Herein, we report a dielectrophoretic microdevice mathematical model to achieve 3D focusing for micro‐scale entities. The device has two pairs of independently controllable electrodes with each pair positioned on the microchannel's sides; every electrode of each pair protrudes slightly into the microchannel. The model is composed of equations describing voltage, electric field, fluid flow and equations of motion. The model took consideration of different forces including dielectrophoresis, drag, gravity, buoyancy, virtual mass and inertia to the motion of the micro‐scale entity. The model is solved specifically by finite difference methods. The micro‐scale entity is 3D focused at microchannel centre for equal applied voltage and focused away from the channel for unequal applied voltage. Steady‐state vertical position is dependent on applied voltages, electrode protrusion width and microchannel height while being independent of volumetric flow rate, initial positions and radius of micro‐scale entity. No increase in vertical position occurs beyond the threshold values of microchannel height and applied voltage. The model is validated with experimental results from literature.

An experimentally validated mathematical model of a microfluidic device with nozzle-shaped electrode configuration for realizing dielectrophoresis based 3D-focusing is presented in the article. Two right-triangle shaped electrodes on the top and bottom surfaces make up the nozzle-shaped electrode configuration. The mathematical model consists of equations describing the motion of microparticles as well as profiles of electric potential, electric field, and fluid flow inside the microchannel. The influence of forces associated with inertia, gravity, drag, virtual mass, dielectrophoresis, and buoyancy are taken into account in the model. The performance of the microfluidic device is quantified in terms of horizontal and vertical focusing parameters. The influence of operating parameters, such as applied electric potential and volumetric flow rate, as well as geometric parameters, such as electrode dimensions and microchannel dimensions, are analyzed using the model. The performance of the microfluidic device enhances with an increase in applied electric potential and reduction in volumetric flow rate. Additionally, the performance of the microfluidic device improves with reduction in microchannel height and increase in microparticle radius while degrading with increase in reduction in electrode length and width. The model is of great benefit as it allows for generating working designs of the proposed microfluidic device with the desired performance metrics.

This article details the mathematical model of a microfluidic device aimed at separating any binary heterogeneous sample of microparticles into two homogeneous samples based on size with sub-micron resolution. The device consists of two sections, where the upstream section is dedicated to focusing of microparticles, while the downstream section is dedicated to separation of the focused stream of microparticles into two samples based on size. Each section has multiple planar electrodes of finite size protruding into the microchannel from the top and bottom of each sidewall; each top electrode aligns with a bottom electrode and they form a pair leading to multiple pairs of electrodes on each side. The focusing section subjects all microparticles to repulsive dielectrophoretic force, from each set of the electrodes, to focus them next to one of the sidewalls. This separation section pushes the big microparticles toward the interior, away from the wall, of the microchannel using repulsive dielectrophoretic force, while the small microparticles move unaffected to achieve the desired degree of separation. The operating frequency of the set of electrodes in the separation section is maintained equal to the cross-over frequency of the small microparticles. The working of the device is demonstrated by separating a heterogeneous mixture consisting of polystyrene microparticles of different size (radii of 2 and 2.25 μm) into two homogeneous samples. The mathematical model is used for parametric study, and the performance is quantified in terms of separation efficiency and separation purity; the parameters considered include applied electric voltages, electrode dimensions, outlet widths, number of electrodes, and volumetric flowrate. The separation efficiencies and separation purities for both microparticles are 100% for low volumetric flow rates, a large number of electrode pairs, large electrode dimensions, and high differences between voltages in both sections.

Model-based analysis of a dielectrophoretic microfluidic device for realising 3D-focusing is presented in this work. The electrode configuration is made up of several finite-sized planar electrodes positioned on either side of the microchannel's top and bottom surfaces; the electrodes on the top surface and bottom surface of the same side form a pair. The forces associated with inertia, buoyancy, gravity, and dielectrophoresis are included in the model. As per the model, it is possible to use the proposed device to achieve 3D-focusing at the desired location along the width of the microchannel. Also, the proposed device can achieve 3D-focusing irrespective of the type of micro-scale entity. Two parameters for quantifying the efficacy of the microfluidic device in achieving 3D-focusing are presentedhorizontal and vertical focusing parameters. The model demonstrates that the radius of micro-scale entity, electrode/gap lengths, electrode width, microchannel height, number of electrodes, applied electric potentials, and volumetric flow rate influence horizontal and vertical focusing parameters. The mathematical model is thus useful in designing dielectrophoresis-based 3D-focusing with desired performance metrics for on-chip flow cytometry.

The cover image is based on the Research Article 3D Focusing of Micro‐Scale Entities in Dielectrophoretic Microdevice by Fadi Alnaimat, Salini Krishna, Ali Hilal‐Alnaqbi, Anas Alazzam, Sawsan Dagher, Bobby Mathew. DOI