Direct numerical simulation of AC dielectrophoretic particle–particle interactive motions

One-step formation of three-dimensional interconnected T-shaped microstructures inside composites by orthogonal bidirectional self-assembly method

The fillers inside a polymer matrix should typically be self-assembled in both the horizontal and vertical directions to obtain 3-dimentional (3D) percolation pathways, whereby the fields of application can be expanded and the properties of organic-inorganic composite films improved. Conventional dielectrophoresis techniques can typically only drive fillers to self-assemble in only one direction. We have devised a one-step dielectrophoresis-driven approach that effectively induces fillers self-assembly along two orthogonal axes, which results in the formation of 3D interconnected T-shaped iron microstructures (3D-T CIP) inside a polymer matrix. This approach to carbonyl iron powder (CIP) embedded in a polymer matrix results in a linear structure along the thickness direction and a network structure on the top surface of the film. The fillers in the polymer were controlled to achieve orthogonal bidirectional self-assembly using an external alternating current (AC) electric field and a non-contact technique that did not lead to electrical breakdown. The process of 3D-T CIP formation was observed in real time using in situ observation methods with optical microscopy, and the quantity and quality of self-assembly were characterized using statistical and fractal analysis. The process of fillers self-assembly along the direction perpendicular to the electric field was explained by finite element analogue simulations, and the results indicated that the insulating polyethylene terephthalate (PET) film between the electrode and the CIP/prepolymer suspension was the key to the formation of the 3D-T CIP. In contrast to the traditional two-step method of fabricating sandwich-structured film, the fabricated 3D-T CIP film with 3D electrically conductive pathways can be applied as magnetic field sensor.

Microparticle electrical conductivity measurement using optoelectronic tweezers

When it comes to simulate or calculate an optoelectronic tweezer (OET) response for a microparticle suspended in a given medium, a precise electrical conductivity (later referred to as conductivity) value for the microparticle is critical. However, there are not well-established measurements or well-referenced values for microparticle conductivities in the OET realm. Thus, we report a method based on measuring the escape velocity of a microparticle with a standard OET system to calculate its conductivity. A widely used 6 μm polystyrene bead (PSB) is used for the study. The conductivity values are found to be invariant around 2×10-3 S/m across multiple different aqueous media, which helps clarify the ambiguity in the usage of PSB conductivity. Our convenient approach could principally be applied for the measurement of multiple unknown OET-relevant material properties of microparticle-medium systems with various OET responses, which can be beneficial to carry out more accurate characterization in relevant fields.

Comparing machine learning and deep learning regression frameworks for accurate prediction of dielectrophoretic force

An intelligent sensing framework using Machine Learning (ML) and Deep Learning (DL) architectures to precisely quantify dielectrophoretic force invoked on microparticles in a textile electrode-based DEP sensing device is reported. The prediction accuracy and generalization ability of the framework was validated using experimental results. Images of pearl chain alignment at varying input voltages were used to build deep regression models using modified ML and CNN architectures that can correlate pearl chain alignment patterns of Saccharomyces cerevisiae(yeast) cells and polystyrene microbeads to DEP force. Various ML models such as K-Nearest Neighbor, Support Vector Machine, Random Forest, Neural Networks, and Linear Regression along with DL models such as Convolutional Neural Network (CNN) architectures of AlexNet, ResNet-50, MobileNetV2, and GoogLeNet have been analyzed in order to build an effective regression framework to estimate the force induced on yeast cells and microbeads. The efficiencies of the models were evaluated using Mean Absolute Error, Mean Absolute Relative, Mean Squared Error, R-squared, and Root Mean Square Error (RMSE) as evaluation metrics. ResNet-50 with RMSPROP gave the best performance, with a validation RMSE of 0.0918 on yeast cells while AlexNet with ADAM optimizer gave the best performance, with a validation RMSE of 0.1745 on microbeads. This provides a baseline for further studies in the application of deep learning in DEP aided Lab-on-Chip devices.

Deep-Learning Based Estimation of Dielectrophoretic Force

The ability to accurately quantify dielectrophoretic (DEP) force is critical in the development of high-efficiency microfluidic systems. This is the first reported work that combines a textile electrode-based DEP sensing system with deep learning in order to estimate the DEP forces invoked on microparticles. We demonstrate how our deep learning model can process micrographs of pearl chains of polystyrene (PS) microbeads to estimate the DEP forces experienced. Numerous images obtained from our experiments at varying input voltages were preprocessed and used to train three deep convolutional neural networks, namely AlexNet, MobileNetV2, and VGG19. The performances of all the models was tested for their validation accuracies. Models were also tested with adversarial images to evaluate performance in terms of classification accuracy and resilience as a result of noise, image blur, and contrast changes. The results indicated that our method is robust under unfavorable real-world settings, demonstrating that it can be used for the direct estimation of dielectrophoretic force in point-of-care settings.

Mechanism study of how lipid vesicle electroformation is suppressed by the presence of sodium chloride

Giant lipid vesicles (GLVs) are usually adopted as models of cell membranes and electroformation is the most commonly used method for GLV formation. However, GLV electroformation are known to be suppressed by the presence of salt and the mechanism is not clear so far. In this paper, the lipid hydration and GLV electroformation were investigated as a function of the concentration of sodium chloride by depositing the lipids on the bottom substrates and top substrates. In addition, the electrohydrodynamic force generated by the electroosmotic flow (EOF) on the lipid phase was calculated with COMSOL Multiphysics. It was found that the mechanisms for the failure of GLV electroformation in salt solutions are: 1) the presence of sodium chloride decreases the membrane permeability to aqueous solution by accelerating the formation of well-packed membranes, suppressing the swelling and detachment of the lipid membranes; 2) the presence of sodium chloride decreased the electrohydrodynamic force by increasing the medium conductivity.

Multi-particle interaction in AC electric field driven by dielectrophoresis force

When the dielectrophoresis technology is used to manipulate micron-sized particles, the interaction between particles should not be ignored because of the particle-particle interaction. Especially, when multiple particles (number of particles is above 2) are simultaneously manipulated, the interaction between neighboring particles will affect the results of the manipulation. This research investigates the interaction of particles caused dielectrophoresis effect by the Arbitrary Lagrangian-Eulerian (ALE) method based on the hypothesis of the thin layer of the electric double layer at the microscale. The mathematics model can be solved simultaneously by the finite element method for the AC electric field, the flow field around the suspended particles and the particle mechanics at the micrometer scale. In this study, the particle conductivity and the direction of the electric field are investigated, we find that particle conductivity and electric field direction pose an impact on particle movement, and the research reveal the law of microparticle dielectrophoresis movement, which could offer theoretical and technology support to profoundly understand the precise manipulation of particles in microfluidic chips by the dielectrophoresis effect.

Simulation of BNNSs Dielectrophoretic Motion under a Nanosecond Pulsed Electric Field

Using a nanosecond pulsed electric field to induce orientation and arrangement of insulating flake particles is a novel efficient strategy, but the specific mechanism remains unclear. In this study, the dielectrophoretic motion of boron nitride nanosheets (BNNSs) in ultrapure water under a nanosecond pulsed electric field is simulated for the first time. First, the simulation theory is proposed. When the relaxation polarization time of the dielectric is much shorter than the pulse voltage width, the pulse voltage high level can be considered a short-term DC voltage. On this basis, the Arbitrary Lagrangian–Euler (ALE) method is used in the model, considering the mutual ultrapure water–BNNS particles-nanosecond pulsed electric field dielectrophoretic interaction, to study the influence of different BNNSs self-angle α and relative angle β on local orientation and global arrangement. The particles are moved by the dielectrophoretic force during the pulse voltage high level and move with the ultrapure water flow at the zero level, without their movement direction changing during this period, so the orientation angle and distance changes show step-like and wave-like curves, respectively. The model explains the basic mechanism of dielectrophoretic motion of BNNSs under a pulsed electric field and summarizes the motion law of BNNSs, providing a reference for subsequent research.

A Continuous Cell Separation and Collection Approach on a Microfilter and Negative Dielectrophoresis Combined Chip

Cell separation plays an important role in the fields of analytical chemistry and biomedicine. To solve the blockage problem and improve the separation throughput in the traditional microstructure filtration-based separation approach, a continuous cell separation and collection approach via micropost array railing on a microfilter and negative dielectrophoresis combined chip is proposed. By tilting the micropost array at a certain angle, microparticles or cells enter the collection area under micropost array railing. The effects of the inclination angle of the micropost array and the electrode distance on the microparticle collection efficiency were investigated. Based on the optimized microfluidic chip structure, 37- and 16.3-μm particles were collected with 85% and 89% efficiencies, respectively. Additionally, algal cells were separated and collected by using the optimized microchip. The chip also had good separation and collection effects on biological samples, which effectively solved the blockage problem and improved the separation throughput, laying a foundation for subsequent microstructure filtration separation-based research and application.

Theory for hierarchical assembly with dielectrophoresis and the role of particle anisotropy

Nonuniform electric fields cause polarizable particles to move through an effect known as dielectrophoresis (DEP). Additionally, the particles themselves create nonuniform fields due to their induced dipoles. When the nonuniform field of one particle causes another to move, it represents a path to hierarchical assembly termed mutual DEP (mDEP). Anisotropic particles potentially provide further opportunities for assembly through intense and intricate local field profiles. Here, we construct a theoretical framework for describing anisotropic particles as templates for assembly through mDEP by considering the motion of small nanoparticles near larger anisotropic nanoparticles. Using finite element analysis, we study eight particle shapes and compute their field enhancement and polarizability in an orientation-specific manner. Strikingly, we find a more than tenfold enhancement in the field near certain particle shapes, potentially promoting mDEP. To more directly relate the field intensity to the anticipated assembly outcome, we compute the volume experiencing each field enhancement versus particle shape and orientation. Finally, we provide a framework for predicting how mixtures of two distinct particle species will begin to assemble in a manner that allows for the identification of conditions that kinetically bias assembly toward specific hierarchical outcomes.

A new droplet breakup phenomenon in electrokinetic flow through a microchannel constriction

A completely new droplet breakup phenomenon is reported for droplets passing through a constriction in an electrokinetic flow. The breakup occurs during the droplet shape recovery process past the constriction throat by the interplay of the dielectrophoretic stress release and the interface energy for droplets with smaller permittivity than that of the ambient fluid. There are conditions for constriction ratios and droplet size that the droplet breakup occurs. The numerical predictions provided here require experimental verification, and then can give rise to a novel microfluidic device design with novel droplet manipulations.

Nondimensional Streaming Dielectrophoresis Number for a System of Continuous Particle Separation

Cell sorting methods are required in numerous healthcare assays. Although flow cytometry and magnetically actuated sorting are widespread techniques for cell sorting, there is intense research on label-free techniques to reduce the cost and complexity of the process. Among label-free techniques, dielectrophoresis (DEP) offers the capability to separate cells not only on the basis of size but also on their membrane capacitance. This is important because it enables cell discrimination on the basis of specific traits such as viability, identity, fate, and age. StreamingDEP refers to the continuous sorting of cells thanks to the generation of streams of targeted particles by equilibrating the drag and DEP forces acting on targeted particles. In this work, we provide an analytical expression for a streamingDEP number toward enabling the a priori design of DEP devices to agglomerate targeted particles into streams. The nondimensional streamingDEP number (SDN) obtained in this analysis is applied to experiments with 1 μm polystyrene particles and Candida cells. On the basis of these experiments, three characteristic zones are mapped to different values of the SDN: (1) physical capture thanks to DEP for 0 < SDN < 0.6; (2) streaming due to DEP for 0.6 < SDN < 1; (3) elution without experiencing DEP for SDN > 1.

A review of polystyrene bead manipulation by dielectrophoresis

Exploitation of the intrinsic electrical properties of particles has recently emerged as an appealing approach for trapping and separating various scaled particles. Initiative particle manipulation by dielectrophoresis (DEP) showed remarkable advantages including high speed, ease of handling, high precision and being label-free. Herein, we provide a general overview of the manipulation of polystyrene (PS) beads and related particles via DEP; especially, the wide applications of these manipulated PS beads in the quantitative evaluation of device performance for model validation and standardization have been discussed. The motion and polarizability of the PS beads induced by DEP were analyzed and classified into two categories as positive and negative DEP within the time and space domains. The DEP techniques used for bioparticle manipulation were demonstrated, and their applications were conducted in four fields: trapping of single-sized PS beads, separation of multiple-sized PS beads by size, separation of PS beads and non-bioparticles, and separation of PS beads and bioparticles. Finally, future perspectives on DEP-on-a-chip have been proposed to discriminate bio-targets in the network of microfluidic channels.

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.

Expanding the flexibility of dynamics simulation on different size particle-particle interactions by dielectrophoresis

In this paper, we perform flexible and reliable dynamics simulations on different sizes of two or more particles' interactive motions, where they encounter positive or negative dielectrophoresis (DEP) forces. The particles with identical or non-identical size are in close proximity suspended freely in a solution under a homogeneous electric field. According to the description of classic dipole moment, DEP forces make the particles form a straight chain. Therefore, dynamics simulation based on Newton's laws is utilized to understand AC DEP phenomena among multiple particles. To solve the relevant governing equations, Stokes drag and repulsive forces (including wall and particles) are combined with DEP forces to obtain the trajectories of particles. Results show that particles with the same sign of the Clausius-Mossotti (CM) factor revolve clockwise or counterclockwise to attract each other parallel to the electric field direction. Conversely, the particle chain is perpendicular to the field. This programmable advantage is of great benefit to the study of three or four particle motions. Meanwhile, the pearl chain consisting of three or four particles is related not only to an individual CM factor but also to initial spatial configuration. Both the cluster and short chain are dependent on symmetry between the geometric distribution and electric field, while it implies different size particles easily cause the chain structure with less time.

Elucidating the Mechanisms of Two Unique Phenomena Governed by Particle-Particle Interaction under DEP: Tumbling Motion of Pearl Chains and Alignment of Ellipsoidal Particles

Particle-particle interaction plays a crucial role in determining the movement and alignment of particles under dielectrophoresis (DEP). Previous research efforts focus on studying the mechanism governing the alignment of spherical particles with similar sizes in a static condition. Different approaches have been developed to simulate the alignment process of a given number of particles from several up to thousands depending on the applicability of the approaches. However, restricted by the simplification of electric field distribution and use of identical spherical particles, not much new understanding has been gained apart from the most common phenomenon of pearl chain formation. To enhance the understanding of particle-particle interaction, the movement of pearl chains under DEP in a flow condition was studied and a new type of tumbling motion with unknown mechanism was observed. For interactions among non-spherical particles, some preceding works have been done to simulate the alignment of ellipsoidal particles. Yet the modeling results do not match experimental observations. In this paper, the authors applied the newly developed volumetric polarization and integration (VPI) method to elucidate the underlying mechanism for the newly observed movement of pearl chains under DEP in a flow condition and explain the alignment patterns of ellipsoidal particles. The modeling results show satisfactory agreement with experimental observations, which proves the strength of the VPI method in explaining complicated DEP phenomena.

Numerical Investigation of DC Dielectrophoretic Deformable Particle⁻Particle Interactions and Assembly

In a non-uniform electric field, the surface charge of the deformable particle is polarized, resulting in the dielectrophoretic force acting on the surface of the particle, which causes the electrophoresis. Due to dielectrophoretic force, the two deformable particles approach each other, and distort the flow field between them, which cause the hydrodynamic force correspondingly. The dielectrophoresis (DEP) force and the hydrodynamic force together form the net force acting on the particles. In this paper, based on a thin electric double layer (EDL) assumption, we developed a mathematical model under the arbitrary Lagrangian⁻Eulerian (ALE) numerical approach method to simulate the flow field, electric field, and deformable particles simultaneously. Simulation results show that, when two deformable particles' distances are in a certain range, no matter the initial position of the two particles immersed in the fluid field, the particles will eventually form a particle⁻particle chain parallel to the direction of the electric field. In actual experiments, the biological cells used are deformable. Compared with the previous study on the DEP motion of the rigid particles, the research conclusion of this paper provides a more rigorous reference for the design of microfluidics.

Numerical Study of Lateral Migration of Elliptical Magnetic Microparticles in Microchannels in Uniform Magnetic Fields

This work reports numerical investigation of lateral migration of a paramagnetic microparticle of an elliptic shape in a plane Poiseuille flow of a Newtonian fluid under a uniform magnetic field by direct numerical simulation (DNS). A finite element method (FEM) based on the arbitrary Lagrangian–Eulerian (ALE) approach is used to study the effects of strength and direction of the magnetic field, particle–wall separation distance and particle shape on the lateral migration. The particle is shown to exhibit negligible lateral migration in the absence of a magnetic field. When the magnetic field is applied, the particle migrates laterally. The migration direction depends on the direction of the external magnetic field, which controls the symmetry property of the particle rotational velocity. The magnitude of net lateral migration velocity over a π cycle is increased with the magnetic field strength when the particle is able to execute complete rotations, expect for α = 45° and 135°. By investigating a wide range of parameters, our direct numerical simulations yield a comprehensive understanding of the particle migration mechanism. Based on the numerical data, an empirical scaling relationship is proposed to relate the lateral migration distance to the asymmetry of the rotational velocity and lateral oscillation amplitude. The scaling relationship provides useful guidelines on design of devices to manipulate nonspherical micro-particles, which have important applications in lab-on-a-chip technology, biology and biomedical engineering.

Approaches to self-assembly of colloidal monolayers: A guide for nanotechnologists

Self-assembly of quasi-spherical colloidal particles in two-dimensional (2D) arrangements is essential for a wide range of applications from optoelectronics to surface engineering, from chemical and biological sensing to light harvesting and environmental remediation. Several self-assembly approaches have flourished throughout the years, with specific features in terms of complexity of the implementation, sensitivity to process parameters, characteristics of the final colloidal assembly. Selecting the proper method for a given application amidst the vast literature in this field can be a challenging task. In this review, we present an extensive classification and comparison of the different techniques adopted for 2D self-assembly in order to provide useful guidelines for scientists approaching this field. After an overview of the main applications of 2D colloidal assemblies, we describe the main mechanisms underlying their formation and introduce the mathematical tools commonly used to analyse their final morphology. Subsequently, we examine in detail each class of self-assembly techniques, with an explanation of the physical processes intervening in crystallization and a thorough investigation of the technical peculiarities of the different practical implementations. We point out the specific characteristics of the set-ups and apparatuses developed for self-assembly in terms of complexity, requirements, reproducibility, robustness, sensitivity to process parameters and morphology of the final colloidal pattern. Such an analysis will help the reader to individuate more easily the approach more suitable for a given application and will draw the attention towards the importance of the details of each implementation for the final results.

Modeling of dielectrophoretic particle motion: Point particle versus finite-sized particle

Dielectrophoresis (DEP) is a very popular technique for microfluidic bio-particle manipulation. For the design of a DEP-based microfluidic device, simulation of the particle trajectory within the microchannel network is crucial. There are basically two approaches: (i) point-particle approach and (ii) finite-sized particle approach. In this study, many aspects of both approaches are discussed for the simulation of direct current DEP, alternating current DEP, and traveling-wave DEP applications. Point-particle approach is implemented using Lagrangian tracking method, and finite-sized particle is implemented using boundary element method. The comparison of the point-particle approach and finite-sized particle approach is presented for different DEP applications. Moreover, the effect of particle-particle interaction is explored by simulating the motion of closely packed multiple particles for the same applications, and anomalous-DEP, which is a result of particle-wall interaction at the close vicinity of electrode surface, is illustrated.

Deformability-Based Electrokinetic Particle Separation

Deformability is an effective property that can be used in the separation of colloidal particles and cells. In this study, a microfluidic device is proposed and tested numerically for the sorting of deformable particles of various degrees. The separation process is numerically investigated by a direct numerical simulation of the fluid–particle–electric field interactions with an arbitrary Lagrangian–Eulerian finite-element method. The separation performance is investigated with the shear modulus of particles, the strength of the applied electric field, and the design of the contracted microfluidic devices as the main parameters. The results show that the particles with different shear moduli take different shapes and trajectories when passing through a microchannel contraction, enabling the separation of particles based on their difference in deformability.

Electrophoresis of two spheres: Influence of double layer and van der Waals interactions

Considering recent applications of electrophoresis conduced in nanoscaled devices, where particle-particle interaction can play a role, we studied for the first time the electrophoresis of two rigid spheres along their center line, taking account of the hydrodynamic, electric, and van der Waals interactions between them. Under the conditions of constant surface potential and surface charge density, the influences of the level of surface potential/charge density, the bulk salt concentration, and the particle-particle distance on their electrokinetic behaviors are examined. Numerical simulation reveals that these behaviors are much more complicated and interesting than those of isolated particles. In particular, we show that care must be taken in choosing an appropriate particle concentration in relevant experiment to avoid obtaining unreliable mobility data.