In present paper, we simulate the electro-kinetic transport of aqueous solution through a microchannel containing porous media. The micro-channel walls are simulated as complex wavy surface and are modelled by superimposing the three wave functions of different amplitudes but the same wavelength. The micro-channel contains an isotropic, homogenous porous medium, which is analysed with a generalized Darcy law. The nonlinear-coupled governing equations for mass, momentum and electrical potential conservation are simplified using low Reynolds number and long wavelength approximations, and the Debye electro-kinetic linearization. Following non-dimensional transformation of the linearized boundary value problem, closed-form analytical solutions are presented for the velocity components, pressure gradient, local wall shear stress, average flow rate and stream function subject to physically appropriate boundary conditions. Validation with a finite difference method is also conducted. The effect of permeability parameter, Debye length (i.e. characteristic thickness of electrical double layer) and electro-osmotic velocity on flow characteristics is illustrated graphically and interpreted at length. The study finds applications in chromatography, hybrid electro-osmotic micro-pumps, transport phenomena in chemical engineering and energy systems exploiting electro-kinetics.

中文翻译：

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复杂波状多孔表面微通道中的电渗流

在本文中，我们模拟了水溶液通过包含多孔介质的微通道的电动传输。微通道壁被模拟为复杂的波状表面，并通过叠加三个不同幅度但相同波长的波函数来建模。微通道包含各向同性、均质的多孔介质，可使用广义达西定律对其进行分析。质量、动量和电势守恒的非线性耦合控制方程使用低雷诺数和长波长近似以及德拜电动线性化进行了简化。在线性化边值问题的无量纲变换之后，给出了速度分量、压力梯度、局部壁面剪应力的封闭形式解析解，平均流速和流函数受物理适当边界条件的约束。还进行了有限差分法的验证。渗透率参数、德拜长度（即双电层的特征厚度）和电渗速度对流动特性的影响以图形方式说明并在长度上进行解释。该研究在色谱、混合电渗微泵、化学工程中的传输现象和利用电动力学的能源系统中找到了应用。双电层的特征厚度）和电渗速度对流动特性的影响以图形方式说明并详细解释。该研究在色谱、混合电渗微泵、化学工程中的传输现象和利用电动力学的能源系统中找到了应用。双电层的特征厚度）和电渗速度对流动特性的影响以图形方式说明并详细解释。该研究在色谱、混合电渗微泵、化学工程中的传输现象和利用电动力学的能源系统中找到了应用。