This paper presents an analytical study of the cross-stream diffusion of an analyte in a rectangular microchannel under combined electroosmotic flow (EOF) and pressure driven flow to investigate the heterogeneous transport behavior and spatially-dependent diffusion scaling law. An analytical model capable of accurately describing 3D steady-state convection-diffusion in microchannels with arbitrary aspect ratios is developed based on the assumption of the thin Electric Double Layer (EDL). The model is verified against high-fidelity numerical simulation in terms of flow velocity and analyte concentration profiles with excellent agreement (<0.5% relative error). An extensive parametric analysis is then undertaken to interrogate the effect of the combined flow velocity field on the transport behavior in both the positive pressure gradient (PPG) and negative pressure gradient (NPG) cases. For the first time, the evolution from the spindle-shaped concentration profile in the PPG case, via the stripe-shaped profile (pure EOF), and finally to the butterfly-shaped profile in the PPG case is obtained using the analytical model along with a quantitative depiction of the spatially-dependent diffusion layer thickness and scaling law across a wide range of the parameter space.

中文翻译：

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电渗和压力驱动流联合作用下微通道中交叉流扩散的标度定律。

本文介绍了在组合电渗流 (EOF) 和压力驱动流下分析物在矩形微通道中的横向扩散的分析研究，以研究异质传输行为和空间相关的扩散缩放规律。基于薄双电层 (EDL) 的假设，开发了一种能够准确描述具有任意纵横比的微通道中 3D 稳态对流扩散的分析模型。该模型在流速和分析物浓度分布方面经过高保真数值模拟验证，具有极好的一致性（<0.5% 相对误差）。然后进行广泛的参数分析以询问组合流速场对正压力梯度 (PPG) 和负压力梯度 (NPG) 情况下传输行为的影响。首次使用解析模型获得了从 PPG 情况下的纺锤形浓度剖面，经过条形剖面（纯 EOF），最后到 PPG 情况下的蝴蝶形剖面的演变过程，以及在广泛的参数空间范围内对空间相关扩散层厚度和缩放规律的定量描述。