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.
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