Thin Debye Layer Research Articles

Shape- and orientation-dependent diffusiophoresis of colloidal ellipsoids.

We present the diffusiophoresis of ellipsoidal particles induced by ionic solute gradients. Contrary to the common expectation that diffusiophoresis is shape independent, here we show experimentally that this assumption breaks down when the thin Debye layer approximation is relaxed. By tracking the translation and rotation of various ellipsoids, we find that the phoretic mobility of ellipsoids is sensitive to the eccentricity and the orientation of the ellipsoid relative to the imposed solute gradient, and can further lead to nonmonotonic behavior under strong confinement. We show that such a shape- and orientation-dependent diffusiophoresis of colloidal ellipsoids can be easily captured by modifying theories for spheres.

A model for the electric field-driven flow and deformation of a drop or vesicle in strong electrolyte solutions

A model is constructed to describe the flow field and arbitrary deformation of a drop or vesicle that contains and is embedded in an electrolyte solution, where the flow and deformation are caused by an applied electric field. The applied field produces an electrokinetic flow, which is set up on the charge-up time scale $\tau _{*c}=\lambda _{*} a_{*}/D_{*}$ , where $\lambda _{*}$ is the Debye screening length, $a_{*}$ is the inclusion length scale and $D_{*}$ is an ion diffusion constant. The model is based on the Poisson–Nernst–Planck and Stokes equations. These are reduced or simplified by forming the limit of strong electrolytes, for which dissolved salts are completely ionised in solution, together with the limit of thin Debye layers. Debye layers of opposite polarity form on either side of the drop interface or vesicle membrane, together forming an electrical double layer. Two formulations of the model are given. One utilises an integral equation for the velocity field on the interface or membrane surface together with a pair of integral equations for the electrostatic potential on the outer faces of the double layer. The other utilises a form of the stress-balance boundary condition that incorporates the double layer structure into relations between the dependent variables on the layers’ outer faces. This constitutes an interfacial boundary condition that drives an otherwise unforced Stokes flow outside the double layer. For both formulations relations derived from the transport of ions in each Debye layer give additional boundary conditions for the potential and ion concentrations outside the double layer.

Numerical study on diffusiophoresis of a hydrophobic nanoparticle in a monovalent or multivalent electrolyte

A numerical study on the diffusiophoresis of a hydrophobic charged colloid driven by an imposed concentration gradient of an electrolyte is made. Our numerical model is based on the computation of Navier-Stokes-Nernst-Planck-Poisson equations. Diffusiophoresis of hydrophobic particles and size-based sorting has not been attempted before. The present numerical model elucidates the nonlinear effects on diffusiophoresis in a valence asymmetric electrolyte, which have been ignored in previous studies. The particle hydrophobicity, characterized by the slip length, modifies the ζ-potential and the Debye layer, which in turn creates a significant impact on the particle diffusiophoresis. An analytical solution, valid for a lower range of slip length and imposed concentration gradient is obtained under the thin Debye layer consideration, which compares well with the numerical solution for a thin Debye length when the slip length is a few tens of nanometer. We investigate the impact of slip length on the diffusiophoresis by considering different types of monovalent and valence asymmetric electrolytes. The surface hydrophobicity enhances the particle ζ-potential by reducing the shielding effect and the impact becomes stronger at a thinner Debye layer. For this, the mobility reversal manifests for a hydrophobic particle when the electrophoresis and chemiphoresis parts are competitive. Hydrophobicity enhances the mobility of the particle when electrophoresis and chemiphoreis are cooperative. The higher valence of the counterions of the electrolyte enhances the mobility for the moderate range of the Debye length by increasing the chemiphoresis part. The size-based sorting of the particle by diffusiophoresis is analyzed. At a thinner Debye length the diffusiophoretic mobility of a hydrophobic particle exhibits a size dependency.

The electrochemical impedance spectrum of asymmetric electrolytes across low to moderate frequencies

• New mathematical analysis for the electrochemical impedance spectrum of asymmetric electrolytes. • Double plateau behavior in the real part of impedance predicted across low to moderate frequencies. • Low frequency response is caused transient bulk diffusion, or concentration polarization, of salt across an electrochemical cell. We develop new mathematical expressions for the electrochemical impedance spectrum of an asymmetric electrolyte. Specifically, we consider the Poisson-Nernst-Planck (PNP) equations governing ion transport in a binary asymmetric electrolyte with unequal valences and diffusivities, flanked by planar, parallel, blocking electrodes. The electrodes are subject to an oscillating voltage of small amplitude comparable to the thermal voltage scale. We further consider the limit practically applicable to liquid electrolytes of thin Debye layers ∊ = 1 / ( κ L ) ≪ 1 , where κ - 1 is the Debye screening length and L is the length of the half cell. The impedance is then obtained from the current in the external circuit, defined as the rate of change of electric field at either electrode. We identify two distinct asymptotic regimes for the frequency ( ω ) in the limit ∊ → 0 : low frequencies, on the order of the inverse bulk diffusion time ω = O ( D A / L 2 ) ; and moderate frequencies, on the order of the inverse RC charging time scale ω = O ( D A κ / L ) . Here D A = ( z + + z - ) D + D - / ( z + D + + z - D - ) is the ambipolar diffusion coefficient of the salt, z ± are the ionic valences, and D ± are the ionic diffusivities. Our analysis provides new, concise expressions for the impedance at low and moderate frequencies, that account for ionic valence asymmetry. Further, in the moderate frequency analysis, higher order contributions (in ∊ ) to the impedance reveal that the real part (i.e. the resistance) appears to diverge as ω - 1 / 2 in the limit ω L / ( κ D A ) → 0 , akin to a semi-infinite Warburg element. We determine that this occurs due to the existence of oscillating diffusion layers, O ( ∊ 1 / 2 L ) in width, that bridge the ion transport between the O ( ∊ L ) wide Debye layers adjacent to each electrode and the O ( L ) wide bulk electro-neutral electrolyte. In the low frequency regime, however, these diffusion layers relax, and effectively merge across the bulk of the cell; consequently, the resistance spectrum attains a plateau in the limit of zero frequency ω L 2 / D A → 0 . Thus, our asymptotic analysis discerns the electrochemical processes that dictate the impedance of asymmetric electrolytes at the low and moderate frequency regimes.

Direct numerical simulation of electroconvection with thin Debye layer matching canonical experiments

Electroconvection has the potential to be applied in electrochemical technologies such as electrodialysis and energy storage, and has thus aroused considerable research interest. This paper describes the direct numerical simulation (DNS) of the dimensionless Poisson–Nernst–Planck and Stokes equations for electroconvection to determine why the dimensionless thin Debye layer in existing simulations does not match the results of canonical experiments. Our DNS results show that the discrepancy between the simulation results and the experimental data is mainly caused by differences in the structural characteristics of the extended space charge layer. A dimensionless thin Debye layer matching those in canonical experiments enhances the driving force of the extended space charge layer, resulting in massive vortices near the permselective membranes that cause the electroconvective flow to transition from the steady state to time-dependent spatiotemporal dynamics. Our DNS results show that choosing the thickness of the dimensionless thin Debye layer to be consistent with canonical experiments is a key factor in the high-precision quantitative analysis of electroconvection characteristics such as the vortex height, dynamic evolution, and pattern formation. These results provide important guidance for the design and instability control of microfluidic chips.

Transitions and Instabilities in Imperfect Ion-Selective Membranes.

Numerical investigation of the underlimiting, limiting, and overlimiting current modes and their transitions in imperfect ion-selective membranes with fluid flow through permitted through the membrane is presented. The system is treated as a three layer composite system of electrolyte-porous membrane-electrolyte where the Nernst–Planck–Poisson–Stokes system of equations is used in the electrolyte, and the Darcy–Brinkman approach is employed in the nanoporous membrane. In order to resolve thin Debye and Darcy layers, quasi-spectral methods are applied using Chebyshev polynomials for their accumulation of zeros and, hence, best resolution in the layers. The boundary between underlimiting and overlimiting current regimes is subject of linear stability analysis, where the transition to overlimiting current is assumed due to the electrokinetic instability of the one-dimensional quiescent state. However, the well-developed overlimiting current is inherently a problem of nonlinear stability and is subject of the direct numerical simulation of the full system of equations. Both high and low fixed charge density membranes (low- and high concentration electrolyte solutions), acting respectively as (nearly) perfect or imperfect membranes, are considered. The perfect membrane is adequately described by a one-layer model while the imperfect membrane has a more sophisticated response. In particular, the direct transition from underlimiting to overlimiting currents, bypassing the limiting currents, is found to be possible for imperfect membranes (high-concentration electrolyte). The transition to the overlimiting currents for the low-concentration electrolyte solutions is monotonic, while for the high-concentration solutions it is oscillatory. Despite the fact that velocities in the porous membrane are much smaller than in the electrolyte region, it is further demonstrated that they can dramatically influence the nature and transition to the overlimiting regimes. A map of the bifurcations, transitions, and regimes is constructed in coordinates of the fixed membrane charge and the Darcy number.

Impact of ion-steric and ion-partitioning effects on electrophoresis of soft particles.

A theoretical study on the electrophoresis of a soft particle is made by taking into account the ion steric interactions and ion partitioning effects under a thin Debye layer consideration with negligible surface conduction. Objective of this study is to provide a simple expression for the mobility of a soft particle which accounts for the finite-ion-size effect and the ion partitioning arise due to the Born energy difference between two media. The Donnan potential in the soft layer is determined by considering the ion steric interactions and the ion partitioning effect. The volume exclusion due to the finite ion size is considered by the Carnahan-Starling equation and the ion partitioning is accounted through the difference in Born energy. The modified Poisson-Boltzmann equation coupled with Stokes-Darcy-Brinkman equations are considered to determine the mobility. A closed-form expression for the electrophoretic mobility is obtained, which reduces to several existing expressions for mobility under various limiting cases.

Interfaces in Materials for Hydrogen Power Engineering

Hydrogen power engineering is based on the production of hydrogen and subsequent oxidation of it to generate electrical energy. Using the example of ion-exchange membranes, catalysts for low-temperature fuel cells, and catalysts for alcohol steam reforming, the features of the transfer, catalysis, and electrocatalysis in hydrogen power engineering are discussed. Particular attention is paid to the role of interfaces. The occurrence of transport processes in ion-exchange membranes is determined by a system of pores and channels that are formed in the membranes owing to self-organization processes. The main selective transport of counterions occurs in a thin Debye layer at the interface between the polymer and the water solution that fills the pores. The transport of gases in these systems occurs through an electrically neutral solution localized in the center of the pores; it can be controlled by introducing nanoparticles into the pores. Catalytic processes in fuel cells occur at the interface between three phases, namely, the catalyst, the support, and the proton-conducting component. The role of the support in the stabilization and enhancement of the power of fuel cells is discussed. Despite the significant difference, the laws governing the catalytic processes of alcohol steam reforming are similar to those of fuel cells in many respects. The nature of metal catalysts is responsible for the preferred direction of the process, whereas the nature of the support largely determines the catalyst performance.

Enhanced electroosmotic flow and ion selectivity in a channel patterned with periodically arranged polyelectrolyte-filled grooves

An enhanced electroosmotic flow through a surface-modulated microchannel is considered. The microchannel is modulated by periodically arranged rectangular grooves filled with polyelectrolyte materials. The flat surface of the walls is maintained at a constant charge density. A nonlinear model based on the Poisson–Nernst–Planck equations coupled with the Darcy–Brinkman–Forchheimer equation in the polyelectrolyte region and Navier–Stokes equations in the clear fluid region is adopted. Going beyond the widely employed Debye–Huckel linearization, we adopt numerical methods to elucidate the effect of pertinent parameters on electroosmosis in the patterned channel. The patterned microchannel results in an enhancement in the average EOF by creating an intrinsic velocity slip at the polyelectrolyte–liquid interface. An analytical solution of the EOF for a limiting case in which the groove width is much higher than the channel height is obtained based on the Debye–Huckel approximation. This analytical solution is in good agreement with the present numerical model when a low charge density and a thin Debye layer are considered. We have also established an analogy between the EOF in a polyelectrolyte-filled grooved-channel with the EOF in which the grooves are replaced by the charged slipping planes.

AC Electrokinetics of Polarizable Tri-Axial Ellipsoidal Nano-Antennas and Quantum Dot Manipulation.

By realizing the advantages of using a tri-axial ellipsoidal nano-antenna (NA) surrounded by a solute for enhancing light emission of near-by dye molecules, we analyze the possibility of controlling and manipulating the location of quantum dots (similar to optical tweezers) placed near NA stagnation points, by means of prevalent AC electric forcing techniques. First, we consider the nonlinear electrokinetic problem of a freely suspended, uncharged, polarized ellipsoidal nanoparticle immersed in a symmetric unbounded electrolyte which is subjected to a uniform AC ambient electric field. Under the assumption of small Peclet and Reynolds numbers, thin Debye layer and ‘weak-field’, we solve the corresponding electrostatic and hydrodynamic problems. Explicit expressions for the induced velocity, pressure, and vorticity fields in the solute are then found in terms of the Lamé functions by solving the non-homogeneous Stokes equation forced by the Coulombic density term. The particular axisymmetric quadrupole-type flow for a conducting sphere is also found as a limiting case. It is finally demonstrated that stable or equilibrium (saddle-like) positions of a single molecule can indeed be achieved near stagnation points, depending on the directions of the electric forcing and the induced hydrodynamic (electroosmotic) and dielectrophoretic dynamical effects. The precise position of a fluorophore next to an ellipsoidal NA, can thus be simply controlled by adjusting the frequency of the ambient AC electric field.

Electrokinetics of a particle attached to a fluid interface: Electrophoretic mobility and interfacial deformation

The electrophoretic mobility of a particle at the interface between two fluids is computed. For thin Debye layers, the Smoluchowki mobility is recovered. Generally, the mobility depends on the contact angle between the fluids and the particle. The interfacial deformation is also calculated.

Ion partitioning effect on the electrophoresis of a soft particle with hydrophobic core.

A theoretical study on the electrophoresis of a soft particle made up of a charged hydrophobic inner core surrounded by polyelectrolyte layer (PEL) is made. The dielectric permittivity of the PEL and aqueous solution are considered to be different, which creates the ion partitioning effect. The ion partitioning effect, which is accounted by the Born energy difference, modifies the distribution of mobile ions in the PEL and hence alters the particle electrophoresis. The combined effects of core hydrophobicity and the ion partitioning effect on the mobility are determined based on the Debye-Huckel approximation under a thin Debye layer assumption. An analytic expression for the electrophoretic mobility taking into account the core hydrophobicity and ion partitioning effect is obtained. The occurrence of zero mobility and reversal of mobility of the soft particle is illustrated.

Nonlinear electrophoresis of a charged polarizable liquid droplet

A numerical study on the electrophoresis of a liquid droplet in an aqueous medium is made by considering the full set of governing equations based on the conservation principle. The surface of the droplet is considered to be charged, and the liquid filling the droplet is nonconducting. The dielectric polarization of the nonconducting droplet is also addressed in the present study. The impact of the surface conduction, double layer polarization, and relaxation effects creates a retardation on the electrophoresis. The occurrence of slip velocity at the droplet surface creates the surface conduction important even at weak electric field and a thin Debye layer for which the double layer polarization and relaxation may become small. The role of the surface conduction, which is measured through the Dukhin number, on the electrophoretic propulsion of the droplet is analyzed. Our numerical solutions for low charge density and thinner Debye length agree well with the existing simplified model and asymptotic analysis. However, a large discrepancy in mobility from these existing results occurs when the droplet size is bigger or droplet viscosity is lower than the suspended liquid medium. The variation of the electrophoretic mobility of a perfectly dielectric droplet as a function of the droplet viscosity, droplet size, and other electrokinetic parameters is analyzed. The dielectric polarization of the droplet and its impact on the electrophoresis are considered in the present work. The drag and the strength of the internal circulation are obtained.

Electroosmotic flow around a dielectric uncharged particle by considering the dielectric decrement effects

We consider the electroosmotic flow (EOF) around a chemically inert uncharged dielectric particle under an applied electric field. In presence of an applied external electric field, a dielectric particle could be polarized to create an inhomogeneous ζ-potential. The electrolyte permittivity is considered to vary with the ionic concentration. The existing studies consider either a perfectly conducting particle or dielectric particles under a thin Debye layer assumption. In the present case, the induced EOF is not only influenced by the applied electric field but also with the dielectric permittivity constant of the particle and Debye length. We have analyzed the EOF without invoking a thin layer or weak applied field assumptions. The governing nonlinear electrokinetic equations are solved numerically. The close agreement of the present computed solutions with the existing asymptotic analysis for limiting cases such as thin Debye layer for a dielectric particle and a conducting particle is encouraging. The surface conductivity, measured by the Dukhin number, found to become larger as the particle dielectric permittivity grows. The Dukhin number has a nonlinear dependence on the applied electric field. The dielectric decrement effects on the EOF have been addressed in the present analysis. It creates a reduction in the EOF around the particle. Our results show that when the Debye length is on the order of the particle size, the dependence of EOF on the applied electric field varies with the dielectric permittivity constant of the particle. However, a quadratic dependence of EOF on the applied field strength occurs at a thin Debye layer. Reduction in the Debye length creates an enhanced induced EOF.

Electroosmotic flow in a slit nanochannel with superhydrophobic walls

Electroosmotic flow (EOF) in a slit channel with alternating charged patches of vanishing slip velocity and uncharged patches of vanishing shear stress is studied by numerically solving the coupled Poisson–Nernst–Planck Navier–Stokes system. It is taken into account that there may exist an arbitrary shift between the patterns at the top and the bottom wall. The studied system should mimic a slit nanochannel with superhydrophobic walls. The results are expressed in form of a flow enhancement factor E f, representing the average flow velocity through the channel divided by the average flow velocity through a channel with planar, unstructured walls of the same zeta potential. Extensive studies are carried out showing how E f varies with the system parameters. While it has been shown that under the assumption of thin-Debye layer values of E f close to 1 should be expected for EOF along a superhydrophobic surface, a substantial flow enhancement is found for the scenario studied here. For the range of parameters considered, a maximum flow enhancement factor of about 7 is obtained. The main mechanism responsible for this flow enhancement is the proximity of regions in which an electric body force exists to gas–liquid interface patches. For the latter, the shear stress is much reduced compared to liquid–solid interface patches, reducing the net friction coefficient of the electrically driven flow.

Numerical study of the influence of solid polarization on electrophoresis at finite Debye thickness.

The influence of solid polarization on the electrophoresis of a uniformly charged dielectric particle for finite values of the particle-to-fluid dielectric permittivity ratio is analyzed quantitatively without imposing the thin Debye length or weak-field assumption. Present analysis is based on the computation of the coupled Poisson-Nernst-Planck and Stokes equations in the fluid domain along with the Laplace equation within the solid. The electrophoretic velocity is determined through the balance of forces acting on the particle. The solid polarization of the charged particle produces a reduction on its electrophoretic velocity compared to a nonpolarizable particle of the same surface charge density. In accordance with the existing thin-layer analysis, our computed results for thin Debye layer shows that the solid polarization is important only when the applied electric field is strong. When the Debye length is in the order of the particle size, the electrophoretic velocity decreases with the rise of the particle permittivity and attains a saturation limit at large values of the permittivity. Our computed solution for electrophoretic velocity is in agreement with the existing asymptotic analyses based on a thin Debye layer for limiting cases.

Electrodiffusive model for neuronal and astrocytic ion concentration dynamics

Electrical signaling in neurons is typically modeled using the cable equation, where dendrites or axons are represented as one-dimensional electrical cables [1]. The cable model is based on the assumptions that the electrical currents along the cable are negligibly affected by (i) diffusion (due to ion concentration gradients), and (ii) variation in resistivities (due to varying ion concentrations). An electrodiffusive model, based on the Nernst-Planck equations, has been developed for situations when these assumptions do not hold [2]. Like the standard cable model, the electrodiffusive model assumes that transport phenomena are essentially one-dimensional. Unlike the standard cable model, the electrodiffusive model explicitly includes ion-concentration dynamics and its effect on diffusive currents and resistivities. A limitation with the model [2] is that it only considered intracellular dynamics, whereas extracellular conditions were assumed to be constant. The extracellular space (ECS) comprises only about 20% of the total tissue volume, whereas the remaining 80% is the intracellular space (ICS) of various cells. When groups of cells perform similar functions simultaneously, the impact on ionic concentrations may therefore be of the same order in the ICS and ECS. For instance, during periods of intense neural signaling, the extracellular K+-concentration may locally increase by several millimolars. Clearance of excess K+ likely depends partly on diffusion in the ECS, partly on local uptake via astrocytic K+-uptake mechanisms, and partly by intracellular transport within astrocytes [3]. To model such processes, we need an electrodiffusive formalism that includes both the ICS and ECS explicitly. Here, we derive a simple, general mathematical framework for modeling the dynamics of the membrane potential (vM) and the ion concentrations (ck) for a set (k) of ionic species in an intra- and extracellular domain. The formalism is based on the constraint of electroneutrality, except in the thin Debye-layers surrounding the capacitive membrane. Like the one-domain model [2], the formalism ensures (i) a consistent relationship between vM and ck, and (ii) accounts for diffusion and concentration dependent variations in resistivities. Unlike the one-domain model, the formalism ensures (iii) global particle/charge conservation, and (iv) that the charges on either side of a piece of membrane must be equal in magnitude and opposite in sign. The latter constraint is implicit when the membrane is assumed to be a parallel plate capacitor, an assumption made in most models of excitable cells (see e.g., (1-3, 16)). The formalism was implemented in a model of ionic exchange between astrocytes and the extracellular space. By simulations, we estimated the contribution of astrocytes in K+ removal from high concentration regions, and revealed a (to our knowledge) novel mechanism that astrocytes may utilize to remove K+ from extracellular high concentration regions.

Hydrodynamic flow in the vicinity of a nanopore induced by an applied voltage

Continuum simulation is employed to study ion transport and fluid flow through a nanopore in a solid-state membrane under an applied potential drop. The results show the existence of concentration polarization layers on the surfaces of the membrane. The nonuniformity of the ionic distribution gives rise to an electric pressure that drives vortical motion in the fluid. There is also a net hydrodynamic flow through the nanopore due to an asymmetry induced by the membrane surface charge. The qualitative behavior is similar to that observed in a previous study using molecular dynamic simulations. The current–voltage characteristics show some nonlinear features but are not greatly affected by the hydrodynamic flow in the parameter regime studied. In the limit of thin Debye layers, the electric resistance of the system can be characterized using an equivalent circuit with lumped parameters. Generation of vorticity can be understood qualitatively from elementary considerations of the Maxwell stresses. However, the flow strength is a strongly nonlinear function of the applied field. Combination of electrophoretic and hydrodynamic effects can lead to ion selectivity in terms of valences and this could have some practical applications in separations.

A numerical analysis of nanofluidic charge based separations using a combination of electrokinetic and hydrodynamic flows

In this article, the nanofluidic separation of non-neutral analytes using a pressure-gradient in combination with a counteracting electroosmotic flow field has been theoretically investigated. This approach takes advantage of simultaneous separation due to axial electrophoresis and solute interaction with the channel surface charges under optimal flow conditions to yield over an order of magnitude reduction in the separation length compared to that required in nanofluidic separations driven by pressure-gradients or electric-fields alone. Optimum results using this strategy are obtained under thin Debye layer and rapid transverse diffusion conditions which are both easy to realize in nanofluidic separation devices. The reported analyses further show that the separation strategy proposed here can allow the assay of charged species with a significantly greater resolving power than that possible using the capillary zone electrophoretic technique. Such an enhancement in resolving power has the potential to not only further miniaturize charge based separations but also permit their operation at reduced voltages. Interestingly, this improvement in the separation performance can be realized for analytes that differ in their electrophoretic mobilities over a wide range of values making this approach a valuable one for enhancing bioanalytical capabilities.

Dipolophoresis of dielectric spheroids under asymmetric fields

Non-spherical particles are common in colloidal science. Spheroidal shapes are particularly convenient for the analysis of the pertinent electrostatic and hydrodynamic problems and are thus widely used to model the manipulation of biological cells as well as deformed drops and bubbles. We study the rotary motion of a dielectric spheroidal micro-particle which is freely suspended in an unbounded electrolyte solution in the presence of a uniform applied electric field, assuming a thin Debye layer. For the common case of a uniform distribution of the native surface-charge density, the rotary motion of the particle is generated by the contributions of the induced-charge electro-osmotic (ICEO) slip and the dielectrophoresis associated with the distribution of the Maxwell stress, respectively. Series solutions are obtained by using spheroidal (prolate or oblate) coordinates. Explicit results are presented for the angular velocity of particles spanning the entire spectrum from rod-like to disk-like shapes. These results demonstrate the non-monotonic variation of the angular speed with the eccentricity of particle shape and the singularity of the multiple limits corresponding to conducting (ideally polarizable) particles of extreme eccentricity (e ≈ 1). The non-monotonic variation of the angular speed with the particle dielectric permittivity is related to the induced-charge contribution. We apply these results to describe the motion of particles subject to a uniform field rotating in the plane. For a sufficiently slow rotation rate, prolate particles eventually become “locked” to the external field with their stationary relative orientation in the plane of rotation being determined by the particle eccentricity and dielectric constant. This effect may be of potential use in the manipulation of poly-disperse suspensions of dielectric non-spherical particles. Oblate spheroids invariably approach a uniform orientation with their symmetry axes directed normal to the external-field plane of rotation.