双曲次扩散阻抗
Hyperbolic subdiffusive impedance
摘要：
本文利用具有分数阶时间导数的双曲型次扩散方程（广义Cattaneo方程）研究了电解质在存在次扩散的介质中的输运过程。在该模型中，通量相对于浓度梯度在非零时间内延迟。特别地，在电场的大脉动和小脉动的限制下，我们得到了空间有限样品的电化学亚扩散阻抗公式。在样品外壁处的边界条件取为次扩散通量和被输送颗粒浓度的线性组合的一般形式。我们还讨论了方程参数（子扩散参数和延迟时间）对奈奎斯特阻抗图的影响。
英文摘要：
We use the hyperbolic subdiffusion equation with fractional time derivatives (the generalized Cattaneo equation) to study the transport process of electrolytes in media where subdiffusion occurs. In this model the flux is delayed in a non-zero time with respect to the concentration gradient. In particular, we obtain the formula of electrochemical subdiffusive impedance of a spatially limited sample in the limit of large and of small pulsation of the electric field. The boundary condition at the external wall of the sample are taken in the general form as a linear combination of subdiffusive flux and concentration of the transported particles. We also discuss the influence of the equation parameters (the subdiffusion parameter and the delay time) on the Nyquist impedance plots.
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