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.

中文翻译：

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基于亚微米级尺寸的分离微粒的介电泳微流控装置。

本文详细介绍了一种微流控设备的数学模型，该模型旨在基于亚微米分辨率的大小，将任何二进制的异质微粒样品分成两个均质样品。该设备由两个部分组成，其中上游部分专用于微粒的聚焦，而下游部分专用于根据尺寸将聚焦的微粒流分成两个样品。每个部分都有多个尺寸有限的平面电极，从每个侧壁的顶部和底部突出到微通道中。每个顶部电极与一个底部电极对齐，并且它们形成一对，从而导致每侧的多对电极。聚焦部分使来自每组电极的所有微粒受到排斥介电泳力，将它们聚焦在侧壁之一附近。该分离部分利用排斥介电电泳力将大微粒推向微通道的内部，远离壁的内部，而小微粒不受影响地移动以实现所需的分离度。分离部分中的电极组的工作频率保持等于小微粒的交叉频率。通过将由大小不同（半径为2和2.25μm的聚苯乙烯微粒）组成的异质混合物分离为两个均质样品，证明了该装置的工作。该数学模型用于参数研究，并根据分离效率和分离纯度对性能进行量化；考虑的参数包括施加的电压，电极尺寸，出口宽度，电极数量和体积流量。对于低体积流量，大量电极对，大电极尺寸以及两个部分中的电压之间的高差异，两种微粒的分离效率和分离纯度均为100％。