Flow and streaming potential of an electrolyte in a channel with an axial temperature gradient
Flow and streaming potential of an electrolyte in a channel with an axial temperature gradient
复制标题
DOI：
10.1017/jfm.2016.844
复制
发表时间：
2012-11
影响因子：
3.7
通讯作者：
M. Dietzel;S. Hardt
中科院分区：
文献类型：
--
作者：
M. Dietzel;S. Hardt
研究了轴向温度梯度对压力驱动对称电解质在狭缝通道中的流动分布和诱导流势的影响。基于非等温的能斯特-普朗克方程和润滑近似中的泊松方程，导出了双电层（EDL）中离子分布的表达式。发现热电泳离子运动和温度相关的电泳离子迁移率随着温度的升高而增加了局部EDL厚度，而温度相关的介电常数则使EDL缩小。在debye - h<s:1> ckel近似中，求解了具有相应电体力项的Navier-Stokes方程。导出了非等温条件下的流场和诱导流场的解析表达式。结果表明，在这种情况下，感应电场是至少七个单独贡献的线性叠加。对于非常宽的通道，只有当受到温度梯度（Soret平衡）时通常存在于大块电解质中的热电场以及传统的压力诱导流场是重要的。与直觉相反的是，对于后者，虽然仍然受到介电常数和局部盐浓度的温度依赖性的影响，但粘度，菲克扩散系数和离子电迁移率的温度依赖性完全相互抵消。对于窄通道，五个额外的贡献是相关的，它们-类似于Soret电压-在外部施加的压力梯度被移除的情况下不会消失。第一个是由温度依赖的电泳离子迁移率和离子与表面壁电荷的相互作用之间的相互作用所驱动的选择性热电迁移引起的。这种非平流效应在极端限制下达到最大。对于宽度与EDL厚度相同数量级的通道，四种热渗透效应变得显著。除了众所周知的热渗透（由于（扩展的）Korteweg-Helmholtz力中介电常数的温度依赖性）外，还证明了-与等温条件相比-热梯度使EDL中的离子云脱离机械平衡。在这种情况下，研究表明，热泳动离子（即离子的固有索雷特效应）和温度相关的离子电迁移率以及温度相关的介电常数不仅导致EDL电位的轴向梯度，而且同时导致热源压力，使流体进入平流运动。相应的现象以前没有在文献中讨论过，可以解释为EDL内明显的热诱导滑移速度。随后，与这种热渗透流动相关的离子平流可能诱导出与更常规的热效应所引起的热电场相似的数量级。
The effect of an axial temperature gradient on the flow profile and the induced streaming potential of a pressure-driven symmetric electrolyte in a slit channel is investigated. Based on the non-isothermal Nernst–Planck equations, as well as the Poisson equation in the lubrication approximation, expressions for the ion distribution in the electric double layer (EDL) are derived. It is found that thermophoretic ion motion and a temperature-dependent electrophoretic ion mobility increase the local EDL thickness with temperature, whereas a temperature-dependent permittivity shrinks the EDL. Within the Debye–Hückel approximation, the Navier–Stokes equation with the corresponding electric body force terms is solved. Analytical expressions for the flow profile and the induced (streaming) field under non-isothermal conditions are derived. It is shown that for such a situation the induced electric field is the linear superposition of at least seven individual contributions. For very wide channels, only the thermoelectric field typically present in bulk electrolytes when subjected to a temperature gradient (Soret equilibrium) as well as the conventional pressure-induced streaming field are of importance. Counterintuitively, for the latter, while still being affected by the temperature dependence of the dielectric permittivity and local salt concentration, the temperature dependencies of the viscosity, Fickian diffusion coefficients and ion electromobilities exactly cancel each other. For narrow channels, five additional contributions become relevant, which – similar to the Soret voltage – do not vanish in the case that the externally applied pressure gradient is removed. The first is caused by selective thermo-electromigration driven by the interplay between the temperature-dependent electrophoretic ion mobility and the interaction of the ions with the surface wall charge. This non-advective effect is at its maximum under extreme confinement. For channels whose widths are of the same order as the EDL thickness, four thermoosmotic effects become significant. Besides the well-known thermoosmosis due to the temperature dependence of the dielectric permittivity in the (extended) Korteweg–Helmholtz force, it is demonstrated that – by contrast to isothermal conditions – a thermal gradient renders the ion cloud in the EDL out of mechanical equilibrium. In this context it is shown that a thermophoretic ion motion (i.e. the intrinsic Soret effect of the ions) and a temperature-dependent ion electromobility as well as a temperature-dependent permittivity not only cause an axial gradient of the EDL potential, but simultaneously lead to a pressure of thermal origin, which sets the fluid into an advective motion. Corresponding phenomena were not previously discussed in the literature and may be interpreted as an apparent, thermally induced slip velocity within the EDL. Subsequently, the ion advection affiliated with such thermoosmotic flow may induce a thermoelectric field of a similar order of magnitude to that caused by more conventional thermal effects.