Electrophoretic motion of a colloidal cylinder near a plane wall

An analytical study is presented for the electrophoretic motion of a circular cylindrical particle in an electrolyte solution with a transversely imposed electric field near a large plane wall parallel to its axis in the quasisteady limit. The electric double layers at the solid surfaces are assumed to be thin relative to the particle radius and to the particle–wall gap width, but the polarization effect of the diffuse ions in the double layer surrounding the particle is incorporated. The presence of the confining wall causes two basic effects on the particle velocity: first, the local ionic electrochemical potential gradients on the particle surface are altered by the wall, thereby affecting the motion of the particle; secondly, the wall enhances the viscous retardation of the moving particle. Through the use of cylindrical bipolar coordinates, the transport equations governing this problem are solved and the wall effects on the electrophoresis of the cylinder are determined for various cases. The presence of the plane wall prescribed with the ionic electrochemical potentials consistent with the far-field distributions reduces the electrophoretic mobility of the particle, which depends upon the properties of the particle–solution system, the relative particle–wall separation distance, and the direction of the applied electric field relative to the plane wall. The direction of the electrophoretic migration of a cylindrical particle near a plane wall is different from that of the prescribed electric field, except when it is oriented parallel or perpendicular to the wall. The effects of the plane wall on the electrophoresis of a cylinder are found to be much more significant than those for a sphere at the same separation.     

Electrophoresis of a colloidal sphere with double-layer polarization in a microtube

A theoretical study is presented for the electrophoretic motion of a spherical particle in an electrolyte solution along the axis of a circular microtube, whose wall may be either insulating or prescribed with the linear far-field electric potential distribution. The electric double layers adjoining the charged particle surface and tube wall are finitely thin, and the polarization of the diffuse layer at the particle surface is allowed. The general solutions to the electrostatic and hydrodynamic governing equations are constructed in combined cylindrical and spherical coordinates, and the boundary conditions are enforced on the tube wall by the Fourier transform and along the particle surface by a collocation method. The collocation results for the electrophoretic mobility of the confined particle, which agree well with the asymptotic formulas obtained by using a method of reflections, are obtained for various values of the particle, wall, and solution characteristics. An insulating tube wall and a tube wall with the far-field potential distribution affect the electrophoresis of the particle quite differently. Although the particle mobility in a tube with uncharged wall in general decreases with an increase in the particle-to-tube radius ratio a/b, it can increase with an increase in a/b as this ratio is close to unity for some cases because of the competition between the wall effects of hydrodynamic retardation and possible electrochemical enhancement on the particle migration. When the zeta potential of the tube wall is comparable to that of the particle, the electroosmotic flow of the bulk fluid induced by the tube wall dominates the electrokinetic migration of the particle.     

Eccentric electrophoretic motion of a sphere in circular cylindrical microchannels

The eccentric electrophoretic motion of a spherical particle in an aqueous electrolyte solution in circular cylindrical microchannels is studied in this paper. The objective is to investigate the influences of separation distance and channel size on particle motion. A theoretical model is developed to describe the electric field, the flow field and the particle motion. A finite element based direct numerical simulation method is employed to solve the model. Numerical results show that, when the particle is eccentrically positioned in the channel, the electric field and the flow field are not symmetric, and the strongest electric field and the highest flow velocity occur in the small gap region. It is shown that the rotational velocity of the particle increases with the decrease of the separation distance. With the decrease of the separation distance, the translational velocity increases in a smaller channel; while it decreases first and then increases in a relatively large channel. When a particle moves eccentrically at a smaller separation distance from the channel wall, both the translational velocity and the rotational velocity increase with the decrease of the channel size.     

Electrophoresis of a finite rod along the axis of a long cylindrical microchannel filled with Carreau fluids

The boundary effect on the electrophoretic behavior of a particle in a non-Newtonian fluid is studied by considering the electrophoresis of a finite rod along the axis of a cylindrical microchannel filled with shear-thinning Carreau fluids, which include both Newtonian and power-law fluids as special cases. Under the conditions of low surface potential and weak applied electric field, the influences of the radius of the microchannel, the aspect ratio of the rod, the thickness of double layer, and the nature of the Carreau fluid on the mobility of the rod are investigated. We show that due to the shear-thinning effect, the mobility of the rod in the present case can be significantly larger than that in the corresponding Newtonian case; the former is more sensitive to the variation in the thickness of double layer than the latter, and the difference between the two increases with decreasing thickness of double layer. The shear-thinning effect is important under the following conditions: the double layer is thin, the boundary effect is important, and/or the aspect ratio is large. We show that increasing the aspect ratio can either raise or lessen its mobility, which is not found previously, and can play an important role in electrophoresis measurement.     

Electrophoresis of a spherical particle in a spherical cavity

The electrophoretic motion of a charged spherical particle situated at an arbitrary position within a charged spherical cavity along the line connecting their centers is studied theoretically for the case of thin electric double layers. To solve the electrostatic and hydrodynamic governing equations, the general solutions are constructed using the two spherical coordinate systems based on the particle and cavity, and the boundary conditions are satisfied by a collocation technique. Numerical results for the electrophoretic velocity of the particle are presented for various values of the zeta potential ratio, radius ratio, and relative center-to-center distance between the particle and cavity. In the particular case of a concentric cavity, these results agree excellently with the available exact solution. The contributions from the electroosmotic flow occurring along the cavity wall and from the wall-corrected electrophoretic driving force to the particle velocity are equivalently important and can be superimposed due to the linearity of the problem. The normalized migration velocity of the particle decreases with increases in the particle-to-cavity radius ratio and its relative distance from the cavity center and increases with an increase in the cavity-to-particle zeta potential ratio. The boundary effects on the electrokinetic migration of the particle are significant and interesting.     

Motion of a rigid cylinder between parallel plates in stokes flow : Part 1: Motion in a quiescent fluid and sedimentation

A general numerical scheme for solution of two-dimensional Stokes equations in a multiconnected domain of arbitrary shape [1, 2] is applied to the motion of a rigid circular cylinder between plane parallel boundaries. Numerically generated boundary-conforming coordinates are used to transform the flow domain into a domain with rectilinear boundaries. The transformed Stokes equations in vorticity-stream function form are then solved on a uniform grid using an iterative algorithm. In Part I coefficients of the resistance matrix representing the forces and torque on the cylinder due to its translational motion parallel or perpendicular to the boundaries or due to rotation about its axis are calculated. The solutions are obtained for a wide range of particle radii and positions across the channel. It is found that the force on a particle translating parallel to the boundaries without rotation exhibits a minimum at a position between the channel centerline and the wall and a local maximum on the centerline.

The resistance matrix is utilized to calculate translational and angular velocities of a free particle settling under gravity in a vertical channel. It is found that the translational velocity has a maximum at some lateral position and a minimum on the centerline; the particle angular velocity is opposite in sign to that of a particle rolling along the nearer channel wall except when the gap between the particle and the wall is very small. These results are compared with existing analytical solutions for a small cylindrical particle situated on the channel centerline, and with solutions of related 3-D problems for a spherical particle in a circular tube and in a place channel. It is shown that the behavior of cylindrical and spherical particles in a channel in many cases is qualitatively different. This is attributed to different flow patterns in these two cases. The motion of a spherical particle in a circular tube has qualitative and quantitative features similar to those for a cylindrical particle in a plane channel.     

Broadening of neutral analyte band in electroosmotic flow through slit channel with different zeta potentials of the walls

The study is concerned with addressing hydrodynamic dispersion of an electroneutral non-adsorbed solute being transported by electroosmotic flow through a slit channel formed by walls with different zeta potentials. The analysis is conducted in terms of the plate height which, using the Van Deemter equation, can be expressed through the cross-sectional mean flow velocity, the solute molecular diffusion coefficient and a length scale parameter having meaning of the minimum achievable plate height and depending on the velocity distribution within the channel cross-section. The minimum plate height is determined by substituting distribution of electroosmotic velocity into the preliminary derived integral expression that is valid for any given velocity distribution within a slit channel cross-section. The electroosmotic velocity distribution within the slit channel cross-section is obtained by solving one-dimensional version of the Stokes equation accounting for electric force exerted on the local equilibrium electric space charge. The major obtained result is an analytical expression which represents the minimum plate height normalized by half of channel width as a function of two dimensionless parameters, namely, half of channel width normalized by the Debye length, and the ratio of the wall zeta potentials. The obtained result reveals a substantial increase in the minimum plate height compared with the case of equal wall zeta potentials. Different limiting cases of the obtained relationships are analyzed and possible applications are discussed.     

Electrophoresis and diffusiophoresis of a colloidal sphere with double-layer polarization in a concentric charged cavity

The electrophoretic and diffusiophoretic motions of a dielectric spherical particle situated at the center of a spherical cavity filled with an electrolyte solution are studied analytically. The applied electric field and electrolyte concentration gradient are uniform; the electric double layers at the particle surface and cavity wall are thin relative to the radius of the particle and distance between the solid surfaces, but the diffuse-layer polarization effect over the particle surface is considered. After solving the equations of conservation governing the systems, explicit formulas for the electrophoretic and diffusiophoretic velocities of the confined particle are obtained and their results relative to those of a particle under identical conditions in an unbounded solution are presented for various values of the radius ratio and zeta potential ratio between the particle and the cavity and of other parameters in the systems. The contributions from the electroosmotic and diffusioosmotic flows occurring along the cavity wall and from the wall-corrected electrophoretic and diffusiophoretic driving forces to the particle velocities are equivalently important and can be superimposed due to the linearity of the problems. The normalized migration velocities of the particle in general decrease with an increase in the particle-to-cavity radius ratio and increase with an increase in the cavity-to-particle zeta potential ratio. The effects of the charged cavity wall on the electrokinetic migrations of the particle are significant and can reverse their directions.     

Acoustic infinite elements for non-separable geometries

We present new infinite element formulations for solving acoustic scattering and radiation problems in the exterior of long, slender bodies. The new infinite elements are geometrically constructed from a prolate spheroid inscribed by the scatterer. These elements need not begin on a level surface of the prolate spheroidal coordinate system. Instead, they may be attached to any convex surface, including that of the scatterer itself. This scheme reduces, or even completely eliminates, finite element modeling of the exterior medium. The formulations may easily be extended to the cases of an interior oblate spheroid or ellipsoid. We present both conjugated and unconjugated formulations without any weighting factors, although it would be simple to include them. We describe a fast numerical scheme for computing the element integrals based on Chebychev approximation. We include numerical results for scattering from spheres and capped cylinders. These results demonstrate the accuracy and the dramatic reduction in computational expense of our new formulations compared to other coupled finite element/infinite element methods.     

Experimental characterization of electrical current leakage in poly(dimethylsiloxane) microfluidic devices

Poly(dimethylsiloxane) (PDMS) is usually considered as a dielectric material and the PDMS microchannel wall can be treated as an electrically insulated boundary in an applied electric field. However, in certain layouts of microfluidic networks, electrical leakage through the PDMS microfluidic channel walls may not be negligible, which must be carefully considered in the microfluidic circuit design. In this paper, we report on the experimental characterization of the electrical leakage current through PDMS microfluidic channel walls of different configurations. Our numerical and experimental studies indicate that for tens of microns thick PDMS channel walls, electrical leakage through the PDMS wall could significantly alter the electrical field in the main channel. We further show that we can use the electrical leakage through the PDMS microfluidic channel wall to control the electrolyte flow inside the microfluidic channel and manipulate the particle motion inside the microfluidic channel. More specifically, we can trap individual particles at different locations inside the microfluidic channel by balancing the electroosmotic flow and the electrophoretic migration of the particle.     

Hofmeister effect for electrokinetic transport at ordered DNA layers

Development of DNA nanotechnology provides the basis to construct novel biomimetic DNA nanochannels. In this work, we report electrokinetic transport behavior of the fluid through the surfaces consisting of double-stranded DNA molecules based on all-atom molecular dynamics simulations. The results show that an electric double layer forms close to the DNA surface, and the fluid can be driven by an externally applied electric field. At large DNA–DNA separation, a velocity jump is observed when the electric field is exerted along the direction of the central axis of DNA. Increasing the DNA separation does not influence the flow velocity in the model parameters investigated. It was also found that the magnitude of electroosmotic flow velocity obeys the Hofmeister series.     

Characterization of the electrophoretic mobility of gold nanoparticles with different sizes using the nanoporous alumina membrane system

This work presents a new analytical system to study the electrophoretic mobility of gold nanoparticles with different sizes, in which the platinum-coated alumina membranes are used as the separator due to the high pore densities, rigid support structure, chemical and thermal stability. It is shown that the electrophoretic mobility of gold nanoparticles is dependent on the nature of mobile phase and interfacial properties of alumina channels. The transport performance of nanoparticles are improved with the addition of sodium dodecyl sulfate (SDS) into the mobile phase, because SDS not only decreases the physical adsorption of gold nanoparticles on the nano-channel wall of alumina membrane, but also reduces the thickness of the electric double layer (decreasing the apparent size of particles). When the alumina membranes were modified with 6-aminohexanoic acid, it was further confirmed that the physical adsorption played a key role for the electrophoretic mobility of gold nanoparticles. Under optimized conditions, the mobility of gold nanoparticles had a fairly linear dependence on particle size (R² > 0.99), reiterating that our membrane system was also capable of characterizing gold nanoparticles in nanometer-size regimes.     

Diffusiophoresis of a charged particle in a charged cavity with arbitrary electric double layer thickness

An analysis is presented for the diffusiophoretic motion of a charged colloidal sphere located at the center of a charged spherical cavity filled with an electrolyte solution at the quasisteady state for the case of arbitrary electric double layers. The electrokinetic equations governing the ionic concentration, electric potential, and velocity distributions in the fluid are linearized with assumption that the system is slightly distorted from equilibrium. These linearized differential equations are solved using a perturbation method with the zeta potentials of the particle and cavity as the small perturbation parameters. An explicit formula for the diffusiophoretic velocity of the particle as a combination of the electrophoretic and chemiphoretic contributions valid for arbitrary values of \(\kappa a\) and \(a/b\) is obtained by balancing the electrostatic and hydrodynamic forces exerted on it, where \(\kappa\) is the Debye screening parameter, \(a\) is the radius of the particle, and \(b\) is the radius of the cavity. The effect of the charged cavity wall on the diffusiophoresis of the particle is interesting and can be significant. The contributions from the diffusioosmotic (electroosmotic and chemiosmotic) flow taking place along the cavity wall and from the wall-corrected diffusiophoretic force to the particle velocity are comparably important, and this diffusioosmotic flow can reverse the direction of diffusiophoresis. The particle velocity in general increases with an increase in \(\kappa a\) and decreases with an increase in \(a/b\), but exceptions exist.     

双电层对纳米流体润滑与摩擦影响的MD模拟 (2.东南大学MEMS教育部重点实验室 南京 210096）

采用分子动力学方法对带电和不带电两硅板之间的水分子润滑薄膜进行模拟研究,通过加双电层的水分子薄膜润滑与未加双电层薄膜润滑摩擦属性的对比,发现摩擦系数在存在双电层的情况下比未加双电层时要小,两板相对滑动速度对摩擦系数的影响与未加双电层时相似,相对滑动速度越大,摩擦系数在一定的速度范围内平稳增大.当速度大于某个数值时,摩擦系数增大变快.两板之间水分子以及离子密度或数目分布在靠近壁面的地方较大,中间密度相对较小.     

Geometrically induced stress singularities in a piezoelectric body of revolution

An eigenfunction expansion approach is combined with a power series solution technique to establish the asymptotic solutions for geometrically induced electroelastic singularities in a piezoelectric body of revolution, with its direction of polarization not parallel to the axis of revolution. The asymptotic solutions are obtained by directly solving the three-dimensional equilibrium and Maxwell’s equations in terms of displacement components and electric potential. When the direction of polarization is not along the axis of revolution, the assumption of axisymmetric deformation that is often made in the published literature is not valid, and the direction of polarization and the circular coordinate variable can substantially affect the singularities. The numerical results related to singularity orders are shown in graphical form for bodies of revolution that comprise a single material (PZT-4 or PZT-5H) or bonded piezo/piezo (PZT-4/PZT-5H) or piezo/isotropic elastic (PZT-4/Al or PZT-5H/Al) materials. This is the first study to present results for the direction of polarization not along the axis of revolution.     

New scheme of the Discrete Sources Method for investigation of a near field enhancement by coupled particles

Numerical scheme of the Discrete Sources Method has been modified to examine near fields for the polarized light scattering by two coupled noble metal particles. The new scheme enables to compute a near field enhancement of several orders with high accuracy degree. The developed computer model has been employed to investigate plasmonic resonance of two prolate spheroids. Both the electric field intensity between coupled particles and the Scattering Cross-Section have been examined versus particle distance and particles aspect ratio.     

Experimental study of the separation behavior of nanoparticles in micro- and nanochannels

In this article, we investigate the effects of pH, ionic strength, and channel height on the mobility and diffusivity of charged spherical particles within planar microfluidic channels. Specifically, we report results of a broad experimental study on the transport and separation behavior of 50 and 100 nm spherical carboxylated polystyrene nanoparticles, confined in 20 μm, 1 μm, and 250 nm deep fluidic channels. We find that pH, ionic strength, and channel height have coupled impacts on mobility changes. In particular, we show that, depending on pH, the dependence of particle mobility on channel size can have opposing behavior. In addition, we also show that at the nanoscale, at lower ionic strengths, there is a substantial increase in mobility, due to enhanced electric fields within the nanochannels. These effects are important to understand in order to avoid potential downfalls in terms of separation efficiency as well as design for better tuning of separation performance in micro- and nanochannels. Finally, we propose a method to estimate the effective zeta potential of spherical particles from measured electrophoretic mobility data. This could prove useful in characterizing a heterogeneous collection of particles having a distribution over a range of values of the zeta potential.     

Sequential Field-Flow Cell Separation Method in a Dielectrophoretic Chip With 3-D Electrodes

This paper presents a sequential dielectrophoretic field-flow separation method for particle populations using a chip with a 3-D electrode structure. A unique characteristic of our chip is that the walls of the microfluidic channels also constitute the device's electrodes. This property confers the opportunity to use the electrodes' shape to generate not only the electric field gradient required for dielectrophoretic force but also a fluid velocity gradient. This interesting combination gives rise to a new solution for the dielectrophoretic separation of two particle populations. The proposed sequential field-flow separation method consists of four steps. First, the microchannel is filled with the mixture of the two populations of particle. Second, the particle populations are trapped in different locations of the microfluidic channels. The population, which exhibits positive dielectrophoresis (DEP), is trapped in the area where the distance between the electrodes is the minimum, while the other population that exhibits negative DEP is trapped in locations of maximum distance between electrodes. In the next step, increasing the flow in the microchannels will result in an increased hydrodynamic force that sweeps the cell population trapped by positive DEP out of the chip. In the last step, the electric field is removed, and the second population is swept out and collected at the outlet. For theoretical and experimental exemplification of the separation method, a population of viable and nonviable yeast cells was considered.     

Numerical simulation of the whispering gallery modes in prolate spheroids

In this paper, we discuss the progress in the numerical simulation of the so-called ‘whispering gallery’ modes (WGMs) occurring inside a prolate spheroidal cavity. These modes are mainly concentrated in a narrow domain along the equatorial line of a spheroid and they are famous because of their extremely high quality factor. The scalar Helmholtz equation provides a sufficient accuracy for WGM simulation and (in a contrary to its vector version) is separable in spheroidal coordinates. However, the numerical simulation of ‘whispering gallery’ phenomena is not straightforward. The separation of variables yields two spheroidal wave ordinary differential equations (ODEs), first only depending on the angular, second on the radial coordinate. Though separated, these equations remain coupled through the separation constant and the eigenfrequency, so that together with the boundary conditions they form a singular self-adjoint two-parameter Sturm–Liouville problem.     

Ghost-cell method for analysis of inviscid three-dimensional flows on Cartesian-grids

The present paper deals with the implementation of non-penetration boundary conditions at solid walls for three-dimensional inviscid flow computations on Cartesian grids. The crux of the method is the curvature-corrected symmetry technique (CCST) developed by the present authors for body-fitted grids. The method introduces ghost cells near the boundaries whose values are developed from an assumed flow-field model in vicinity of the wall consisting of a vortex flow, with locally symmetric distribution of entropy and total enthalpy. In three dimensions this procedure is implemented in the so-called “osculating plane”. This method was shown to be substantially more accurate than traditional surface boundary condition approaches. This improved boundary condition is adapted to a Cartesian mesh formulation, which we have termed the “ghost-cell method”. In this approach, all cell centers exterior to the body are computed with fluxes at the six surrounding cell faces, without any cut cell. A multiple-valued point technique is used to compute sharp edges. The merits of the ghost-cell method for three-dimensional inviscid flow computations are established by computing compressible and transonic flows about a sphere, an oblate and a prolate spheroid, a cylindrical wing with an end-plate, the ONERA M6 wing and detailed comparison to body-fitted grid computations and to published data. The computed results show the surface non-penetration condition to be satisfied in the limit of vanishing cell size and the method to be second-order accurate in space. The comparison with body-fitted results proves that the accuracy is comparable to the accuracy of CCST computations on body-fitted grids and remarkably superior to body-fitted computations based on traditional pressure extrapolation, non-penetration boundary conditions. In addition, we prove that the results are independent of the position of the body with respect to the grid. Finally, we show that the ONERA M6 wing results compare very well with published data.