The prediction of electrokinetic phenomena within multiparticle systems

Levine, S.; Neale, Graham H.; Epstein, Norman

doi:10.1016/0021-9797(76)90221-6

Cited by 118 publications

(131 citation statements)

References 16 publications

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“…[16] that no ion fluxes are allowed to cross the slipping plane if a DSL is absent (r is the unit normal directed outward from the particle surface). According to the Kuwabara cell model, the liquid velocity at the outer surface of the unit cell must satisfy ν r = −ν e cos θ = −u e E cos θ at r = b [17] ω = ∇ × v = 0 at r = b, [18] which mean, respectively, that the liquid velocity is parallel to the electrophoretic velocity, and the vorticity is equal to 0 at the outer surface of the cell. Now, we will assume that the electrical double layer around the particle is only slightly distorted due to the electric field (the external field must be low enough for this condition to be valid; it is most often fulfilled in practical situations), so that a linear perturbation scheme for the above-mentioned quantities can be used, i.e.,…”

Section: Governing Equations and Boundary Conditionsmentioning

confidence: 99%

“…However, in a great number of practical situations, suspensions are usually more concentrated than those typically considered as dilute, so some theoretical approaches to the issue of concentrated suspensions, including electrophoresis (16), sedimentation (17,18), electrical conductivity (19), and electroacoustic phenomena (20)(21)(22), to mention just a few, have been published in the past few decades. The majority of them have in common the use of cell models (23,24), to account for particle-particle interactions.…”

Section: Introductionmentioning

confidence: 99%

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Electrokinetics of Concentrated Suspensions of Spherical Colloidal Particles with Surface Conductance, Arbitrary Zeta Potential, and Double-Layer Thickness in Static Electric Fields

Carrique¹,

Arroyo

Delgado

2002

Journal of Colloid and Interface Science

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Section: Governing Equations and Boundary Conditionsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Electrokinetics of Concentrated Suspensions of Spherical Colloidal Particles with Surface Conductance, Arbitrary Zeta Potential, and Double-Layer Thickness in Static Electric Fields

Carrique¹,

Arroyo

Delgado

2002

Journal of Colloid and Interface Science

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“…11,12 Special efforts have been devoted to the development and improvement of theoretical electrokinetic models for phenomena such as electrophoresis, sedimentation, electrical conductivity, and electroacoustic effects in concentrated colloidal suspensions. [13][14][15][16][17][18][19][20] On the other hand, Midmore and O'Brien 21 obtained a cellmodel formula for the low frequency conductivity of a concentrated suspension of spheres with thin double layers, starting from a cell-model conductivity formula derived by De Backer and Watillon. 22 In general, the most relevant studies of the conductivity in concentrated suspensions are based on the Levine-Neale boundary condition 13 for the electrical potential, which is of the Neumann type.…”

Section: Introductionmentioning

confidence: 99%

Numerical and Analytical Studies of the Electrical Conductivity of a Concentrated Colloidal Suspension

et al. 2006

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In the past few years, different models and analytical approximations have been developed facing the problem of the electrical conductivity of a concentrated colloidal suspension, according to the cell-model concept. Most of them make use of the Kuwabara cell model to account for hydrodynamic particle-particle interactions, but they differ in the choice of electrostatic boundary conditions at the outer surface of the cell. Most analytical and numerical studies have been developed using two different sets of boundary conditions of the Neumann or Dirichlet type for the electrical potential, ionic concentrations or electrochemical potentials at that outer surface. In this contribution, we study and compare numerical conductivity predictions with results obtained using different analytical formulas valid for arbitrary zeta potentials and thin double layers for each of the two common sets of boundary conditions referred to above. The conductivity will be analyzed as a function of particle volume fraction, φ, zeta potential, , and electrokinetic radius, κa (κ -1 is the double layer thickness, and a is the radius of the particle). A comparison with some experimental conductivity results in the literature is also given. We demonstrate in this work that the two analytical conductivity formulas, which are mainly based on Neumann-and Dirichlet-type boundary conditions for the electrochemical potential, predict values of the conductivity very close to their corresponding numerical results for the same boundary conditions, whatever the suspension or solution parameters, under the assumption of thin double layers where these approximations are valid. Furthermore, both analytical conductivity equations fulfill the Maxwell limit for uncharged nonconductive spheres, which coincides with the limit κa f ∞. However, some experimental data will show that the Neumann, either numerical or analytical, approach is unable to make predictions in agreement with experiments, unlike the Dirichlet approach which correctly predicts the experimental conductivity results. In consequence, a deeper study has been performed with numerical and analytical predictions based on Dirichlettype boundary conditions.

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“…An alternative expression was proposed in [43]: (36) where φ L is the volume fraction of liquid in the plug (or void volume fraction). Other estimates of A c /L can be found in [44][45][46].…”

confidence: 99%

“…4. If such a velocity cannot be measured, the convenient physical quantity becomes the electro-osmotic flow rate, Q eo (m 3 s -1 ), given by (46) where dS is the elementary surface vector at the location in the channel where the fluid velocity is v eo . The counterparts of Q eo are Q eo,E (flow rate divided by electric field) and Q eo,I (flow rate divided by current).…”

Section: Operational Definitions; Recommended Symbols and Terminologymentioning

confidence: 99%

Measurement and Interpretation of Electrokinetic Phenomena (IUPAC Technical Report)

2006

Chemistry International -- Newsmagazine for IUPAC

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Republication or reproduction of this report or its storage and/or dissemination by electronic means is permitted without the Measurement and interpretation of electrokinetic phenomena (IUPAC Technical Report)Abstract: In this report, the status quo and recent progress in electrokinetics are reviewed. Practical rules are recommended for performing electrokinetic measurements and interpreting their results in terms of well-defined quantities, the most familiar being the ζ-potential or electrokinetic potential. This potential is a property of charged interfaces, and it should be independent of the technique used for its determination. However, often the ζ-potential is not the only property electrokinetically characterizing the electrical state of the interfacial region; the excess conductivity of the stagnant layer is an additional parameter. The requirement to obtain the ζ-potential is that electrokinetic theories be correctly used and applied within their range of validity. Basic theories and their application ranges are discussed. A thorough description of the main electrokinetic methods is given; special attention is paid to their ranges of applicability as well as to the validity of the underlying theoretical models. Electrokinetic consistency tests are proposed in order to assess the validity of the ζ-potentials obtained. The recommendations given in the report apply mainly to smooth and homogeneous solid particles and plugs in aqueous systems; some attention is paid to nonaqueous media and less ideal surfaces.

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The prediction of electrokinetic phenomena within multiparticle systems

Cited by 118 publications

References 16 publications

Electrokinetics of Concentrated Suspensions of Spherical Colloidal Particles with Surface Conductance, Arbitrary Zeta Potential, and Double-Layer Thickness in Static Electric Fields

Electrokinetics of Concentrated Suspensions of Spherical Colloidal Particles with Surface Conductance, Arbitrary Zeta Potential, and Double-Layer Thickness in Static Electric Fields

Numerical and Analytical Studies of the Electrical Conductivity of a Concentrated Colloidal Suspension

Measurement and Interpretation of Electrokinetic Phenomena (IUPAC Technical Report)

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