Dielectrophoretic trapping of particles flowing through an array of conductive cylinders

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).