Department of Mechanical Engineering, IIT Kharagpur-721302, India.
Langmuir. 2010 Jul 6;26(13):11589-96. doi: 10.1021/la1009237.
In this article, we investigate the implications of ionic conductivity variations within the electrical double layer (EDL) on the streaming potential estimation in pressure-driven fluidic transport through narrow confinements. Unlike the traditional considerations, we do not affix the ionic conductivities apriori by employing preset values of dimensionless parameters (such as the Dukhin number) to estimate the streaming potential. Rather, utilizing the Gouy-Chapman-Grahame model for estimating the electric potential and charge density distribution within the Stern layer, we first quantify the Stern layer electrical conductivity as a function of the zeta potential and other pertinent parameters quantifying the interaction of the ionic species with the charged surface. Next, by invoking the Boltzmann model for cationic and anionic distribution within the diffuse layer, we obtain the diffuse layer electrical conductivity. On the basis of these two different conductivities pertaining to the two different portions of the EDL as well as the bulk conductivity, we define two separate Dukhin numbers that turn out to be functions of the dimensionless zeta potential and the channel height to Debye length ratio. We derive analytical expressions for the streaming potential as a function of the fundamental governing parameters, considering the above. The results reveal interesting and significant deviations between the streaming potential predictions from the present considerations against the corresponding predictions from the classical considerations in which electrochemically consistent estimates of variable EDL conductivity are not traditionally accounted for. In particular, it is revealed that the variations of streaming potential with zeta potential are primarily determined by the competing effects of EDL electromigration and ionic advection. Over low and high zeta potential regimes, the Stern layer and diffuse layer conductivities predominantly dictate the streaming potential variations whereas ionic advection governs the streaming potential characteristics over intermediate zeta potential regimes. It is also inferred that traditional considerations may grossly overpredict the magnitude of streaming potential for narrow confinements in which significant conductivity gradients may prevail across the EDL.
在本文中，我们研究了电双层（EDL）中离子电导率变化对狭窄约束下压力驱动流体传输中流动电势估计的影响。与传统考虑不同，我们不预先确定离子电导率，而是利用Gouy-Chapman-Grahame 模型来估计 Stern 层内的电势和电荷密度分布，从而通过使用无量纲参数（如 Dukhin 数）的预设值来估计流动电势。首先，我们将 Stern 层电导率量化为zeta 电势和其他描述离子物种与带电表面相互作用的相关参数的函数。接下来，通过调用 Boltzmann 模型来获得扩散层内阳离子和阴离子的分布，我们得到扩散层电导率。基于这两个与 EDL 的两个不同部分以及体相电导率相关的不同电导率，我们定义了两个单独的 Dukhin 数，它们是无量纲 zeta 电势和通道高度与 Debye 长度比的函数。我们根据上述考虑，推导了流动电势作为基本控制参数的函数的解析表达式。结果表明，与传统考虑相比，从本研究得出的流动电势预测存在有趣且显著的偏差，因为传统考虑中通常没有考虑可变 EDL 电导率的电化学一致估计。特别是，流动电势随 zeta 电势的变化主要由 EDL 电迁移和离子对流的竞争效应决定。在低和高 zeta 电势区域，Stern 层和扩散层电导率主要决定流动电势的变化，而在中间 zeta 电势区域，离子对流控制流动电势的特征。还推断出，传统考虑可能会严重高估狭窄约束下流动电势的幅度，因为在 EDL 中可能存在显著的电导率梯度。
