Deviation from the classical colloid filtration theory in the presence of repulsive DLVO interactions

A growing body of experimental evidence suggests that the deposition behavior of microbial particles (e.g., bacteria and viruses) is inconsistent with the classical colloid filtration theory (CFT). Well-controlled laboratory-scale column deposition experiments were conducted with uniform model particles and collectors to obtain insight into the mechanisms that give rise to the diverging deposition behavior of microorganisms. Both the fluid-phase effluent particle concentration and the profile of retained particles were systematically measured over a broad range of physicochemical conditions. The results indicate that, in the presence of repulsive Derjaguin-Landau-Verwey-Overbeek (DLVO) interactions, the concurrent existence of both favorable and unfavorable colloidal interactions causes significant deviation from the CFT. A dual deposition mode model is presented which considers the combined influence of "fast" and "slow" particle deposition. This model is shown to adequately describe both the spatial distribution of particles in the packed bed and the suspended particle concentration at the column effluent.     

Particle deposition onto micropatterned charge heterogeneous substrates: trajectory analysis

A trajectory analysis of particles near a micropatterned charged substrate under radial impinging jet flow conditions is presented to investigate the effect of surface charge heterogeneity on particle trajectory and deposition efficiency. The surface charge heterogeneity is modeled as concentric bands of specified width and pitch having positive and negative surface potentials. The flow distribution is obtained using finite element analysis of the governing Navier-Stokes equations. The particle trajectory analysis takes into consideration the hydrodynamic interactions, gravity, van der Waals and electrostatic double layer interactions. The presence of surface charge heterogeneity on the substrate gives rise to an oscillating particle trajectory near the collector surface due to repulsive and attractive forces. As a result of the coupled effects of hydrodynamic and colloidal forces, the particle trajectories and deposition efficiencies are increasingly affected by surface charge heterogeneity as one moves radially away from the stagnation point. The results indicate that it is possible to render collectors with up to 50% favorable surface fraction completely unfavorable by modifying the ratio of the radial to normal fluid velocity. Utilizing the real favorable area fraction of the collector, the patch model expression for calculating the deposition efficiency is modified for impinging jet flow geometry.     

A continuous DC-insulator dielectrophoretic sorter of microparticles

A lab-on-a-chip device is described for continuous sorting of fluorescent polystyrene microparticles utilizing direct current insulating dielectrophoresis (DC-iDEP) at lower voltages than previously reported. Particles were sorted by combining electrokinetics and dielectrophoresis in a 250 μm wide PDMS microchannel containing a rectangular insulating obstacle and four outlet channels. The DC-iDEP particle flow behaviors were investigated with 3.18, 6.20 and 10 μm fluorescent polystyrene particles which experience negative DEP forces depending on particle size, DC electric field magnitude and medium conductivity. Due to negative DEP effects, particles are deflected into different outlet streams as they pass the region of high electric field density around the obstacle. Particles suspended in dextrose added phosphate buffer saline (PBS) at conductivities ranging from 0.50 to 8.50 mS/cm at pH 7.0 were compared at 6.85 and 17.1 V/cm. Simulations of electrokinetic and dielectrophoretic forces were conducted with COMSOL Multiphysics^® to predict particle pathlines. Experimental and simulation results show the effect of medium and voltage operating conditions on particle sorting. Further, smaller particles experience smaller iDEP forces and are more susceptible to competing nonlinear electrostatic effects, whereas larger particles experience greater iDEP forces and prefer channels 1 and 2. This work demonstrates that 6.20 and 10 μm particles can be independently sorted into specific outlet streams by tuning medium conductivity even at low operating voltages. This work is an essential step forward in employing DC-iDEP for multiparticle sorting in a continuous flow, multiple outlet lab-on-a-chip device.     

DFT and surface-enhanced Raman scattering study of tryptophan-silver complex

Electric field-induced assembly of biological and synthetic particles has proven useful in two- and three-dimensional fabrication of composite materials, microwires, photonic crystals, artificial tissues, and more. Biological particles are typically irregularly shaped, and using non-spherical synthetic particles has the ability to expand current applications. However, there is much to be understood about the dielectrophoretic (DEP) interaction that takes place between particles of general shape. In this work, we numerically study the DEP interaction between two prolate spheroid particles suspended in an unbounded fluid. The boundary-element method (BEM) is applied to solve the coupled electric field, Stokes flow, and particle motion, and the DEP forces are obtained by integrating the Maxwell stress tensor over the particle surfaces. Effects of the initial configuration and aspect ratio are investigated. Results show that the particles go through a self-rotation process, that is, electro-orientation, while translating slowly to form a chain pair. The final formation resembles the chaining pattern observed previously in experiments using densely distributed ellipsoidal particles. Thus, the transient behavior and particle-particle interaction exhibited in the current study could be used as the fundamental mechanism to explain the phenomenon in the experiment.     

Cross-scale electric manipulations of cells and droplets by frequency-modulated dielectrophoresis and electrowetting

Two important electric forces, dielectrophoresis (DEP) and electrowetting-on-dielectric (EWOD), are demonstrated by dielectric-coated electrodes on a single chip to manipulate objects on different scales, which results in a dielectrophoretic concentrator in an EWOD-actuated droplet. By applying appropriate electric signals with different frequencies on identical electrodes, EWOD and DEP can be selectively generated on the proposed chip. At low frequencies, the applied voltage is consumed mostly in the dielectric layer and causes EWOD to pump liquid droplets on the millimetre scale. However, high frequency signals establish electric fields in the liquid and generate DEP forces to actuate cells or particles on the micrometre scale inside the droplet. For better performance of EWOD and DEP, square and strip electrodes are designed, respectively. Mammalian cells (Neuro-2a) and polystyrene beads are successfully actuated by a 2 MHz signal in a droplet by positive DEP and negative DEP, respectively. Droplet splitting is achieved by EWOD with a 1 kHz signal after moving cells or beads to one side of the droplet. Cell concentration, measured by a cell count chamber before and after experiments, increases 1.6 times from 8.6 x 10(5) cells ml(-1) to 1.4 x 10(6) cells ml(-1) with a single cycle of positive DEP attraction. By comparing the cutoff frequency of the voltage drop in the dielectric layer and the cross-over frequency of Re(fCM) of the suspended particles, we can estimate the frequency-modulated behaviors between EWOD, positive DEP, and negative DEP. A proposed weighted Re(fCM) facilitates analysis of the DEP phenomenon on dielectric-coated electrodes.     

DC-electrokinetic motion of colloidal cylinder(s) in the vicinity of a conducting wall

The boundary effects on DC-electrokinetic behavior of colloidal cylinder(s) in the vicinity of a conducting wall is investigated through a computational model. The contribution of the hydrodynamic drag, gravity, electrokinetic (i.e., electrophoretic and dielectrophoretic), and colloidal forces (i.e., forces due to the electrical double layer and van der Waals interactions) are incorporated in the model. The contribution of electrokinetic and colloidal forces are included by introducing the resulting forces as an external force acting on the particle(s). The colloidal forces are implemented with the prescribed expressions from the literature, and the electrokinetic force is obtained by integrating the corresponding Maxwell stress tensor over the particles' surfaces. The electrokinetic slip-velocity together with the thin electrical double layer assumption is applied on the surfaces. The position and velocity of the particles and the resulting electric and flow fields are obtained and the physical insight for the behavior of the colloidal cylinders are discussed in conjunction with the experimental observations in the literature.     

On the behavior of electrokinetic streaming potential during protein filtration with fully and partially retentive nanopores

An experimental investigation of the electrokinetic streaming potentials of both fully and partially retentive nanopores as compared with the filtration progress of dilute globular protein solution under different surface charge conditions was performed using hollow fibers. The streaming potential is generated by the electrokinetic flow effect within the electric double layer of the charged surface. Depending on the solution pH, both the protein and the pore wall can be either repulsive or attractive due to the long-range electrostatic interaction. The repulsive electrostatic interaction allows the protein particles to stay in a suspended state above the outer surface of hollow fibers instead of being deposited. The apparent streaming potential value at partially retentive pores is larger than that at fully retentive pores for the oppositely charged case; however, the opposite behavior is shown for the same-charged case. The axial-position-dependent streaming potential was also observed in order to explore the development of a concentration polarization layer during the cross-flow filtration. The time evolution of the streaming potential during the filtration of protein particles is related to the filtrate flux, from which it can be found to provide useful real-time information on particle deposition onto the outer surfaces of hollow fibers.     

Quantitative modeling of dielectrophoretic traps

We present quantitative modeling software for simulating multiple forces acting on a single particle in a microsystem. In this paper, we focus on dielectrophoretic (DEP) trapping of single cells against fluid flow. The software effectively models the trapping behavior for a range of particles including beads, mammalian cells, viruses, and bacteria. In addition, the software can be used to reveal useful information about the DEP traps - such as multipolar DEP force effects, trap size-selectivity, and effects from varying the flow chamber height. Our modeling software thus serves as a predictive tool, enabling the design of novel DEP traps with superior performance over existing trap geometries. In addition, the software can evaluate a range of trap dimensions to determine the effects on trapping behavior, thus optimizing the trap geometry before it is even fabricated. The software is freely available to the scientific community at: .     

Ultrasonic standing wave manipulation technology integrated into a dielectrophoretic chip

Several cell-based biological applications in microfluidic systems require simultaneous high-throughput and individual handling of cells or other bioparticles. Available chip-based tools for contactless manipulation are designed for either high-precision handling of individual particles, or high-throughput handling of ensembles of particles. In order to simultaneously perform both, we have combined two manipulation technologies based on ultrasonic standing waves (USWs) and dielectrophoresis (DEP) in a microfluidic chip. The principle is based on the competition between long-range ultrasonic forces, short-range dielectrophoretic forces and viscous drag forces from the fluid flow. The ultrasound is coupled into the microchannel resonator by an external transducer with a refractive element placed on top of the chip, thereby allowing transmission light microscopy to continuously monitor the biological process. The DEP manipulation is generated by an electric field between co-planar microelectrodes placed on the bottom surface of the fluid channel. We demonstrate flexible and gentle elementary manipulation functions by the use of USWs and linear or curved DEP deflector elements that can be used in high-throughput biotechnology applications of individual cells.     

Microfluidic system for dielectrophoretic separation based on a trapezoidal electrode array

This paper presents a novel microfluidic device for dielectrophoretic separation based on a trapezoidal electrode array (TEA). In this method, particles with different dielectric properties are separated by the device composed of the TEA for the dielectrophoretic deflection of particles under negative dielectrophoresis (DEP) and poly(dimethylsiloxane)(PDMS) microfluidic channel with a sinuous and expanded region. Polystyrene microparticles are exposed to an electric field generated from the TEA in the microfluidic channel and are dielectrophoretically focused to make all of them line up to one sidewall. When these particles arrive at the region of another TEA for dielectrophoretic separation, they are separated having different positions along the perpendicular direction to the fluid flow due to their different dielectrophoretic velocities. To evaluate the separation process and performance, both the effect of the flow rate on dielectrophoretic focusing and the influence of the number of trapezoidal electrodes on dielectrophoretic separation are investigated. Now that this method utilizes the TEA as a source of negative DEP, non-specific particle adhering to the electrode surface can be prevented; conventional separation approaches depending on the positive DEP force suffer from this problem. In addition, since various particle types are continuously separated, this method can be easily applicable to the separation and analysis of various dielectric particles with high particle recovery and selectivity.     

Brownian dynamics simulations of single-wall carbon nanotube separation by type using dielectrophoresis

We theoretically investigate the separation of individualized metallic and semiconducting single-wall carbon nanotubes (SWNTs) in a dielectrophoretic (DEP) flow device. The SWNT motion is simulated by a Brownian dynamics (BD) algorithm, which includes the translational and rotational effects of hydrodynamic, Brownian, dielectrophoretic, and electrophoretic forces. The device geometry is chosen to be a coaxial cylinder because it yields effective flow throughput, the DEP and flow fields are orthogonal to each other, and all the fields can be described analytically everywhere. We construct a flow-DEP phase map showing different regimes, depending on the relative magnitudes of the forces in play. The BD code is combined with an optimization algorithm that searches for the conditions that maximize the separation performance. The optimization results show that a 99% sorting performance can be achieved with typical SWNT parameters by operating in a region of the phase map where the metallic SWNTs completely orient with the field, whereas the semiconducting SWNTs partially flow-align.     

Dielectrophoretic choking phenomenon in a converging‐diverging microchannel for Janus particles

The dielectrophoretic (DEP) choking phenomenon is revisited for Janus particles that are transported electrokinetically through a microchannel constriction by a direct‐current (DC) electric field. The negative DEP force that would block a particle with a diameter significantly smaller than that of the constriction at its inlet is seen to be relaxed by the rotation of the Janus particle in a direction that minimizes the magnitude of the DEP force. This allows the particle to pass through the constriction completely. An arbitrary Lagrangian‐Eulerian (ALE) numerical method is used to solve the nonlinearly coupled electric field, flow field, and moving particle, and the DEP force is calculated by the Maxwell stress tensor (MST) method. The results show how Janus particles with non‐uniform surface potentials overcome the DEP force and present new conditions for the DEP choking by a parametric study. Particle transportation through microchannel constrictions is ubiquitous, and particle surface properties are more likely to be non‐uniform than not in practical applications. This study provides new insights of importance for non‐uniform particles transported electrokinetically in a microdevice.     

Insulator-based dielectrophoresis of microorganisms: theoretical and experimental results

Dielectrophoresis (DEP) is the motion of particles due to polarization effects in nonuniform electric fields. DEP has great potential for handling cells and is a non-destructive phenomenon. It has been utilized for different cell analysis, from viability assessments to concentration enrichment and separation. Insulator-based DEP (iDEP) provides an attractive alternative to conventional electrode-based systems; in iDEP, insulating structures are used to generate nonuniform electric fields, resulting in simpler and more robust devices. Despite the rapid development of iDEP microdevices for applications with cells, the fundamentals behind the dielectrophoretic behavior of cells has not been fully elucidated. Understanding the theory behind iDEP is necessary to continue the progress in this field. This work presents the manipulation and separation of bacterial and yeast cells with iDEP. A computational model in COMSOL Multiphysics was employed to predict the effect of direct current-iDEP on cells suspended in a microchannel containing an array of insulating structures. The model allowed predicting particle behavior, pathlines and the regions where dielectrophoretic immobilization should occur. Experimental work was performed at the same operating conditions employed with the model and results were compared, obtaining good agreement. This is the first report on the mathematical modeling of the dielectrophoretic response of yeast and bacterial cells in a DC-iDEP microdevice.     

Energy of interaction in colloids and its implications in rheological modeling

This work deals with the problem of deriving theoretical connections between rheology and interparticle forces in colloidal suspensions. The nature of interparticle forces determines the colloidal structure (crystalline order due to long range repulsive forces, flocculation due to attractive forces, etc.) and hence, the flow behavior of suspensions. The aim of this article is to discuss how these interactions enter the modeling of rheometric functions, in particular, the shear viscosity. In this sense, the main interactions commonly appearing in colloids are reviewed, as well as the role they play in phase transition behavior. Then, a series of approaches relating the interaction potential to viscosity is examined. The results of applying these models to experimental data are also discussed. Finally, examples of viscosity modeling for different interaction potentials are given, by using the structural model proposed previously by the authors. The possibility of relating the flow behavior of colloidal suspensions to the interaction between particles offers new perspectives for the study and technical applications of these systems.     

Continuous separation of microparticles by size with direct current-dielectrophoresis

Direct current-dielectrophoresis (DC-DEP), the induced motion of the dielectric particles in a spatially nonuniform DC electric field, is demonstrated to be a highly efficient method to separate the microparticles by size. The locally nonuniform electric field is generated by an insulating block fabricated inside a polydimethylsiloxane microchannel. The particle experiences a negative DEP (accordingly a repulsive force) at the corners of the block, where the local electric-field strength is the strongest. Thus, the particle deviates from the streamline and the degree of deviation is dependent on the DEP force (i.e., the particle size). Combined with the electrokinetic flow, mixed polystyrene particles of a few micrometers difference in diameter can be continuously separated into distinct reservoirs. For separating target particles of a specific size, it is required to simply adjust the voltage outputs of the electrodes. A numerical model based on the Lagrangian tracking method is developed to simulate the particle motion and the results showed a reasonable agreement with the experimental data.     

Breakdown of colloid filtration theory: role of the secondary energy minimum and surface charge heterogeneities

The mechanisms and causes of deviation from the classical colloid filtration theory (CFT) in the presence of repulsive Derjaguin-Landau-Verwey-Overbeek (DLVO) interactions were investigated. The deposition behavior of uniform polystyrene latex colloids in columns packed with spherical soda-lime glass beads was systematically examined over a broad range of physicochemical conditions, whereby both the fluid-phase effluent particle concentration and the profile of retained particles were measured. Experiments conducted with three different-sized particles in a simple (1:1) electrolyte solution reveal the controlling influence of secondary minimum deposition on the deviation from CFT. In a second series of experiments, sodium dodecyl sulfate (SDS) was added to the background electrolyte solution with the intent of masking near-neutrally charged regions of particle and collector surfaces. These results indicate that the addition of a small amount of anionic surfactant is sufficient to reduce the influence of certain surface charge inhomogeneities on the deviation from CFT. To verify the validity of CFT in the absence of surface charge heterogeneities, a third set of experiments was conducted using solutions of high pH to mask the influence of metal oxide impurities on glass bead surfaces. The results demonstrate that both secondary minimum deposition and surface charge heterogeneities contribute significantly to the deviation from CFT generally observed in colloid deposition studies. It is further shown that agreement with CFT is obtained even in the presence of an energy barrier (i.e., repulsive colloidal interactions), suggesting that it is not the general existence of repulsive conditions which causes deviation but rather the combined occurrence of "fast" and "slow" particle deposition.     

Effect of electrostatic, hydrodynamic, and Brownian forces on particle trajectories and sieving in normal flow filtration

Particle deposition and fouling are critical factors governing the performance of microfiltration and ultrafiltration systems. Particle trajectories were evaluated by numerical integration of the Langevin equation, accounting for the combined effects of electrostatic repulsion, enhanced hydrodynamic drag, and Brownian diffusion. In the absence of Brownian forces, particles are unable to enter the membrane pores unless the drag associated with the filtration velocity can overcome the electrostatic repulsion. Brownian forces significantly alter this behavior, allowing some particles to enter the pore even at low filtration velocities. The average particle transmission, evaluated from the probability of having a particle enter the pore, increases with increasing filtration velocity due to the greater hydrodynamic drag force on the particle. These results provide important insights into particle behavior in membrane systems.     

Dynamic drag force based on iterative density mapping: A new numerical tool for three‐dimensional analysis of particle trajectories in a dielectrophoretic system

Dielectrophoresis is a widely used means of manipulating suspended particles within microfluidic systems. In order to efficiently design such systems for a desired application, various numerical methods exist that enable particle trajectory plotting in two or three dimensions based on the interplay of hydrodynamic and dielectrophoretic forces. While various models are described in the literature, few are capable of modeling interactions between particles as well as their surrounding environment as these interactions are complex, multifaceted, and computationally expensive to the point of being prohibitive when considering a large number of particles. In this paper, we present a numerical model designed to enable spatial analysis of the physical effects exerted upon particles within microfluidic systems employing dielectrophoresis. The model presents a means of approximating the effects of the presence of large numbers of particles through dynamically adjusting hydrodynamic drag force based on particle density, thereby introducing a measure of emulated particle–particle and particle–liquid interactions. This model is referred to as “dynamic drag force based on iterative density mapping.” The resultant numerical model is used to simulate and predict particle trajectory and velocity profiles within a microfluidic system incorporating curved dielectrophoretic microelectrodes. The simulated data are compared favorably with experimental data gathered using microparticle image velocimetry, and is contrasted against simulated data generated using traditional “effective moment Stokes‐drag method,” showing more accurate particle velocity profiles for areas of high particle density.