A thin double layer analysis of asymmetric rectified electric fields (AREFs)
A thin double layer analysis of asymmetric rectified electric fields (AREFs)
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DOI：
10.1007/s10665-021-10139-x
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发表时间：
2021-06
影响因子：
1.3
通讯作者：
Bhavya Balu;Aditya S. Khair
中科院分区：
文献类型：
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作者：
Bhavya Balu;Aditya S. Khair
我们使用微扰方法来分析的“不对称整流电场（AREF）”时产生的振荡电压施加在一个模型的电化学电池组成的二元，不对称的电解质由平面，平行，封闭电极的边界。AREF是指电解质内电势梯度的稳定分量，如Hashemi Amrei et.（Phys Rev Lett 121（18）：185504）。我们采用Poisson-Nernst-Planck框架在稀电解质中的离子输运，考虑到不等的离子扩散系数。我们考虑薄德拜层在数学上的奇异性和实际上的极限，其中是德拜长度，L是半胞的长度。“本体”电解质中的电势和离子强度的动力学（即，德拜层外）的德拜尺度输运的考虑得到的有效边界条件下求解。我们具体分析的情况下，当所施加的电压有一个频率相当于逆体离子扩散时间尺度，其中是双极扩散率，和离子扩散率。在这种情况下，AREF延伸到整个细胞的主体，在长度尺度上成比例变化，并且具有到的幅度。这是玻尔兹曼常数，T是温度，D是质子的电荷。我们得到了弱电压下的AREF的解析近似，其中是电压的幅值，AREF为。我们的渐近方案也被用来计算数值近似的AREF，是有效的，以几何大电压，。AREF的存在意味着带电胶体粒子在外加振荡电压下经历净电泳运动。此外，由离子扩散率的差异引起的体离子强度的梯度导致整流扩散泳颗粒运动。在这里，我们预测的刚性，球形，胶体颗粒的电泳和扩散电泳速度。扩散电泳速度的大小与电泳速度相当，因此可以显著影响AREF中的粒子运动。
We use perturbation methods to analyze the “asymmetric rectified electric field (AREF)” generated when an oscillating voltage is applied across a model electrochemical cell consisting of a binary, asymmetric electrolyte bounded by planar, parallel, blocking electrodes. The AREF refers to the steady component of the electric potential gradient within the electrolyte, as discovered via numerics by Hashemi Amrei et. al. (Phys Rev Lett 121(18):185504). We adopt the Poisson–Nernst–Planck framework for ion transport in dilute electrolytes, taking into account unequal ionic diffusivities. We consider the mathematically singular, and practically relevant, limit of thin Debye layers,, whereis the Debye length, andLis the length of the half-cell. The dynamics of the electric potential and ionic strength in the “bulk” electrolyte (i.e., outside the Debye layers) are solved subject to effective boundary conditions obtained from consideration of the Debye-scale transport. We specifically analyze the case when the applied voltage has a frequency comparable to the inverse bulk ion diffusion time scale,, whereis the ambipolar diffusivity, andare the ionic diffusivities. In this regime, the AREF extends throughout the bulk of the cell, varying on a lengthscale proportional to, and has a magnitude ofto leading order in. Here,is the Boltzmann constant,Tis temperature, andeis the charge on a proton. We obtain an analytical approximation for the AREF at weak voltages,, whereis the amplitude of the voltage, for which the AREF is. Our asymptotic scheme is also used to calculate a numerical approximation to the AREF that is valid up to logarithmically large voltages,. The existence of an AREF implies that a charged colloidal particle undergoes net electrophoretic motion under the applied oscillatory voltage. Additionally, a gradient in the bulk ionic strength, caused by the difference in ionic diffusivities, leads to rectified diffusiophoretic particle motion. Here, we predict the electrophoretic and diffusiophoretic velocities for a rigid, spherical, colloidal particle. The diffusiophoretic velocity is comparable in magnitude to the electrophoretic velocity, and can thus affect particle motion in an AREF significantly.