Single and Pairwise Motion of Particles near an Ideally Polarizable Electrode

2015

Phys. Rev. E

A novel approach is presented for analyzing the double-layer interaction force between charged particles in electrolyte solution, in the limit where the Debye length is small compared with both inter-particle separation and particle size. The method, developed here for two planar convex particles of otherwise arbitrary geometry, yields a simple asymptotic approximation limited to neither small zeta potentials nor the "close-proximity" assumption underlying Derjaguin's approximation.Starting from the nonlinear Poisson-Boltzmann formulation, boundary-layer solutions describing the thin diffuse-charge layers are asymptotically matched to a WKBJ expansion valid in the bulk, where the potential is exponentially small. The latter expansion describes the bulk potential as superposed contributions conveyed by "rays" emanating normally from the boundary layers. On a special curve generated by the centres of all circles maximally inscribed between the two particles, the bulk stress -associated with the ray contributions interacting nonlinearly -decays exponentially with distance from the centre of the smallest of these circles. The force is then obtained by integrating the traction along this curve using Laplace's method. We illustrate the usefulness of our theory by comparing it, alongside Derjaguin's approximation, with numerical simulations in the case of two parallel cylinders at low potentials. By combining our result and Derjaguin's approximation, the interaction force is provided at arbitrary inter-particle separations. Our theory can be generalized to arbitrary three dimensional geometries, non-ideal electrolyte models, and other physical scenarios where exponentially decaying fields give rise to forces.

Section: Introductionmentioning

confidence: 99%

Ray-theory approach to electrical-double-layer interactions

2015

Phys. Rev. E

“…A more thorough analysis, while still making use of the near-contact limit, should also describe the forces acting on the particle in the vertical direction, as in Ref. [16]: presumably, such an analysis would eventually justify the observed near-contact separation (see Ref. [13]).…”

Section: Discussionmentioning

confidence: 99%

“…It is evident that ϕ diminishes near the upper electrode which is remote from the particle [and hence so does the zeta-potential disturbance ζ at that electrode; see (2. 16)]. The voltage condition (2.17) then gives for the zeta-potential disturbance on the lower electrode…”

Section: Large-cell Approximationmentioning

confidence: 99%

“…[15]). For simplification, we focus our attention at the very beginning upon high frequencies, where chemical reactions are negligible [1] (as was the case in the recent experiments of Wirth et al [16]). At these conditions, the Ohmic current entering the electrode is transformed into a temporal derivative of the local Debye-layer charge [14], itself related to (the local value of) the electrode zeta potential.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Electrokinetic particle-electrode interactions at high frequencies

Yariv

2013

Phys. Rev. E

We provide a macroscale description of electrokinetic particle-electrode interactions at high frequencies, where chemical reactions at the electrodes are negligible. Using a thin-double-layer approximation, our starting point is the set of macroscale equations governing the "bounded" configuration comprising of a particle suspended between two electrodes, wherein the electrodes are governed by a capacitive charging condition and the imposed voltage is expressed as an integral constraint. In the large-cell limit the bounded model is transformed into an effectively equivalent "unbounded" model describing the interaction between the particle and a single electrode, where the imposed-voltage condition is manifested in a uniform field at infinity together with a Robin-type condition applying at the electrode. This condition, together with the standard no-flux condition applying at the particle surface, leads to a linear problem governing the electric potential in the fluid domain in which the dimensionless frequency ω of the applied voltage appears as a governing parameter. In the high-frequency limit ω>>1 the flow is dominated by electro-osmotic slip at the particle surface, the contribution of electrode electro-osmosis being O(ω(-2)) small. That simplification allows for a convenient analytical investigation of the prevailing case where the clearance between the particle and the adjacent electrode is small. Use of tangent-sphere coordinates allows to calculate the electric and flows fields as integral Hankel transforms. At large distances from the particle, along the electrode, both fields decay with the fourth power of distance.

“…In many scenarios even a slight diffuselayer overlap gives rise to a force which is appreciable, in the sense that it is comparable with other forces present in the system [10]. For example, a balance with van der Waals attraction regulates the stability of colloidal solutions to aggregation [11]; a balance with gravity enables levitation of a micron-sized particle above an electrode [12,13]; and a balance with various coiling mechanisms determines the conformation of DNA molecules in solution [14,15]. EDL interactions are also important in various environmental applications such as coal flotation [16], biological phenomena [17][18][19][20], and interpreting AFM measurements in conducting liquids for imaging [21] or in fundamental surface-physics studies [22,23].…”

Section: Introductionmentioning

confidence: 99%

A generalized Derjaguin approximation for electrical-double-layer interactions at arbitrary separations

The Journal of Chemical Physics

Morozov

2015

Derjaguin's approximation provides the electrical-double-layer interaction force between two arbitrary convex surfaces as the product of the corresponding one-dimensional parallel-plate interaction potential and an effective radius R (function of the radii of curvature and relative orientation of the two surfaces at minimum separation). The approximation holds when both the Debye length 1/κ and minimum separation h are small compared to R. We show here that a simple transformation,yields an approximation uniformly valid for arbitrary separations h; here K i is the Gaussian curvature of particle i at minimum separation, and [ · ] is an operator which adds h/2 to all radii of curvature present in the expression on which it acts. We derive this result in two steps. First, we extend the two-dimensional ray-theory analysis of Schnitzer [Physical Review E, 91 022307 2015], valid for κh, κR 1, to three dimensions. Using this approach we obtain a general closed form expression for the force by matching nonlinear diffuse-charge boundary layers with a WKBJ description of the bulk potential, and subsequent integration via Laplace's method of the traction over the medial surface generated by all spheres maximally inscribed between the two surfaces.Second, we exploit the existence of an overlap domain, 1 κh κR, where both the ray-theory and the Derjaguin approximations hold, to systematically form the generalized mapping. The validity of the result is demonstrated by comparison with numerical computations.