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.     

Electrophoresis of an axisymmetric particle along its axis of revolution perpendicular to two parallel plane walls

The axisymmetric electrophoretic motion of a dielectric particle of revolution situated at an arbitrary position in a slit microchannel is studied theoretically at the quasisteady state. The applied electric field is uniform, along the axis of symmetry of the particle, and perpendicular to the two plane walls of the slit. The electric double layer at the particle surface is assumed to be thin relative to the particle size and to the particle–wall gap widths. A method of distribution of a set of spherical singularities along the axis of symmetry within a prolate particle or on the fundamental plane within an oblate particle is used to find the general solutions for the electric potential distribution and fluid velocity field. The apparent slip condition on the particle surface is satisfied by applying a boundary collocation technique to these general solutions. Numerical results for the electrophoretic velocity of a prolate or oblate spheroid along its axis of revolution and perpendicular to two plane walls are obtained with good convergence behavior for various cases. The effect of the confining walls is to reduce the velocity of the particle, irrespective of its aspect ratio or the relative particle–wall separation distances. For fixed separation parameters, the normalized velocity of the spheroid decreases with a decrease in its axial-to-radial aspect ratio, and the boundary effect on electrophoresis of an oblate spheroid can be very significant. When a spheroid with a specified aspect ratio is located near a first plane wall, the approach of a second wall far from the particle can first increase the electrophoretic mobility to a maximum, then reduce this mobility when the second wall is close to the particle, and finally lead to a minimum mobility when it reaches to the same distance from the particle as the first wall. For a given separation between the two plane walls relative to the axial size of the spheroid, the electrophoretic mobility has a maximum when the spheroid is located midway between the walls and decreases as it approaches either of the walls.     

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.     

Particle flow control by induced dipolar interaction of superparamagnetic microbeads

Magnetic particles diluted in liquid agglomerate in rod-like particle arrays if an external homogeneous magnetic field is applied. This work introduces a method to specifically exploit particle–particle interaction to obtain flow control of magnetic particles without changing the motion state of the carrier liquid. Experiments show the possibility to uncouple the particle flux from the motion state of liquid. We show how this method may be applied to design a microfluidic geometry in which the particle flow in a specific direction is either enabled or suppressed by the relative orientation of the fluid velocity and the external field.     

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.     

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.     

Equilibrium molecular dynamics studies on nanoscale-confined fluids

Fluid behavior within nanoscale confinements is studied for argon in dilute gas, dense gas, and liquid states. Molecular dynamics simulations are used to resolve the density and stress variations within the static fluid. Normal stress calculations are based on the Irving–Kirkwood method, which divides the stress tensor into its kinetic and virial parts. The kinetic component recovers pressure based on the ideal-gas law. The particle–particle virial increases with increased density, whereas the surface–particle virial develops because of the surface-force field effects. Normal stresses within nanoscale confinements show anisotropy primarily induced by the surface-force field and local variations in the fluid density near the surfaces. For dilute and dense gas cases, surface-force field that extends typically 1 nm from each wall induces anisotropic normal stress. For liquid case, this effect is further amplified by the density fluctuations that extend beyond the force field penetration region. Outside the wall-force field penetration and density fluctuation regions, the normal stress becomes isotropic and recovers the thermodynamic pressure, provided that sufficiently large force cut-off distances are used in the computations.     

Slow viscous flow around two particles in a cylinder

This article describes the motion of two arbitrarily located free moving particles in a cylindrical tube with background Poiseuille flow at low Reynolds number. We employ the Lamb’s general solution based on spherical harmonics and construct a framework based on cylindrical harmonics to solve the flow field around the particles and the flow within the tube, respectively. The two solutions are performed in an iterated framework using the method of reflections. We compute the drag force and torque coefficients of the particles which are dependent on the distances among the cylinder wall and the two particles. In addition, we provide detailed flow field in the vicinity of the two particles including streamlines and velocity contour. Our analysis reveals that the particle–particle interaction can be neglected when the separation distance is three times larger than the sum of particles radii when the two particles are identical. Furthermore, the direction of Poiseuille flow, the particle position relative to the axis and the particle size can make the two particles attract or repel. Unlike the single particle case, the two particles can move laterally due to the hydrodynamic interaction. Such analysis can give insights to understand the mechanisms of collision and aggregation of particles in microchannels.     

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.     

Modeling and experimental characterization of peak tailing in DNA gel electrophoresis

Capillary electrophoresis (CE) is an efficient separation method in analytical chemistry. It exploits the difference in electrophoretic migration velocities between charged molecular species in aqueous or diluted polymer solution when an external electric field is applied to achieve separation. Despite the standard assumption that electrophoretic data obtained from pulse-loaded molecular species should have Gaussian peak shapes, experimentally observed peaks are frequently distorted or highly asymmetric. Interaction of charged species with the wall of the capillary is the primary source for serious band broadening and peak tailing. This paper reports a mathematical model for the peak profiles in capillary electrophoresis, taking adsorption on capillary wall into account. The model is based on the advection–diffusion equation, Langmuir second order kinetic equation and appropriate boundary conditions. It is applied to simulate the gel electrophoretic separation of the 11 fragment Φ X174-Hae III double stranded DNA ladders in a polymeric microchip. By using the migration velocities and diffusivities from the measurement, and properly selecting two fitting parameters, namely adsorption and desorption coefficients, the simulated peak shapes show remarkable similarity with the experimental electrophoretic results. The effect of adsorption and desorption coefficients are also investigated and the result shows that adsorption of analytes from the main analyte zone and desorption of these analytes appear to be the reasons of peak tailing, with the latter being the major cause.     

Motion of a rigid cylinder between parallel plates in stokes flow : Part 2: Poiseuille and couette flow

A numerical solution is presented for the motion of a neutrally buoyant circular cylinder in Poiseuille and Couette flows between two plane parallel boundaries. The force and torque on a stationary particle are calculated for a wide range of particle sizes and poisitions across the channel. The resistance matrix calculated in Ref. [1] (henceforth referred to as Part 1) is utilized to find the translational and angular velocity for a drag- and torque-free particle. The results are compared with analytical perturbation solutions for a small cylindrical particle situated on the channel centerline, and for the motion of a spherical particle in a circular tube or between plane parallel boundaries. It is found the behavior of flow around a cylindrical particle in a channel is qualitatively similar to the behavior of flow around a spherical particle in a tube, while the flow around a spherical particle in a channel frequently exhibits different trends from the above two cases.     

Reachability and controllability of a particle in a dielectrophoretic system

A dielectrophoretic (DEP) force is a result of the interaction between a nonuniform electric field and a polarizable particle. As the electric field is dominant at the micro/nano scale, this force can be effectively used to manipulate and control particles on this scale. We consider the motion of a particle on an invariant line with the suspending medium being a fluid with a low Reynolds number. This DEP system has two states and two parameters: the two states are indicative of the particle’s position and the induced dipole moment and the two parameters are α and c which depend upon the electric properties of the particle and the medium. The system is described by a set of ordinary differential equations with a quadratic term in the control variable (control being the applied voltage on the electrodes which induces the electric field) making the system non-affine in control. In the existing literature, the controllability studies of the DEP system have been restricted to reachability issues in the context of the time-optimal control problem. Here we present a comprehensive study of reachability, accessibility and controllability.     

Numerical analysis on electroosmotic flows in a microchannel with rectangle-waved surface roughness using the Poisson–Nernst–Planck model

The present study has numerically investigated two-dimensional electroosmotic flows in a microchannel with dielectric walls of rectangle-waved surface roughness to understand the roughness effect. For the study, numerical simulations are performed by employing the Nernst–Planck equation for the ionic species and the Poisson equation for the electric potential, together with the traditional Navier–Stokes equation. Results show that the steady electroosmotic flow and ionic-species transport in a microscale channel are well predicted by the Poisson–Nernst–Planck model and depend significantly on the shape of surface roughness such as the amplitude and periodic length of wall wave. It is found that the fluid flows along the surface of waved wall without involving any flow separation because of the very strong normal component of EDL (electric double layer) electric field. The flow rate decreases exponentially with the amplitude of wall wave, whereas it increases linearly with the periodic length. It is mainly due to the fact that the external electric-potential distribution plays a crucial role in driving the electroosmotic flow through a microscale channel with surface roughness. Finally, the present results using the Poisson–Nernst–Planck model are compared with those using the traditional Poisson–Boltzmann model which may be valid in these scales.     

A comparative study on particle�Cfluid interactions in micro and nanofluids of aluminium oxide

Stable dispersions of micro and nanosized Al₂O₃ particles in ethylene glycol are prepared with the aid of sonication. The temperature dependant acoustic properties such as ultrasonic velocity, adiabatic compressibility, attenuation and acoustic impedance are studied and reported in this paper. In microfluids the particle–fluid interaction is observed to decrease with increase of concentration of particles whereas in nanofluids it is observed to increase up to the critical concentration (0.6 Wt%) and above which the particle–particle interaction dominates due to agglomeration of particles. A range of concentration with significant particle–fluid interaction is identified for effective nanofluid applications.     

Electrophoretic motion of two spherical particles in a rectangular microchannel

The electrophoretic motion of two spherical particles in an aqueous electrolyte solution in a small rectangular microchannel was studied in this paper. A theoretical model was developed to describe the electric field, the flow field, and the particle motion. A direct numerical simulation method using the finite element method is employed to solve the model. The simulation results clearly show how the presence of one particle influences the electric field, the flow field, and the motion of the adjacent particle. Such an influence weakens with the separation distance. In addition to the zeta potentials, the particles motion depends on their sizes: the smaller particle moves slightly faster. For a faster particle moving from behind of a slower particle, the simulation results show that the faster particle will climb and then pass the slower particle when the two particles centers are not located on the same line parallel to the applied electric field.     

Diffusioosmosis of electrolyte solutions in fibrous porous media

An analytical study is presented for the diffusioosmotic flow of an electrolyte solution in the fibrous medium constructed by an ordered array of parallel charged circular cylinders at the steady state. The prescribed electrolyte concentration gradient is constant but can be oriented arbitrarily with respect to the axes of the cylinders. The electric double layer surrounding each cylinder may have an arbitrary thickness relative to the radius of the cylinder. A unit cell model which allows for the overlap of the double layers of adjacent cylinders is employed to account for the effect of fibers on each other. The electrostatic potential distribution in the fluid phase of a cell is obtained by solving the linearized Poisson–Boltzmann equation, which applies to the case of low surface potential of the cylinders. The macroscopic electric field induced by the imposed electrolyte concentration gradient through the fluid phase in a cell is determined as a function of the radial position. A closed-form formula for the fluid velocity profile of the electrolyte solution due to the combination of electroosmotic and chemiosmotic contributions as a function of the porosity of the array of cylinders correct to the second order of their surface charge density or zeta potential is derived as the solution of a modified Navier–Stokes equation. The diffusioosmotic velocity can have more than one reversal in direction over a small range of the zeta potential. For a given electrolyte concentration gradient in a cell, the fluid flow rate does not necessarily increase with an increase in the electrokinetic radius of the cylinder, which is the cylinder radius divided by the Debye screening length. The effect of the radial distribution of the induced axial electric field in the double layer on the diffusioosmotic flow is found to be of dominant significance in most practical situations.     

Cell separation in a microfluidic channel using magnetic microspheres

Magnetophoretic isolation of biological cells in a microfluidic environment has strong relevance in biomedicine and biotechnology. A numerical analysis of magnetophoretic cell separation using magnetic microspheres in a straight and a T-shaped microfluidic channel under the influence of a line dipole is presented. The effect of coupled particle–fluid interactions on the fluid flow and particle trajectories are investigated under different particle loading and dipole strengths. Microchannel flow and particle trajectories are simulated for different values of dipole strength and position, particle diameter and magnetic susceptibility, fluid viscosity and flow velocity in both the microchannel configurations. Residence times of the captured particles within the channel are also computed. The capture efficiency is found to be a function of two nondimensional parameters, α and β. The first parameter denotes the ratio of magnetic to viscous forces, while the second one represents the ratio of channel height to the distance of the dipole from the channel wall. Two additional nondimensional parameters γ (representing the inverse of normalized offset distance of the dipole from the line of symmetry) and σ (representing the inverse of normalized width of the outlet limbs) are found to influence the capture efficiency in the T-channel. Results of this investigation can be applied for the selection of a wide range of operating and design parameters for practical microfluidic cell separators.     

Experiments on opto-electrically generated microfluidic vortices

Strong microfluidic vortices are generated when a near-infrared (1,064 nm) laser beam is focused within a microchannel and an alternating current (AC) electric field is simultaneously applied. The electric field is generated from a parallel-plate, indium tin oxide (ITO) electrodes separated by 50 μm. We present the first μ-PIV analysis of the flow structure of such vortices. The vortices exhibit a sink-type behavior in the plane normal to the electric field and the flow speeds are characterized as a function of the electric field strength and biasing AC signal frequency. At a constant AC frequency of 100 kHz, the fluid velocity increases as the square of the electric field strength. At constant electric field strength fluid velocity does not change appreciably in the 30–50 kHz range and it decreases at larger frequencies (>1 MHz) until at approximately 5 MHz when Brownian motion dominates the movement of the 300 nm μ-PIV tracer particles. Presence of strongly focused laser beams in an interdigitated-electrode configuration can also lead to strong microfluidic vortices. When the center of the illumination is focused in the middle of an electrode strip, particles experiencing negative dielectrophoresis are carried towards the illumination and aggregate in this area.     

Electrokinetically driven concentration of particles and cells by dielectrophoresis with DC-offset AC electric field

Insulator-based dielectrophoresis (iDEP) has been successfully used for on-chip manipulations of biological samples. Despite its effectiveness, iDEP typically requires high DC voltages to achieve sufficient electric field; this is mainly due to the coupled phenomena among linear electrokinetics: electroosmosis (EO) and electrophoresis (EP) and nonlinear electrokinetics: dielectrophoresis (DEP). This paper presents a microfluidic technique using DC-offset AC electric field for electrokinetic concentration of particles and cells by repulsive iDEP. This technique introduces AC electric field for producing iDEP which is decoupled from electroosmosis (EO) and electrophoresis (EP). The repulsive iDEP is generated in a PDMS tapered contraction channel that induces non-uniform electric field. The benefits of introducing AC electric field component are threefold: (i) it contributes to DEP force acting on particles, (ii) it suppresses EO flow and (iii) it does not cause any EP motion. As a result, the required DC field component that is mainly used to transport particles on the basis of EO and EP can be significantly reduced. Experimental results supported by numerical simulations showed that the total DC-offset AC electric field strength required to concentrate 15-μm particles is significantly reduced up to 85.9% as compared to using sole DC electric field. Parametric experimental studies showed that the higher buffer concentration, larger particle size and higher ratio of AC-to-DC electric field are favorable for particle concentration. In addition, the proposed technique was demonstrated for concentration of yeast cells.     

AC electroosmotic flow in a DNA concentrator

Experimental velocity measurements are conducted in an AC electrokinetic DNA concentrator. The DNA concentrator is based upon Wong et al. (Transducers 2003, Boston, pp 20–23, 2003a; Anal Chem 76(23):6908–6914, 2004)and consists of two concentric electrodes that generate AC electroosmotic flow to stir the fluid, and dielectrophoretic and electrophoretic force fields that trap DNA near the centre of the inside electrode. A two-colour micro-PIV technique is used to measure the fluid velocity without a priori knowledge of the electric field in the device or the electrical properties of the particles. The device is also simulated computationally. The results indicate that the numerical simulations agree with experimental data in predicting the velocity field structure, except that the velocity scale is an order of magnitude higher for the simulations. Simulation of the dielectrophoretic forces allows the motion of the DNA within the device to be studied. It is suggested that the simulations can be used to study the phenomena occurring in the device, but that experimental data is required to determine the practical conditions under which these phenomena occur.