomena, like molecular dissociation and microvortex instability, with distinct distinguished limits of dimensionless parameters. Applications to biosensing are discussed. [Preview Abstract] |
Monday, November 21, 2011 9:18AM - 9:44AM |
G26.00004: Concentration Polarization and Nonequilibrium Electro-osmotic Instability at an Ion-Selective Surface Admitting Normal Flow Invited Speaker: We revisit and build upon on the prototypical problem of ion transport across a flat ideal ion-selective surface. Specifically, we examine the influence of imposed fluid flows on concentration polarization (CP) and electrokinetic instability at over-limiting currents. We consider an ion-selective surface, or membrane, that admits a uniform flow across itself. The membrane contacts an electrolyte, whose concentration is uniform in a well-mixed region at a prescribed distance from the membrane. A voltage across the system drives an ionic current, leading to CP in the ``unstirred layer'' between the membrane and well-mixed bulk. The CP reflects a balance between advection of ions with the ``normal flow'' and diffusion. A Peclet number, Pe, parameterizes their relative importance; note, Pe is signed, as the flow can be toward or away from the membrane. An asymptotic analysis for thin Debye layers reveals a nonlinear CP profile, in contrast to the familiar linear profile at Pe=0. Next, we consider over-limiting currents, wherein a non-equilibrium space-charge layer emerges near the membrane surface. Finally, we examine the instability of the quiescent concentration polarization due to second-kind electro-osmosis in the space-charge layer. A stability analysis shows that the imposed normal flow can enhance or retard the instability, depending on its direction. [Preview Abstract] |
Monday, November 21, 2011 9:44AM - 10:10AM |
G26.00005: Electrokinetics over liquid/liquid interfaces Invited Speaker: Since liquid-liquid interfaces flow in response to an applied stress, one might expect electrokinetic flows at liquid-liquid interfaces to be significantly higher than over liquid-solid interfaces. The earliest predictions for the electrophoretic mobility of charged mercury drops -- distinct approaches by Frumkin and Levich (1946), and Booth (1951) -- differed by ${\cal O}(a/\lambda_D)$, where $a$ is the radius of the drop and $\lambda_D$ is the Debye screening length. Seeking to reconcile this rather striking discrepancy, Levine (1973) showed double-layer polarization to be the key ingredient. Without a physical mechanism by which electrokinetic effects are enhanced, however, it is difficult to know how general the enhancement is -- whether it holds only for liquid metal surfaces, or more generally, for all liquid/liquid surfaces. By considering a series of systems in which a planar metal strip is coated with either a liquid metal or liquid dielectric, we show that the central physical mechanism behind the enhancement predicted by Frumkin and Levich (1946) is the presence of an unmatched electrical stress upon the electrolyte-liquid interface, which establishes a Marangoni stress on the droplet surface and drives it into motion. The source of the unbalanced electrokinetic stress on a liquid metal surface is clear -- metals represent equipotential surfaces, so no field exists to drive an equal and opposite force on the surface charge. This might suggest that liquid metals represent a unique system, since dielectric liquids can support finite electric fields, which might be expected to exert an electrical stress on the surface charge that balances the electric stress. We demonstrate, however, that electrical and osmotic stresses on relaxed double-layers internal to dielectric liquids precisely cancel, so that internal electrokinetic stresses generally vanish in closed, ideally polarizable liquids. The enhancement for liquid mercury drops can thus be expected quite generally over clean, ideally polarizable liquid drops. More broadly, the ability to reliably engineer liquid interfaces in microfluidic systems, then, may provide a path to significantly enhanced electrokinetic flows. [Preview Abstract] |
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