Nonlinear electrokinetics and “superfast” electrophoresis

2010

Proc. R. Soc. A.

Electrokinetic self-propulsion was conceptually proven in recent experiments wherein bimetallic nano-rods were observed to migrate when placed in aqueous solutions. We present here a systematic theoretical model of the self-propulsion mechanism, analysing the steady-state transport occurring about an autonomously moving inhomogeneous particle. The non-uniform catalysis on the particle surface is modelled via positiondependent cation redox coefficients. The particle shape is axisymmetric but otherwise arbitrary, as are the distributions of the (possibly discontinuous) kinetic coefficients along its boundary. We formulate the mathematical problem governing this electrokinetic transport. In the thin-Debye-layer limit, the microscale description is transformed into a macroscale one, applying in the electro-neutral bulk. Effective boundary conditions represent asymptotic matching with the Debye-layer fields. A linearized model is derived for weak variation of the kinetic coefficients and is solved for a spherical-particle geometry. With a view towards understanding existing experiments, the macroscale model is used for analysing slender particles. Matched asymptotic expansions provide the particle velocity as a functional of its shape and kinetic-coefficient distributions. The predicted self-propulsion is in the direction observed in nanorod experiments.

Section: (C) Consistency Conditionmentioning

confidence: 99%

Electrokinetic self-propulsion by inhomogeneous surface kinetics

2010

Proc. R. Soc. A.

“…We have already mentioned diffusio-phoresis, where salt gradients are enforced with zero net integral current. Another situation happens near ion-selective membranes (Rubinstein and Zaltzman, 2001;Rubinstein and Shtilman, 1979;Dukhim, 1991;Ben and Chang, 2002;Ben et al, 2004;Zaltzman and Rubinstein, 2007). In that case, the steady-state situation involves a nonzero net integral current that is entirely associated with cation flux.…”

Section: Electrokinetic Formulationmentioning

confidence: 99%

An Asymptotic Derivation of the Thin-Debye-Layer Limit for Electrokinetic Phenomena

Chemical Engineering Communications

2009

“…1974; O'Brien 1983;Anderson 1989;Schnitzer & Yariv 2012a), ion-selective granules (Ben, Demekhin & Chang 2004;Yariv 2010), metal drops (Ohshima, Healy & White 1984;Schnitzer, Frankel & Yariv 2013a), and gas bubbles (Schnitzer, Frankel & Yariv 2014).…”

Section: Introductionmentioning

confidence: 99%

The Taylor–Melcher leaky dielectric model as a macroscale electrokinetic description

Schnitzer

2015

J. Fluid Mech.

While the Taylor-Melcher electrohydrodynamic model entails ionic charge carriers, it addresses neither ionic transport within the liquids nor the formation of diffuse spacecharge layers about their common interface. Moreover, as this model is hinged upon the presence of nonzero interfacial-charge density, it appears to be in contradiction with the aggregate electro-neutrality implied by ionic screening. Following a brief synopsis published by Baygents & Saville (Third International Colloquium on Drops & Bubbles, vol. 7, 1989, p. 7) we systematically derive here the macroscale description appropriate for leaky dielectric liquids, starting from the primitive electrokinetic equations and addressing the double limit of thin space-charge layers and strong fields. This derivation is accomplished through the use of matched asymptotic expansions between the narrow space-charge layers adjacent to the interface and the electro-neutral bulk domains, which are homogenized by the strong ionic advection. Electrokinetic transport within the electrical 'triple layer' comprising the genuine interface and the adjacent space-charge layers is embodied in effective boundary conditions; these conditions, together with the simplified transport within the bulk domains, constitute the requisite macroscale description. This description essentially coincides with the familiar equations of Taylor & Melcher (Annu. Rev. Fluid Mech., vol. 1, 1969, p. 111). A key quantity in our macroscale description is the 'apparent' surface-charge density, provided by the transversely-integrated triple-layer microscale charge. At leading order, this density vanishes due to the expected Debye-layer screening; its asymptotic correction provides the 'interfacial' surface-charge density appearing in the Taylor-Melcher model. Our unified electrohydrodynamic treatment provides a reinterpretation of both the Taylor-Melcher conductivity-ratio parameter and the electrical Reynolds number. The latter, expressed in terms of fundamental electrokinetic properties, becomes O(1) only for intense applied fields, comparable with the transverse field within the space-charge layers; at this limit, however, the asymptotic scheme collapses. Surface-charge advection is accordingly absent in the macroscale description. Because of the inevitable presence of (screened) net charge on the genuine interface, the drop also undergoes electrophoretic motion. The associated flow, however, is asymptotically smaller than that corresponding to the the Taylor-Melcher circulation. Our successful matching procedure contrasts the analysis of Baygents & Saville (1989), who considered more general electrolytes and were unable to directly match the inner and outer regions. We discuss this difference in detail.