This article presents a three-dimensional analytical model to investigate cross-stream diffusion transport in rectangular microchannels with arbitrary aspect ratios under pressure-driven flow. The Fourier series solution to the three-dimensional convection-diffusion equation is obtained using a double integral transformation method and associated eigensystem calculation. A phase diagram derived from the dimensional analysis is presented to thoroughly interrogate the characteristics in various transport regimes and examine the validity of the model. The analytical model is verified against both experimental and numerical models in terms of the concentration profile, diffusion scaling law, and mixing efficiency with excellent agreement (with <0.5% relative error). Quantitative comparison against other prior analytical models in extensive parameter space is also performed, which demonstrates that the present model accommodates much broader transport regimes with significantly enhanced applicability.

中文翻译：

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任意纵横比微通道中压力驱动流动下的交叉流扩散：使用三维分析模型的相图研究。

本文提出了一个三维分析模型，用于研究在压力驱动流下具有任意纵横比的矩形微通道中的横流扩散传输。三维对流扩散方程的傅立叶级数解是使用双积分变换方法和相关的本征系统计算获得的。提出了从量纲分析得出的相图，以彻底询问各种运输方式的特征并检查模型的有效性。分析模型在浓度分布、扩散缩放规律和混合效率方面都经过实验和数值模型验证，具有极好的一致性（相对误差 <0.5%）。