Electrical Double Layer Interaction between Dissimilar Spherical Colloidal Particles and between a Sphere and a Plate: The Linearized Poisson-Boltzmann Theory

Carnie, Steven L.; Chan, Derek Y. C.; Gunning, James

doi:10.1021/la00021a024

Cited by 124 publications

(146 citation statements)

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“…For more detailed calculations which also are valid at higher potentials and which explicitly take into account the geometry see Refs. [405][406][407][408][409].…”

Section: Electrostatic Double-layer Force and Dlvo Theorymentioning

confidence: 99%

Force measurements with the atomic force microscope: Technique, interpretation and applications

Butt

Cappella

Kappl

2005

Surface Science Reports

3,242

2,949

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“…For more detailed calculations which also are valid at higher potentials and which explicitly take into account the geometry see Refs. [405][406][407][408][409].…”

Section: Electrostatic Double-layer Force and Dlvo Theorymentioning

confidence: 99%

Force measurements with the atomic force microscope: Technique, interpretation and applications

Butt

Cappella

Kappl

2005

Surface Science Reports

3,242

2,949

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“…The coefficients can be found by a boundary Galerkin method (24) or boundary collocation (25). For the sphere-plane geometry these approaches are outlined in (26). The double layer charge density and surface charge density can then be calculated for constant potential or constant charge conditions.…”

Section: Electrophoresis Of a Sphere Perpendicular To A Perfectly Conmentioning

confidence: 99%

Electrophoretic Motion of a Spherical Particle with a Thick Double Layer in Bounded Flows

Shugai

Carnie

1999

Journal of Colloid and Interface Science

100

148

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“…particles). For low voltages, the problem can be linearized, paving the way to simplified numerics and various analytic methods, though the latter tend to be rather cumbersome and limited to specific idealized geometries [16][17][18]. Much more useful is Derjaguin's (or Deryagin's) "close-proximity approximation", where the force between generic (convex) non-planar surfaces is provided by multiplying the one-dimensional parallel-plate interaction potential by an "effective radius" depending on the local radii of curvature of the surfaces at minimum separation.…”

Section: Introductionmentioning

confidence: 99%

Ray-theory approach to electrical-double-layer interactions

Schnitzer

2015

Phys. Rev. E

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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.

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Electrical Double Layer Interaction between Dissimilar Spherical Colloidal Particles and between a Sphere and a Plate: The Linearized Poisson-Boltzmann Theory

Cited by 124 publications

References 0 publications

Force measurements with the atomic force microscope: Technique, interpretation and applications

Force measurements with the atomic force microscope: Technique, interpretation and applications

Electrophoretic Motion of a Spherical Particle with a Thick Double Layer in Bounded Flows

Ray-theory approach to electrical-double-layer interactions

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