A note on the electrostatic force and torque acting on an isolated body in an electric field

Rivette, N. J.; Baygents, James C.

doi:10.1016/s0009-2509(96)00337-5

Cited by 28 publications

(18 citation statements)

References 17 publications

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“…Indeed, the problem governing the O(β) potentials ϕ −1 andφ −1 is uncoupled to the flow, and is animated by the inhomogeneous far-field condition (5.18a); so, aside from an additive constant, both potentials must be proportional to cos θ. In the absence of a monopole term, and with a far-field approach to a uniform field, the electric field associated with ϕ −1 cannot result in a net electrostatic force at O(β 2 ), see Rivette & Baygents (1996). The force acting on the drop at that asymptotic order in solely contributed by Newtonian stresses associated with leading-order O(β 2 ) flow (represented by the first two terms in the integrand of (5.19)).…”

Section: Conductivity Ratiomentioning

confidence: 99%

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

Schnitzer

Yariv

2015

J. Fluid Mech.

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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.

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Section: Conductivity Ratiomentioning

confidence: 99%

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

Schnitzer

Yariv

2015

J. Fluid Mech.

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“…Finally, as the Maxwell stresses associated with (38) do not contribute 35 to the force-free constraint (28), this constraint simply implies the vanishing of the hydrodynamic force, or, equivalently, the absence of a Stokeslet term in u 0 .…”

Section: A Zero Dukhin Numbers: Smoluchowski's Formulamentioning

confidence: 99%

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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“…2. These assumptions lead us to a slight modification of dielectrophoresis results obtained by Rivette and Baygents [49] and Jones [50] for the force and torque on a rod-like metal and dielectric particles respectively. The analysis is also extended to include the effects of stripes along the length of the particle on the translation and rotation of the metal particles.…”

Section: B Thick Edl Modelmentioning

confidence: 99%

“…Using a multipole expansion and ignoring far-field effects, Rivette and Baygents [49] reformed Eqs. 6a-b in terms of the applied electric field, E ∞ ,…”

Section: B Thick Edl Modelmentioning

confidence: 99%

“…The time-averaged translation and rotation may be computed by substituting the field E ∞ (x',t) for E ∞ (x') in the velocities in Eqs. 5 and 27 then integrating them as [49] ( ) The resulting time-averaged velocities in a spatially uniform field will be 〈u〉 = 0 for all translational velocities. Similarly, the time-averaged rotational velocities due to the permanent dipole on a particle with thick or thin EDL will be 〈ω nat 〉 = 0.…”

Section: Ac Field Effectmentioning

confidence: 99%

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Rotational electrophoresis of striped metallic microrods

et al. 2007

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Analytical models are developed for the translation and rotation of metallic rods in a uniform electric field. The limits of thin and thick electric double layers are considered. These models include the effect of stripes of different metals along the length of the particle. Modeling results are compared to experimental measurements for metallic rods. Experiments demonstrate the increased alignment of particles with increasing field strength and the increase in degree of alignment of thin versus thick electric double layers. The metal rods polarize in the applied field and align parallel to its direction due to torques on the polarized charge. The torque due to polarization has a second order dependence on the electric field strength. The particles are also shown to have an additional alignment torque component due to non-uniform densities along their length. The orientation distributions of dilute suspensions of particles are also shown to agree well with results predicted by a rotational convective-diffusion equation.

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A note on the electrostatic force and torque acting on an isolated body in an electric field

Cited by 28 publications

References 17 publications

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

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

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

Rotational electrophoresis of striped metallic microrods

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