On the propagation of concentration polarization from microchannel-nanochannel interfaces. Part I: Analytical model and characteristic analysis.
On the propagation of concentration polarization from microchannel-nanochannel interfaces. Part I: Analytical model and characteristic analysis.
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DOI：
10.1021/la803317p
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发表时间：
2009-04-09
期刊：
影响因子：
--
通讯作者：
Santiago JG
中科院分区：
文献类型：
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作者：
Mani A;Zangle TA;Santiago JG
我们建立了两个模型来描述离子在微通道和纳米通道中的传输。对于第一个模型，我们得到了一个一维（非定常）偏微分方程，该方程控制了通过浅而宽的电动通道的流动和电荷输运。在该模型中，利用泊松-玻尔兹曼方程的精确解考虑了双电层对轴向输运的影响。第二个更简单的模型是可分析的，它假设edl被限制在近壁区域。通过特征分析，我们发现后一种模型捕获了浓度极化（CP）效应，并对其动力学提供了有用的见解。确定了两种不同的CP制度：CP具有传播，其中富集和耗尽冲击向外传播；极化效应停留在微纳通道界面局部的无传播CP。发现每一种状态的存在取决于纳米通道Dukhin数和电渗透迁移率非量纲化的共离子的迁移率。有趣的是，微通道尺寸和轴向扩散对CP是否传播的影响并不显著。CP传播的稳态条件由通道高度、表面化学和共离子迁移率控制，而不是由储层条件控制。这两个模型在这两个论文系列的第二部分的实验结果进行了验证。
We develop two models to describe ion transport in microchannels and nanochannels. For the first model, we obtain a one-dimensional (unsteady) partial differential equation governing flow and charge transport through a shallow and wide electrokinetic channel. In this model, the effects of electric double layer (EDL) on axial transport are taken into account using exact solutions of the Poisson-Boltzmann equation. The second simpler model, which is approachable analytically, assumes that the EDLs are confined to near-wall regions. Using a characteristics analysis, we showed that the latter model captures concentration polarization (CP) effects and provides useful insight into its dynamics. Two distinct CP regimes are identified: CP with propagation in which enrichment and depletion shocks propagate outward; and CP without propagation where polarization effects stay local to micro-nanochannel interfaces. The existence of each regime is found to depend on a nanochannel Dukhin number and mobility of the co-ion nondimensionalized by electroosmotic mobility. Interestingly, microchannel dimensions and axial diffusion are found to play an insignificant role in determining whether CP propagates. The steady state condition of propagating CP is shown to be controlled by channel heights, surface chemistry and co-ion mobility instead of the reservoir condition. Both models are validated against experimental results in Part II of this two paper series.