Electrophoresis of an insulating sphere normal to a conducting plane
TL;DR: In this article, the electrophoresis of an insulating sphere, having a double layer thin with respect to the particle diameter, is studied analytically. And the calculated correction to Smoluchowski's equation is not due to double-layer interactions but becomes significant at greater separations.
About: This article is published in Journal of Colloid and Interface Science.The article was published on 1970-05-01. It has received 75 citations till now. The article focuses on the topics: Plane (geometry).
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TL;DR: In this article, a review of the fundamental aspects of electrophoretic deposition technique, factors influencing the deposition process, kinetic aspects, types of EPD, the driving forces, preconditioning electrophoreic suspension, stability and control of suspension, mechanisms involved in EPD and drying of deposits obtained by EPD are discussed.
1,827 citations
Cites methods from "Electrophoresis of an insulating sp..."
...The flow fields with finite boundary conditions, the wall effects were accounted for by Morrison and Stukel [79] and Keh and Anderson [80] (i....
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TL;DR: The existence of a slip velocity at solid/fluid interfaces opens a class of flow problems not generally recognized by the fluid-dynamics community as mentioned in this paper, and the existence of slip velocities at solid and fluid interfaces has been studied in the literature.
Abstract: In a historical context the interface between two phases has played only a minor role in the physics of fluid dynamics. It is of course true that boundary conditions at interfaces, usually imposed as continuity of ve locity and stress, determine the velocity field of a given flow; however, this is a more or less passive use of the interface that allows one to ignore the structure of the transition between two phases. When an interface has been assigned a more active role in flow processes, it generally has been assumed that one parameter, the interfacial (surface) tension, accounts for all mech anical phenomena (Young et al. 1 959, Levich & Krylov 1969). In these studies, kinematic effects of the interface were not considered, and the "no-slip" condition on the velocity at interfaces was retained. The basic message of this article is that the interface is a region of small but finite thickness, and that dynamical processes occurring within this region lead not only to interfacial stresses but also to an apparent "slip velocity" that, on a macroscopic length scale, appears to be a violation of the no-slip condition. The existence of a slip velocity at solid/fluid interfaces opens a class of flow problems not generally recognized by the fluid-dynamics community. Three previous articles in this series deal with flow caused by interactions between interfaces and external fields such as electrical potential, tem perature, and solute concentration. Melcher & Taylor ( 1969) and Levich & Krylov (1969) consider fluid/fluid interfaces where stresses produced at the interface by the external field dictate the flow. Saville ( 1977), on the other hand, discusses the action of an electric field on a charged solid/fluid interface and reviews the currently accepted model for electrophoretic
1,343 citations
TL;DR: In this paper, an analysis of the electrophoretic motion of a charged nonconducting sphere in the proximity of rigid boundaries is presented for three boundary configurations: a single flat wall, two parallel walls, and a long circular tube.
Abstract: An analysis is presented for electrophoretic motion of a charged non-conducting sphere in the proximity of rigid boundaries. An important assumption is that κa → ∞, where a is the particle radius and κ is the Debye screening parameter. Three boundary configurations are considered: single flat wall, two parallel walls (slit), and a long circular tube. The boundary is assumed a perfect electrical insulator except when the applied field is directed perpendicular to a single wall, in which case the wall is assumed to have a uniform potential (perfect conductor). There are three basic effects causing the particle velocity to deviate from the value given by Smoluchowski's classic equation: first, a charge on the boundary causes electro-osmotic flow of the suspending fluid; secondly, the boundary alters the interaction between the particle and applied electric field; and, thirdly, the boundary enhances viscous retardation of the particle as it tries to move in response to the applied field. Using a method of reflections, we determine the particle velocity for a constant applied field in increasing powers of λ up to O(λ6), where λ is the ratio of particle radius to distance from the boundary. Ignoring the O(λ0) electro-osmotic effect, the first effect attributable to proximity of the boundary is O(λ3) for all boundary configurations, and in cases when the applied field is parallel to the boundaries the electrophoretic velocity is proportional to ζp − ζw, the difference in zeta potential between the particle and boundary.
278 citations
TL;DR: In this article, the electric potential around a charged spherical colloid near an electrode was studied theoretically and experimentally to understand the nature of long-range particle-particle attraction near electrodes.
Abstract: Electrohydrodynamic (EHD) flow around a charged spherical colloid near an electrode was studied theoretically and experimentally to understand the nature of long-range particle–particle attraction near electrodes. Numerical computations for finite double-layer thicknesses confirmed the validity of an asymptotic methodology for thin layers. Then the electric potential around the particle was computed analytically in the limit of zero Peclet number and thin double layers for oscillatory electric fields at frequencies where Faradaic reactions are negligible. Streamfunctions for the steady component of the EHD flow were determined with an electro-osmotic slip boundary condition on the electrode surface. Accordingly, it was established how the axisymmetric flow along the electrode is related to the dipole coefficient of the colloidal particle. Under certain conditions, the flow is directed toward the particle and decays as r−4, in accord with observations of long-range particle aggregation. To test the theory, particle-tracking experiments were performed with fluorescent 300 nm particles around 50μm particles over a wide range of electric field strengths and frequencies. Treating the particle surface conductivity as a fitting parameter yields velocities in excellent agreement with the theoretical predictions. The observed frequency dependence, however, differs from the model predictions, suggesting that the effect of convection on the charge distribution is not negligible as assumed in the zero Peclet number limit.
134 citations
Cites methods from "Electrophoresis of an insulating sp..."
...(4.11) To determine the An coefficients, we follow Morrison & Stukel (1970) and use the orthogonality relations for Legendre polynomials in integral form....
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...Specification of a constant potential along the electrode, as used in previous analyses of electrophoretic processes near electrodes (Morrison & Stukel 1970; Reed & Morrison 1976), omits the presence of tangential potential gradients in the outer part of the polarization layer that give rise to EHD…...
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TL;DR: In this article, an exact analytical study of the electrophoretic motion of a dielectric sphere in the proximity of a large nonconducting plane is presented, where the applied electric field is parallel to the plane and uniform over distances comparable with the particle radius.
Abstract: An exact analytical study is presented for the electrophoretic motion of a dielectric sphere in the proximity of a large non-conducting plane. The applied electric field is parallel to the plane and uniform over distances comparable with the particle radius. The particle and plane surfaces are assumed uniformly charged and the thin-double-layer assumption is employed. The presence of the wall causes three basic effects on the electrophoretic velocity: first, an electro-osmotic flow of the suspending fluid exists owing to the interaction between the electric field and the charged wall; secondly, the electrical field lines around the particle are squeezed by the wall, thereby speeding up the particle; and thirdly, the wall enhances viscous retardation of the moving particle. In the analysis, corrections to Smoluchowski's classic equation for the electrophoretic velocity in an unbounded fluid are presented for various separation distances between the particle and the wall. Of particular interest is the electrophoresis for small gap widths, in which case the net effect of the plane wall is to enhance the particle velocity. The particle mobility can be increased by as much as 23% when the surface-to-surface spacing is about 0.5% of the sphere radius. For the case of moderate to large separations, the electrophoretic velocity of the particle is reduced by the wall, but this effect is much weaker than for sedimentation. In addition to the translational migration, the electrophoretic sphere rotates at the same time in the direction opposite to that which would occur if the sphere sedimented parallel to a plane wall. The ratio of rotational-to-translational speeds of the sphere is in general larger for electrophoresis than for sedimentation.
119 citations
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9,185 citations
TL;DR: In this paper, bipolar co-ordinates are employed to obtain exact solutions of the equations of slow viscous flow for the steady motion of a solid sphere towards or away from a plane surface of infinite extent.
1,507 citations
TL;DR: In this paper, the effects of nonuniform electric fields on nonconducting liquids have been investigated, and the results show that the effect can be used to produce a fairly efficient pumping action of nonconducted liquids, to cause continuous and easily measureable separations in coarse suspensions, to produce selective precipitation, and to produce mixing.
Abstract: Some of the more interesting effects of nonuniform electric fields are described in this report. Experimental and theoretical studies show the effects to be rather striking for particles larger than molecular size. The results show that the effect can be used to produce a fairly efficient pumping action of nonconducting liquids, to cause continuous and easily measureable separations in coarse suspensions, to cause selective precipitation, and to produce mixing.By this means, liquids may be thrown several feet into the air with an electromechanical efficiency of about 25%. A separation factor of at least 2.5 in continuous separatory operation may be produced in a suspension of polyvinyl chloride in carbon tetrachloride‐benzene mixture. Suspensions of polar materials in less polar liquids may be either dispersed or precipitated. In one interesting ``demonstration'' type experiment, drops were ``hung'' in mid‐air.
383 citations
TL;DR: In this article, the authors extended the calculations of Stimson and Jeffery of the force on two spheres moving coaxially through a viscous liquid to the case when the spheres move at different rates.
Abstract: The calculations of Stimson and Jeffery of the force on two spheres moving coaxially through a very viscous liquid are extended to the case when the spheres move at different rates. This result is used to calculate the effect of the bottom of the vessel in a falling sphere viscometer and that of the upper surface of the liquid. Approximate solutions are also found in a form suitable for practical use.
194 citations