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Dielectrophoresis (DEP) is a label-free electrokinetic method for selectively trapping polarizable particles using non-uniform electric fields. While co-planar electrode systems are common, their inherent DEP force distribution limits throughput. This study presents a computationally efficient framework for modeling two-dimensional DEP-based particle trapping in ordered arrays of conductive cylinders. These cylinders are modeled at a range of sizes, from micrometers to nanometers, to represent microfluidic systems consisting of conductive pillars, nanofibers, etc. Analytical solutions for fluid flow and electric potential were derived using eigenfunction expansions and collocation, then used in a particle tracking model that includes hydrodynamic drag, Brownian motion, and multipolar DEP forces. Although focused on conductive arrays, this framework is extensible to other configurations. This work provides a foundation for future work in the design of high-throughput DEP systems. Both dimensionless and dimensional analyses were performed across a wide range of particle sizes (30 nm to 3 μm), voltages (10 mV to 100 V), and array geometries. No specific optimal cylinder size was found; instead, optimal performance arises from a balance between DEP force distribution and flow through the cylinder array gap. Diamond-oriented arrays exhibited enhanced trapping under moderate dielectrophoretic velocity-to-fluid velocity ratios (up to 39% greater), while square arrays performed better under low-field and large-cylinder conditions (up to 40% greater). 

Dielectrophoresis at the nanoscale has gained significant attention in recent years as a low-cost, rapid, efficient, and label-free technique. This method holds great promise for various interdisciplinary applications related to micro- and nanoscience, including biosensors, microfluidics, and nanomachines. The innovation and development of such devices and platforms could promote wider applications in the field of nanotechnology. This review aims to provide an overview of recent developments and applications of nanoparticle dielectrophoresis, where at least one dimension of the geometry or the particles being manipulated is equal to or less than 100 nm. By offering a theoretical foundation to understand the processes and challenges that occur at the nanoscale—such as the need for high field gradients—this article presents a comprehensive overview of the advancements and applications of nanoparticle dielectrophoresis platforms over the past 15 years. This period has been characterized by significant progress, as well as persistent challenges in the manipulation and separation of nanoscale objects. As a foundation for future research, this review will help researchers explore new avenues and potential applications across various fields. 

Trapped nanoparticles on a nanofiber electrode due to AC dielectrophoresis.