Boundary-induced electrophoresis of uncharged conducting particles: near-contact approximation

A zero net charge ideally polarizable particle is suspended within an electrolyte solution, nearly in contact with an uncharged non-polarizable wall. This system is exposed to a uniform electric field that is applied parallel to the wall. Assuming a thin Debye thickness, the induced-charge electro-osmotic flow is investigated with the goal of obtaining an approximation for the force experienced by the particle. Singular perturbations in terms of the dimensionless gap width δ are used to represent the small-gap singular limit δ ≪1. The fluid is decomposed into two asymptotic regions: an inner gap region, where the electric field and strain rate are large, and an outer region, where they are moderate. The leading contribution to the force arises from hydrodynamic stresses in the inner region, while contributions from both hydrodynamic stresses at the outer region and Maxwell stresses in both regions appear in higher order correction terms.

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The elongated shape of a dielectric drop deformed by a strong electric field

Journal of Fluid Mechanics ◽

10.1017/s0022112010004581 ◽

2010 ◽

Vol 664 ◽

pp. 286-296 ◽

Cited By ~ 5

Author(s):

DOV RHODES ◽

EHUD YARIV

Keyword(s):

Electric Field ◽

Electric Fields ◽

Strong Electric Field ◽

Outer Region ◽

Spherical Shape ◽

Problem Formulation ◽

Boundary Integral ◽

Uniform Electric Field ◽

Cross Sectional ◽

Drop Shape

A dielectric drop is suspended within a dielectric liquid and is exposed to a uniform electric field. Due to polarization forces, the drop deforms from its initial spherical shape, becoming prolate in the field direction. At strong electric fields, the drop elongates significantly, becoming long and slender. For moderate ratios of the permittivities of the drop and surrounding liquid, the drop ends remain rounded. The slender limit was originally analysed by Sherwood (J. Phys. A, vol. 24, 1991, p. 4047) using a singularity representation of the electric field. Here, we revisit it using matched asymptotic expansions. The electric field within the drop is continued into a comparable solution in the ‘inner’ region, at the drop cross-sectional scale, which is itself matched into the singularity representation in the ‘outer’ region, at the drop longitudinal scale. The expansion parameter of the problem is the elongated drop slenderness. In contrast to familiar slender-body analysis, this parameter is not provided by the problem formulation, and must be found throughout the course of the solution. The drop aspect-ratio scaling, with the 6/7-power of the electric field, is identical to that found by Sherwood (J. Phys. A, vol. 24, 1991, p. 4047). The predicted drop shape is compared with the boundary-integral solutions of Sherwood (J. Fluid Mech., vol. 188, 1988, p. 133). While the agreement is better than that found by Sherwood (J. Phys. A, vol. 24, 1991, p. 4047), the weak logarithmic decay of the error terms still hinders an accurate calculation. We obtain the leading-order correction to the drop shape, improving the asymptotic approximation.

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Driven, dissipative, energy-conserving magnetohydrodynamic equilibria. Part 2. The screw pinch

Journal of Plasma Physics ◽

10.1017/s002237780001686x ◽

1993 ◽

Vol 49 (1) ◽

pp. 125-159 ◽

Cited By ~ 2

Author(s):

Michael L. Goodman

Keyword(s):

Thermal Conductivity ◽

Electric Field ◽

Boundary Conditions ◽

Transition Region ◽

Outer Region ◽

Radial Electric Field ◽

Axial Current ◽

Number Density ◽

Energy Conserving ◽

Inner Region

A cylindrically symmetric, electrically driven, dissipative, energy-conserving magnetohydrodynamic equilibrium model is considered. The high-magneticfield Braginskii ion thermal conductivity perpendicular to the local magnetic field and the complete electron resistivity tensor are included in an energy equation and in Ohm's law. The expressions for the resistivity tensor and thermal conductivity depend on number density, temperature, and the poloidal and axial (z-component) magnetic field, which are functions of radius that are obtained as part of the equilibrium solution. The model has plasma-confining solutions, by which is meant solutions characterized by the separation of the plasma into two concentric regions separated by a transition region that is an internal boundary layer. The inner region is the region of confined plasma, and the outer region is the region of unconfined plasma. The inner region has average values of temperature, pressure, and axial and poloidal current densities that are orders of magnitude larger than in the outer region. The temperature, axial current density and pressure gradient vary rapidly by orders of magnitude in the transition region. The number density, thermal conductivity and Dreicer electric field have a global minimum in the transition region, while the Hall resistivity, Alfvén speed, normalized charge separation, Debye length, (ωλ)ion and the radial electric field have global maxima in the transition region. As a result of the Hall and electron-pressure-gradient effects, the transition region is an electric dipole layer in which the normalized charge separation is localized and in which the radial electric field can be large. The model has an intrinsic value of β, about 13·3%, which must be exceeded in order that a plasma-confining solution exist. The model has an intrinsic length scale that, for plasma-confining solutions, is a measure of the thickness of the boundary-layer transition region. If appropriate boundary conditions are given at R = 0 then the equilibrium is uniquely determined. If appropriate boundary conditions are given at any outer boundary R = a then the equilibrium exhibits a bifurcation into two states, one of which exhibits plasma confinement and carries a larger axial current than the other, which is almost homogeneous and cannot confine a plasma. Exact expressions for the two values of the axial current in the bifurcation are derived. If the boundary conditions are given at R = a then a solution exists if and only if the constant driving electric field exceeds a critical value. An exact expression for this critical electric field is derived. It is conjectured that the bifurcation is associated with an electric-field-driven transition in a real plasma, between states with different rotation rates, energy dissipation rates and confinement properties. Such a transition may serve as a relatively simple example of the L—H mode transition observed in tokamaks.

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The root of a comet tail: Rosetta ion observations at comet 67P/Churyumov–Gerasimenko

Astronomy and Astrophysics ◽

10.1051/0004-6361/201832842 ◽

2018 ◽

Vol 616 ◽

pp. A21 ◽

Cited By ~ 10

Author(s):

E. Behar ◽

H. Nilsson ◽

P. Henri ◽

L. Berčič ◽

G. Nicolaou ◽

...

Keyword(s):

Magnetic Field ◽

Solar Wind ◽

Electric Field ◽

Outer Region ◽

Field Measurements ◽

Night Side ◽

Combined Action ◽

Single Night ◽

Inner Region ◽

Comet 67P

Context. The first 1000 km of the ion tail of comet 67P/Churyumov–Gerasimenko were explored by the European Rosetta spacecraft, 2.7 au away from the Sun. Aims. We characterised the dynamics of both the solar wind and the cometary ions on the night-side of the comet’s atmosphere. Methods. We analysed in situ ion and magnetic field measurements and compared the data to a semi-analytical model. Results. The cometary ions are observed flowing close to radially away from the nucleus during the entire excursion. The solar wind is deflected by its interaction with the new-born cometary ions. Two concentric regions appear, an inner region dominated by the expanding cometary ions and an outer region dominated by the solar wind particles. Conclusions. The single night-side excursion operated by Rosetta revealed that the near radial flow of the cometary ions can be explained by the combined action of three different electric field components, resulting from the ion motion, the electron pressure gradients, and the magnetic field draping. The observed solar wind deflection is governed mostly by the motional electric field −uion × B.

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Numerical Simulation on Transient Electrophoretic Motion of a Circular Particle in a T-Shaped Slit Microchannel

Fluids Engineering ◽

10.1115/imece2003-42791 ◽

2003 ◽

Author(s):

Chunzhen Ye ◽

Dongqing Li

Keyword(s):

Numerical Simulation ◽

Liquid Phase ◽

Flow Field ◽

Electric Field ◽

Particle Motion ◽

Outer Region ◽

Double Layers ◽

Circular Particle ◽

Electric Potentials ◽

Inner Region

This paper considers the electrophoretic motion of a circular particle in a T-shaped slit microchannel, where the size of the channel is close to that of the particle. During the process, the electric field (i.e., the gradient of the electric potential) changes with the particle motion, which in return influences the flow field and the particle motion. Therefore, the electric field, the flow field and the particle motion are coupled together, and this is an unsteady process. The objective is to obtain a fundamental understanding of the characteristics of the particle motion in the complicated T-shaped junction region. Such influences on the electric field and the particle motion are investigated as the applied electric potentials, the geometry of the channel and the size of the particle. In the theoretical analysis, the liquid phase is divided into the inner region and the outer region. The inner region consists of the electrical double layers and the outer region consists of the remainder of the liquid. Under the assumption of thin electrical double layer, a mathematical model governing the inner region, the outer region and the particle motion is developed. A direct numerical simulation method using the finite element method is employed. In this method, a continuous hydrodynamic model is adopted. By this model, both the liquid phase in the outer region and the particle phase are governed by the same momentum equations. ALE method is used to track the surface of the particle at each time step. The numerical results show that the electric field is influenced by the applied electric potentials, the geometry of the channel and the particle suspension, and that the particle motion is mainly dominated by the local electric field. It is also found that the magnitude of the particle motion is dependent on its own size in the same channel.

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