Time periodic electro-osmosis (TPEO) is a popular means to pump liquids or manipulate species of interest in today’s micro- and nanofluidic devices. In this article, we propose a double distribution-function lattice Boltzmann (LB) model to describe its oscillatory flows coupled with electrokinetics in micro- and nanochannels. To remove advective effects, we derive the LB model from a linearized Boltzmann Bhatnagar–Gross–Krook-like equation and formulate its equations depending on the alternating current (AC) frequency, instead of time. This treatment facilitates a direct comparison of the LB results to experimental measurements in practical applications. We assessed accuracy of the proposed frequency-based Linearized LB model by simulating time periodic electro-osmotic flows (TPEOFs) with a thin and a thick electric double layer (EDL) at different Stokes parameters. The results are in excellent agreement with analytical solutions. The model was used to simulate TPEOFs with various EDL thicknesses and those driven by an AC electric field combined with an oscillatory pressure gradient. The simulations show distinct distributions of the electric potential and solution velocity subject to different length ratios and frequency ratios in the flows and interesting flow responses to compounding influences of the applied electric and mechanical driving fields. Importantly, diverse vortex patterns and vorticity variations were also revealed for TPEOFs in heterogeneously charged channels. These results demonstrate that the LB model developed in this article can well capture rich TPEO flow characteristics in micro- and nanochannels. It is effective for design and optimization of TPEO-based micro- and nanofluidic devices.

中文翻译：

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用于微通道和纳米通道中时间周期电渗流的线性化格子玻尔兹曼方法

时间周期电渗（TPEO）是一种在当今的微流体和纳米流体设备中泵送液体或操纵感兴趣的物种的流行方法。在本文中，我们提出了一个双分布函数晶格玻尔兹曼（LB）模型来描述其振荡流以及微通道和纳米通道中的电动势。为了消除平流效应，我们从线性化的Boltzmann Bhatnagar–Gross–Krook方程导出LB模型，并根据交流（AC）频率而不是时间来公式化其方程。这种处理有助于将LB结果与实际应用中的实验测量结果进行直接比较。我们通过模拟具有不同斯托克斯参数的薄电层和厚电双层（EDL）的时间周期电渗流（TPEOF），评估了所提出的基于频率的线性化LB模型的准确性。结果与分析解决方案非常吻合。该模型用于模拟各种EDL厚度的TPEOF，以及由交流电场和振荡压力梯度驱动的TPEOF。仿真显示了在不同的长度比率和频率比率的流中，电势和溶液速度的明显分布，以及对施加的电场和机械驱动场的复合影响的有趣的流响应。重要的是，还发现了异质带电通道中TPEOF的不同涡旋模式和涡度变化。这些结果表明，本文开发的LB模型可以很好地捕获微通道和纳米通道中丰富的TPEO流动特性。它对于基于TPEO的微流体和纳米流体设备的设计和优化非常有效。