Particle separation in alternating-current electro-osmotic micropumps using field-flow fractionation

This work presents a novel method for continuous particle separation on the microscale by means of field-flow fractionation. It is based on the use of asymmetric interdigitated electrode arrays on the channel bottom, which induce an electro-osmotic channel flow when driven harmonically. Suspended particles are influenced by viscous fluid drag, sedimentation as well as by dielectrophoretic repulsion forces from the driving electrodes due to the emerging electric field. The significant dependance of the present forces on particle properties allows for separation with respect to particle density and size. This work analyzes electric and flow field by means of the finite element method and investigates the size and density dependent particle motion as a function of driving voltage and frequency of the electrode array. Matching these driving parameters permits the separation of sedimenting particles by their density independently from their size as well as the separation by size. Finally, channel designs are proposed which enable standard separation by means of selective particle mobility in the channel, separation in terms of opposing motion directions, as well as continuous lateral separation.     

Rotational motion and lateral migration of an elliptical magnetic particle in a microchannel under a uniform magnetic field

We have numerically investigated the motion of an elliptical magnetic particle in a microfluidic channel subjected to an external uniform magnetic field. By using the direct numerical simulation method and an arbitrary Lagrangian–Eulerian technique, the involved particle–fluid-magnetic field problem can be solved in a fully coupled manner. The numerical predictions of the particle trajectory and orientation with and without a uniform magnetic field are in qualitative agreement with the existing experimental results, and numerical results have revealed the impacts of key parameters such as inlet flow velocity, magnetic field direction, and particle shape on the rotational motion and lateral migration of the elliptical particle. Meanwhile, the shape-based particle separation in a low Reynolds number flow with the aid of an applied uniform magnetic field has also been numerically demonstrated.     

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.     

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.     

Assessment of cross-type optical particle separation system

This paper describes the optical and hydrodynamic characteristics of particle motion in a cross-type optical particle separator. The retention distance modulated by the optical force on a particle was measured in three dimensions for various vertical and horizontal positions via ??-defocusing digital particle image velocimetry. The experimental data showed that the actual retention distance was smaller than the predicted retention distance under the assumption that the approaching velocity was constant through the cross-section of a microfluidic channel. The retention distance was shown to increase as the injection position of the particle shifted toward the channel side wall at a given vertical position due to a higher residence time within the region of influence of the laser beam. In contrast, the retention distance decreased as the injection position shifted toward the channel top/bottom walls at a given horizontal position. A theoretical modeling study was conducted to support and interpret the experimental measurements. The resolution of the particle separation procedure, which did not require adjusting the flow rate, laser power, or working fluid properties, was studied.     

Numerical study on the cell motility interacting with the chemical flow in microchannels

Beneficial to the steady control of flow properties and concentration gradient profiles, quantification of cell chemotaxis based on microfluidic devices could achieve on the scale of a single cell. However, normal experimental studies assumed that the concentration field was not affected by the existing cell or by the impact of the cell motion. The present paper systematically simulated the interactions of the cell translational and rotational movements with its chemical gradient flow by both 2D and 3D models. The influences of the chemical flow Peclet number, cell’s translational velocity, cell’s rotational velocity and direction on the sensed chemical gradient were investigated. Results showed that both the cell’s translational and rotational movements disturbed its surrounding chemical distribution and affect chemotactic speed and direction later on. Rotating cell brings in flow circulation with it, and consequently the sensed chemical gradient dramatically deviates from the original direction. The cell’s two contrary rotational directions lead to contrary results. 2D model with circular cell is practically feasible due to simplicity, while 3D model with spherical cell is closer to reality. Numerical comparison showed that the 2D model can be used to analyze the cell’s chemotactic tendency, but it also amplifies the cell’s perturbation and then separation to its surrounding chemical flow. Finally, a single cell’s interactive chemotaxis in a micro chamber was simulated based on experimental measured chemotactic coefficient. The interactive chemotactic cell kept moving slightly upstream instead of upright crossing the interface. This work may contribute to the development of chemotactic measurement method and precise evaluation on the cell’s chemotactic sensitivity.     

Viscosity-difference-induced asymmetric selective focusing for large stroke particle separation

We developed a new approach for particle separation by introducing viscosity difference of the sheath flows to form an asymmetric focusing of sample particle flow. This approach relies on the high-velocity gradient in the asymmetric focusing of the particle flow to generate a lift force, which plays a dominated role in the particle separation. The larger particles migrate away from the original streamline to the side of the higher relative velocity, while the smaller particles remain close to the streamline. Under high-viscosity (glycerol–water solution) and low-viscosity (PBS) sheath flows, a significant large stroke separation between the smaller (1.0 μm) and larger (9.9 μm) particles was achieved in a sample microfluidic device. We demonstrate that the flow rate and the viscosity difference of the sheath flows have an impact on the interval distance of the particle separation that affects the collected purity and on the focusing distribution of the smaller particles that affects the collected concentration. The interval distance of 293 μm (relative to the channel width: 0.281) and the focusing distribution of 112 μm (relative to the channel width: 0.107) were obtained in the 1042-μm-width separation area of the device. This separation method proposed in our work can potentially be applied to biological and medical applications due to the wide interval distance and the narrow focusing distribution of the particle separation, by easy manufacturing in a simple device.     

Numerical simulations of particle migration in a viscoelastic fluid subjected to Poiseuille flow

In this work we present 2D numerical simulations on the migration of a particle suspended in a viscoelastic fluid under Poiseuille flow. A Giesekus model is chosen as constitutive equation of the suspending liquid. In order to study the sole effect of the fluid viscoelasticity, both fluid and particle inertia are neglected.The governing equations are solved through the finite element method with proper stabilization techniques to get convergent solutions at relatively large flow rates. An Arbitrary Lagrangian–Eulerian (ALE) formulation is adopted to manage the particle motion. The mesh grid is moved along the flow so as to limit particle motion only in the gradient direction to substantially reduce mesh distortion and remeshing.Viscoelasticity of the suspending fluid induces particle cross-streamline migration. Both large Deborah number and shear thinning speed up the migration velocity. When the particle is small compared to the gap (small confinement), the particle migrates towards the channel centerline or the wall depending on its initial position. Above a critical confinement (large particles), the channel centerline is no longer attracting, and the particle is predicted to migrate towards the closest wall when its initial position is not on the channel centerline. As the particle approaches the wall, the translational velocity in the flow direction is found to become equal to the linear velocity corresponding to the rolling motion over the wall without slip.     

Egomotion analysis based on the Frenet-Serret motion model

In this paper we propose a new model,Frenet-Serret motion, for the motion of an observer in a stationary environment. This model relates the motion parameters of the observer to the curvature and torsion of the path along which the observer moves. Screw-motion equations for Frenet-Serret motion are derived and employed for geometrical analysis of the motion. Normal flow is used to derive constraints on the rotational and translational velocity of the observer and to compute egomotion by intersecting these constraints in the manner proposed in (Duri and Aloimonos 1991) The accuracy of egomotion estimation is analyzed for different combinations of observer motion and feature distance. We explain the advantages of controlling feature distance to analyze egomotion and derive the constraints on depth which make either rotation or translation dominant in the perceived normal flow field. The results of experiments on real image sequences are presented.The support of the Air Force Office of Scientific Research under Grant F49620-93-1-0039 is gratefully acknowledged.     

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.     

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.     

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.     

Numerical investigation of erosion threshold velocity in a pipe with sudden contraction

This paper deals with erosion prediction in a pipe with sudden contraction for the special case of two-phase (liquid and solid) turbulent flow with low particle concentration. The pipe axis was considered vertical and the flow was either in direction of gravity (downflow) or against it (upflow). The mathematical models for the calculations of the fluid velocity field and the motion of the solid particles have been established and an erosion model was used to predict the erosion rate. The fluid velocity (continuous phase) model was based on the time-averaged governing equations of 3-D turbulent flow and the particle-tracking model (discrete phase) was based on the solution of the governing equation of each particle motion taking into consideration the effect of particle rebound behavior. The effects of flow velocity and particle size were investigated for one contraction geometry considering water flow in a steel pipe. The results showed the strong dependence of erosion on both particle size and flow velocity but with little dependence on the direction of flow. The effect of flow direction was found to be significant only for large particle size and moderate flow velocity. The erosion critical area was found to be the inner surface of the tube sheet (connecting the two pipes) in the region close to the small pipe. The results also indicated the presence of a threshold velocity below which erosion is insignificant for all particle sizes.     

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.     

Continuous-flow particle and cell separations in a serpentine microchannel via curvature-induced dielectrophoresis

Particle and cell separations are critical to chemical and biomedical analyses. This study demonstrates a continuous-flow electrokinetic separation of particles and cells in a serpentine microchannel through curvature-induced dielectrophoresis. The separation arises from the particle size-dependent cross-stream dielectrophoretic deflection that is generated by the inherent electric field gradients within channel turns. Through the use of a sheath flow to focus the particle mixture, we implement a continuous separation of 1 and 5 μm polystyrene particles in a serpentine microchannel under a 15 kV/m DC electric field. The effects of the applied DC voltages and the serpentine length on the separation performance are examined. The same channel is also demonstrated to separate yeast cells (range in diameter between 4 and 8 μm) from 3 μm particles under an electric field as low as 10 kV/m. The observed focusing and separation processes for particles and cells in the serpentine microchannel are reasonably predicted by a numerical model.     

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.     

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.     

Analytical model of microfluidic transport of non-magnetic particles in ferrofluids under the influence of a permanent magnet

This study describes an analytical model and experimental verifications of transport of non-magnetic spherical microparticles in ferrofluids in a microfluidic system that consists of a microchannel and a permanent magnet. The permanent magnet produces a spatially non-uniform magnetic field that gives rise to a magnetic buoyancy force on particles within ferrofluid-filled microchannel. We obtained trajectories of particles in the microchannel by (1) calculating magnetic buoyancy force through the use of an analytical expression of magnetic field distributions and a nonlinear magnetization model of ferrofluids, (2) deriving governing equations of motion for particles through the use of analytical expressions of dominant magnetic buoyancy and hydrodynamic viscous drag forces, (3) solving equations of motion for particles in laminar flow conditions. We studied effects of particle size and flow rate in the microchannel on the trajectories of particles. The analysis indicated that particles were increasingly deflected in the direction that was perpendicular to the flow when size of particles increased, or when flow rate in the microchannel decreased. We also studied ??wall effect?? on the trajectories of particles in the microchannel when surfaces of particles were in contact with channel wall. Experimentally obtained trajectories of particles were used to confirm the validity of our analytical results. We believe this study forms the theoretical foundation for size-based particle (both synthetic and biological) separation in ferrofluids in a microfluidic device. The simplicity and versatility of our analytical model make it useful for quick optimizations of future separation devices as the model takes into account important design parameters including particle size, property of ferrofluids, magnetic field distribution, dimension of microchannel, and fluid flow rate.     

On-demand particle enrichment in a microfluidic channel by a locally controlled floating electrode

A flexible strategy for the on-demand control of the particle enrichment and positioning in a microfluidic channel is proposed and demonstrated by the use of a locally controlled floating metal electrode attached to the channel bottom wall. The channel is subjected to an axially acting global DC electric field, but the degree of charge polarization of the floating electrode is governed largely by a local control of the voltage applied to two micron-sized control electrodes (CEs) on either side of the floating electrode (FE). This strategy allows an independent tuning of the electrokinetic phenomena engendered by the floating electrode regardless of the global electric field across the channel, thus making the method for particle manipulation far more versatile and flexible. In contrast to a dielectric microchannel wall possessing a nearly uniform surface charge (or zeta potential), the patterned metal strip (floating electrode) is polarized under electric field resulting in a non-uniform distribution of the induced surface charge with a zero net surface charge, and accordingly induced-charge electro-osmotic (ICEO) flow. The ICEO flow can be regulated by the control electric field through tuning the magnitude and polarity of the voltage applied to the CEs, which in turn affects both the hydrodynamic field as well as the particle motion. By controlling the control electric field, on-demand control of the particle enrichment and its position inside a microfluidic channel has been experimentally demonstrated.     

Electrokinetic motion of single nanoparticles in single PDMS nanochannels

Electrokinetic motion of single nanoparticles in single nanochannels was studied systematically by image tracking method. A novel method to fabricate PDMS-glass micro/nanochannel chips with single nanochannels was presented. The effects of ionic concentration of the buffer solution, particle-to-channel size ratio and electric field on the electrokinetic velocity of fluorescent nanoparticles were studied. The experimental results show that the apparent velocity of nanoparticles in single nanochannels increases with the ionic concentration when the ionic concentration is low and decreases with the ionic concentration when the concentration is high. The apparent velocity decreases with the particle-to-channel size ratio (a/b). Under the condition of low electric fields, nanoparticles can hardly move in single nanochannels with a large particle-to-channel size ratio. Generally, the apparent velocity increases with the applied electric field linearly. The experimental study presented in this article is valuable for future research and applications of transport and manipulation of nanoparticles in nanofluidic devices, such as separation of charged nanoparticles and DNA molecules.