Dielectrophoresis of nanoparticles

A numerical scheme based on the distributed Lagrange multiplier method (DLM) is used to study the motion of nano-sized particles of dielectric suspensions subjected to uniform and nonuniform electric fields. Particles are subjected to both electrostatic and hydrodynamic forces, as well as Brownian motion. The results of the simulations presented in this paper show that uniform electric fields the evolution of the particle structures depends on the ratio of electrostatic particle-particle interactions and Brownian forces. When this ratio is of the order of 100 or greater, particles form stable chains and columns, whereas when it is of the order of 10 or smaller the particle distribution is random. For the nonuniform electric field cases considered in this paper, the relative magnitude of Brownian forces is in the range such that it does not influence the eventual collection of particles by dielectrophoresis and the particular locations where the particles are collected. However, Brownian motion is observed to influence the transient particle trajectories. The deviation of the particle trajectories compared to those determined by the electrostatic and hydrodynamic forces alone is characterized by the ratio of Brownian and dielectrophoretic forces.     

A modeling approach to describe the adhesion of rough, asymmetric particles to surfaces

A combined theoretical and experimental study of the adhesion of alumina particles and polystyrene latex spheres to silicon dioxide surfaces was performed. A boundary element technique was used to model electrostatic interactions between micron-scale particles and planar surfaces when the particles and surfaces were in contact. This method allows quantitative evaluation of the effects of particle geometry and surface roughness on the electrostatic interaction. The electrostatic interactions are combined with a previously developed model for van der Waals forces in particle adhesion. The combined model accounts for the effects of particle and substrate geometry, surface roughness and asperity deformation on the adhesion force. Predictions from the combined model are compared with experimental measurements made with an atomic force microscope. Measurements are made in aqueous solutions of varying ionic strength and solution pH. While van der Waals forces are generally dominant when particles are in contact with surfaces, results obtained here indicate that electrostatic interactions contribute to the overall adhesion force in certain cases. Specifically, alumina particles with complex geometries were found to adhere to surfaces due to both electrostatic and van der Waals interactions, while polystyrene latex spheres were not affected by electrostatic forces when in contact with various surfaces.     

Density profiles and solvation forces for a Yukawa fluid in a slit pore

The effect of varying wall-particle and particle-particle interactions on the density profiles near a single wall and the solvation forces between two walls immersed in a fluid of particles is investigated by grand canonical Monte Carlo simulations. Attractive and repulsive particle-particle and particle-wall interactions are modeled by a versatile hard-core Yukawa form. These simulation results are compared to theoretical calculations using the hypernetted chain integral equation technique, as well as with fundamental measure density functional theory (DFT), where particle-particle interactions are either treated as a first order perturbation using the radial distribution function or else with a DFT based on the direct-correlation function. All three theoretical approaches reproduce the main trends fairly well, but exhibit inconsistent accuracy, particularly for attractive particle-particle interactions. We show that the wall-particle and particle-particle attractions can couple together to induce a nonlinear enhancement of the adsorption and a related "repulsion through attraction" effect for the effective wall-wall forces. We also investigate the phenomenon of bridging, where an attractive wall-particle interaction induces strongly attractive solvation forces.     

Structure, surface excess and effective interactions in polymer nanocomposite melts and concentrated solutions

The Polymer Reference Interaction Site Model (PRISM) theory is employed to investigate structure, effective forces, and thermodynamics in dense polymer-particle mixtures in the one and two particle limit. The influence of particle size, degree of polymerization, and polymer reduced density is established. In the athermal limit, the surface excess is negative implying an entropic dewetting interface. Polymer induced depletion interactions are quantified via the particle-particle pair correlation function and potential of mean force. A transition from (nearly) monotonic decaying, attractive depletion interactions to much stronger repulsive-attractive oscillatory depletion forces occurs at roughly the semidilute-concentrated solution boundary. Under melt conditions, the depletion force is extremely large and attractive at contact, but is proceeded by a high repulsive barrier. For particle diameters larger than roughly five monomer diameters, division of the force by the particle radius results in a nearly universal collapse of the depletion force for all interparticle separations. Molecular dynamics simulations have been employed to determine the depletion force for nanoparticles of a diameter five times the monomer size over a wide range of polymer densities spanning the semidilute, concentrated, and melt regimes. PRISM calculations based on the spatially nonlocal hypernetted chain closure for particle-particle direct correlations capture all the rich features found in the simulations, with quantitative errors for the amplitude of the depletion forces at the level of a factor of 2 or less. The consequences of monomer-particle attractions are briefly explored. Modification of the polymer-particle pair correlations is relatively small, but much larger effects are found for the surface excess including an energetic driven transition to a wetting polymer-particle interface. The particle-particle potential of mean force exhibits multiple qualitatively different behaviors (contact aggregation, steric stabilization, local bridging attraction) depending on the strength and spatial range of the polymer-particle attraction.     

Lattice Boltzmann simulation of particles agglomeration and rheology in a particulate flow

The dynamics and rheology of particles in a Newtonian fluid subjected to shear are simulated using Lattice Boltzmann Method. A computationally-efficient Smoothed Profile Method is used to resolve fluid-solid interactions, and the Lennard-Jones inter-particle potential is implemented to account for inter-particle forces. The use of a bi-periodic computational domain with Lees-Edward boundary conditions allows simulation for systems consisting of a large number of particles under shear. The method is validated for single and dual particle problems and an analysis is performed for multi-particle problems under a range of shear rates and particle fractions. The introduction of particle-particle interactions, which are physically important in many engineering processes, is found to have a considerable impact on the dynamics, agglomeration and rheology. The total stress exhibits high unsteadiness primarily due to the solid component contribution, at higher particle fractions. The simulations underscore the complex interplay between shear, interparticle forces and agglomeration and the complex dependencies of the rheological properties.     

Experimental investigation of electrostatic particle-particle interactions in optoelectronic tweezers

This paper reports experimental and theoretical investigation of electrostatic attraction and repulsion of microparticles in an optoelectronic tweezers (OET). When we manipulate dielectric particles suspended in a fluid using OET, the electrostatic interactions of the polarized particles occur, limiting the effective manipulation of microparticles using a light-induced dielectrophoresis. In this study, we first demonstrate the electrostatic particle-particle interactions in the OET device using a liquid crystal display. At the same time, the experimental investigation of the dipole interactions between two spherical particles has been performed using the OET device. On the basis of the point-dipole model, simulation studies on the dipole forces acting on the particles and their trajectories by the forces are also performed. The experimental results show good agreement with the previously reported numerical studies as well as the results of our simulation studies.     

Electrostatic double layer force between a sphere and a planar substrate in the presence of previously deposited spherical particles

A finite element model of the electrostatic double layer interaction between an approaching colloidal particle and a small region of a charged planar surface containing four previously deposited particles is presented. The electrostatic interaction force experienced by the approaching particle is obtained by solving the Poisson-Boltzmann equation with appropriate boundary conditions representing this complex geometry. The interaction forces obtained from the detailed three-dimensional finite element simulations suggest that for the many-body scenario addressed here, the electrostatic double layer repulsion experienced by the approaching particle is less than the corresponding sphere-plate interaction due to the presence of the previously deposited particles. The reduction in force is quite significant when the screening length of the electric double layer becomes comparable to the particle radius (kappaa approximately 1). The results also suggest that the commonly used technique of pairwise addition of binary interactions can grossly overestimate the net electrostatic double layer interaction forces in such situations. The simulation methodology presented here can form a basis for investigating the influence of several previously deposited particles on the electrostatic repulsion experienced by a particle during deposition onto a substrate.     

Transport and deformation of droplets in a microdevice using dielectrophoresis

In microfluidic devices the fluid can be manipulated either as continuous streams or droplets. The latter is particularly attractive as individual droplets can not only move but also split and fuse, thus offering great flexibility for applications such as laboratory-on-a-chip. We consider the transport of liquid drops immersed in a surrounding liquid by means of the dielectrophoretic force generated by electrodes mounted at the bottom of a microdevice. The direct numerical simulation (DNS) approach is used to study the motion of droplets subjected to both hydrodynamic and electrostatic forces. Our technique is based on a finite element scheme using the fundamental equations of motion for both the droplets and surrounding fluid. The interface is tracked by the level set method and the electrostatic forces are computed using the Maxwell stress tensor. The DNS results show that the droplets move, and deform, under the action of nonuniform electric stresses on their surfaces. The deformation increases as the drop moves closer to the electrodes. The extent to which the isolated drops deform depends on the electric Weber number. When the electric Weber number is small, the drops remain spherical; otherwise, the drops stretch. Two droplets, however, that are sufficiently close to each other, can deform and coalesce, even if the electric Weber number is small. This phenomenon does not rely on the magnitude of the electric stresses generated by the bulk electric field, but instead is due to the attractive electrostatic drop-drop interaction overcoming the surface tension force. Experimental results are also presented and found to be in agreement with the DNS results.     

Magnetic Hetero-flocculation of Paramagnetic Colloidal Particles

The feasibility of a high-gradient magnetic separation process, utilizing magnetite as the energizable element in lieu of stainless steel wool, is evaluated by means of an equilibrium, two-particle, magnetic hetero-flocculation model. The model calculates the net force, defined as the sum of the magnetic, electrostatic, and van der Waals forces, exerted on a paramagnetic nanoparticle that is in the proximity of a fixed magnetite particle. Since the nanoparticle-magnetite system is assumed to be in direct contact with the moving fluid, the influence of the hydrodynamic force on the magnetic attractive force between the two particles is also explored. This model clearly reveals the ranges and conditions over which each of these various forces contributes to the net force relative to Brownian (thermal) motion. The model also reveals the feasibility of using magnetite particles instead of stainless steel as the energizable element for high-gradient magnetic separation. Important variables investigated include the size and surface charge of the particles, the magnetic field, the flow velocity, the electrolyte concentration, and the magnetic susceptibility of the nanoparticle. Copyright 2000 Academic Press.     

Optical trapping forces for colloids at the oil-water interface

We calculate the optical trapping forces exerted by a single laser beam strongly focused on a dielectric sphere located at a two-dimensional (2D) oil-water interface. The calculated lateral trapping forces, based on the geometrical optics approximation (GOA), agree with experimental measurements of the trapping force. Importantly, the calculations verify that the radiation force exerted on particles perpendicular to the interface is not sufficient to induce capillary interactions between particle pairs, which could be mistaken for particle-particle interactions. Finally, we find that the trapping forces depend on the three-phase contact angle of the particle at the interface.     

Dynamic adhesion behavior of micrometer-scale particles flowing over patchy surfaces with nanoscale electrostatic heterogeneity

The dynamic adhesion behavior of micrometer-scale silica particles is investigated numerically for a low Reynolds number shear flow over a planar collecting wall with randomly distributed electrostatic heterogeneity at the 10-nanometer scale. The hydrodynamic forces and torques on a particle are coupled to spatially varying colloidal interactions between the particle and wall. Contact and frictional forces are included in the force and torque balances to capture particle skipping, rolling, and arrest. These dynamic adhesion signatures are consistent with experimental results and are reminiscent of motion signatures observed in cell adhesion under flowing conditions, although for the synthetic system the particle–wall interactions are controlled by colloidal forces rather than physical bonds between cells and a functionalized surface. As the fraction of the surface (Θ) covered by the cationic patches is increased from zero, particle behavior sequentially transitions from no contact with the surface to skipping, rolling, and arrest, with the threshold patch density for adhesion (Θ_crit) always greater than zero and in quantitative agreement with experimental results. The ionic strength of the flowing solution determines the extent of the electrostatic interactions and can be used to tune selectively the dynamic adhesion behavior by modulating two competing effects. The extent of electrostatic interactions in the plane of the wall, or electrostatic zone of influence, governs the importance of spatial fluctuations in the cationic patch density and thus determines if flowing particles contact the wall. The distance these interactions extend into solution normal to the wall determines the strength of the particle–wall attraction, which governs the transition from skipping and rolling to arrest. The influence of Θ, particle size, Debye length, and shear rate is quantified through the construction of adhesion regime diagrams, which delineate the regions in parameter space that give rise to different dynamic adhesion signatures and illustrate selective adhesion based on particle size or curvature. The results of this study are suggestive of novel ways to control particle–wall interactions using randomly distributed surface heterogeneity.     

Electrostatic double-layer interaction between spherical particles inside a rough capillary

Predictions of electrostatic double-layer interaction forces between two similarly charged spherical colloidal particles inside an infinitely long "rough" capillary are presented. A simple model of a rough cylindrical surface is proposed, which assumes the capillary wall to be a periodic function of axial position. The periodic roughness of the wall is characterized by the wavelength and amplitude of the undulations. The electrostatic double-layer interaction force between two spherical particles located axially inside this rough capillary is determined by solving the nonlinear Poisson-Boltzmann equation employing finite element analysis. The effect of surface roughness of the cylindrical enclosure on the interaction force between two particles is extensively studied on the basis of this model. The simulations are carried out for dimensionless amplitudes (amplitude/particle radii) ranging from 0.05 to 0.15 and scaled wavelengths (wavelength/particle radii) ranging from 0.4 to 4.0. The interaction force between the particles is significantly modified by the proximity of the rough capillary wall. Generally, the interaction force for rough capillaries oscillates around the corresponding interaction force in a smooth capillary depending on the magnitudes of the scaled amplitude and wavelength of the roughness. The influence of roughness on the electrostatic interactions becomes more pronounced when the surface potential of the cylinder wall is different from the sphere surface potentials. When the cylinder and the particle surfaces have large potential differences, the axial force experienced by a particle is dominated by the capillary roughness. There are dramatic oscillations of the force, which alternately becomes repulsive and attractive as the particle moves from the crest to the trough of the rough capillary wall. These results suggest that manipulation of colloidal particles in narrow microchannels may be subject to significant force variations owing to the roughness inherent in microfabricated channels etched on metal films.     

Modeling the Effect of the Relative Humidity on the Manipulation of Nanoparticles with an Atomic Force Microscope

In the manipulation of nanoparticles, different behaviors are typically observed including sliding, rolling and rotation. Most of investigations in this field have so far focused on describing the interaction forces under vacuum (dry air) environmental condition, while the effect of the relative humidity has been poorly considered. In this work we developed a model for simulating the dynamic nanoparticle motion (rolling and sliding) in an AFM-based manipulation of nanoparticles in a humid environment. In our method, the interaction forces include the adhesion force, mainly consisting of the capillary force and van der Waals force, the normal force and friction forces. We calculated the adhesion force by considering the contributions from the wet and dry portions of the particle. Our stimulations show that nanoparticles smaller than the AFM tip tend to slide before rolling, while in large nanoparticles the rolling occurs first. The particle motion is achieved if the applied force exceeds a critical value and the direction of the rolling movement depends on the applied force angle. Furthermore, small nanoparticles are more easily manipulated by the tip in low-humidity conditions while the manipulations with large nanoparticles need high-humidity conditions. Preliminary results can be used to adjust proper handling force for the accurate and successful assembly of particles.     

AC electrokinetic templating of colloidal particle assemblies: effect of electrohydrodynamic flows

The use of spatially nonuniform electric fields for the contact-free colloidal particle assembly into ordered structures of various length scales is a research area of great interest. In the present work, numerical simulations are undertaken in order to advance our understanding of the physical mechanisms that govern this colloidal assembly process and their relation to the electric field characteristics and colloidal system properties. More specifically, the electric-field driven assembly of colloidal silica (d(p) = 0.32 and 2 μm) in DMSO, a near index matching fluid, is studied numerically over a range of voltages and concentration by means of a continuum thermodynamic approach. The equilibrium (u(f) = 0) and nonequilibrium (u(f) ≠ 0) cases were compared to determine whether fluid motion had an effect on the shape and size of assemblies. It was found that the nonequilibrium case was substantially different versus the equilibrium case, in both size and shape of the assembled structure. This dependence was related to the relative magnitudes of the electric-field driven convective motion of particles versus the fluid velocity. Fluid velocity magnitudes on the order of mm/s were predicted for 0.32 μm particles at 1% initial solids content, and the induced fluid velocity was found to be larger at the same voltage/initial volume fraction as the particle size decreased, owing to a larger contribution from entropic forces.     

A computational study of the hydrodynamically assisted organization of DNA-functionalized colloids in 2D

We study computationally the self-organization of DNA-functionalized colloidal particles confined to two dimensions and subjected to a linear shear force. We show that hydrodynamic forces allow a more thorough sampling of phase space than thermal or Brownian forces alone. Two particle types are present in each of our dynamic simulations each signifying its own specific oligonucleotide sequence grafted to the particle surface: A-type and B-type. Particles are modeled as interacting via a type-specific DNA attraction where unlike-types have affinities for each other while like-types do not. The particles are small enough to feel Brownian motion while the shear adds motion to the particles. We find the formation of lines of A-type and B-type particles in simulations with an imposed shear. Simulations without imposed shear form a frustrated network with little or no linear order. An orientational distribution function, g2(r), quantifies the degree of linear order. A phase diagram is constructed, finding a linear dependence of the minimum DNA force necessary for line formation on the dimensionless shear rate. A force analysis performed on the structures shows that the lines orient perpendicular to the axis of the elongation component of the shear because it is this orientation that allows the DNA attraction to resist the shear.     

Limitations of differential electrophoresis for measuring colloidal forces: a Brownian dynamics study

Differential electrophoresis experiments are often used to measure subpiconewton forces between two spheres of a heterodoublet. The experiments have been interpreted by solving the electrokinetic equations to obtain a simple Stokes law-type equation. However, for nanocolloids, the effects of Brownian motion alter the interpretation: (1) Brownian translation changes the rate of axial separation. (2) Brownian rotation reduces the alignment of the doublet with the applied electric field. (3) Particles can reaggregate by Brownian motion after they break, forming either heterodoublets or homodoublets, and because homodoublets cannot be broken by differential electrophoresis, this effectively terminates the experiment. We tackle points 1 and 2 using Brownian dynamics simulations (BDS) with electrophoresis as an external force, accounting for convective translation and rotation as well as Brownian translation and rotation. Our simulations identify the lower particle size limit of differential electrophoresis to be about 1 microm for desired statistical accuracy. Furthermore, our simulations predict that particles around 10 nm in size and at ambient conditions will break primarily by Brownian motion, with a negligible effect due to the electric field.     

Continuous dielectrophoretic particle separation via isomotive dielectrophoresis with bifurcating stagnation flow

We present a novel technique for continuous label‐free separation of particles based on their dielectrophoretic crossover frequencies. Our technique relies on our unique microfluidic geometry which performs hydrodynamic focusing, generates a stagnation flow with two outlets, and simultaneously produces an isomotive dielectrophoretic field via wall‐situated electrodes. To perform particle separation, we hydrodynamically focus particles onto stagnation streamlines and use isomotive dielectrophoretic force to nudge the particles off these streamlines and direct them into appropriate outlets. Focusing particles onto stagnation streamlines obviates the need for large forces to be applied to the particles and therefore increases system throughput. The use of isomotive (spatially uniform) dielectrophoretic force increases system reliability. To guide designers, we develop and describe a simple scaling model for the particle separation dynamics of our technique. The model predicts the range of particle sizes that can be separated as well as the processing rate that can be achieved as a function of system design parameters: channel size, flow rate, and applied potential. Finally, as a proof‐of‐principle, we use this technique to separate polystyrene bead and cell mixtures of the same diameters as well as mixtures of both particles with varying diameters.     

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.