AN ASYMPTOTIC ANALYSIS OF SPACE CHARGE LAYERS IN A MATHEMATICAL MODEL OF A SOLID ELECTROLYTE

被引:0
|
作者
Keane, Laura M. [1 ]
Moyles, Iain R. [1 ]
机构
[1] York Univ, Dept Math & Stat, Toronto, ON M3J 1P3, Canada
基金
加拿大自然科学与工程研究理事会;
关键词
lithium-ion battery; solid electrolyte; space charge layer; mathematical modeling; asymptotic analysis; numerical simulation; ELECTROCHEMICAL MODEL; LITHIUM; PERFORMANCE; NANOWIRES; REDUCTION; SILICON;
D O I
10.1137/23M1580954
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
We review a model for a solid electrolyte derived under thermodynamics principles. We nondimensionalize and scale the model to identify small parameters where we identify a scaling that controls the width of the space charge layer in the electrolyte. We present asymptotic analyses and numerical solutions for the one-dimensional zero charge flux equilibrium problem. We introduce an auxiliary variable to remove singularities from the domain in order to facilitate robust numerical simulations. From the asymptotics, we identify three distinct regions: bulk, boundary, and intermediate layers. The boundary and intermediate layers form the space charge layer of the solid electrolyte, which we can further distinguish as strong and weak space charge layers, respectively. The weak space charge layer is characterized by a length, lambda , which is equivalent to the Debye length of a standard liquid electrolyte. The strong space charge layer is characterized by a scaled Debye length, which is larger than lambda . We find that both layers exhibit distinct behavior; we see quadratic behavior in the strong space charge layer and exponential behavior in the weak space charge layer. We find that matching between these two asymptotic regimes is not standard, and we implement a pseudomatching approach to facilitate the transition between the quadratic and exponential behaviors. We demonstrate excellent agreement between asymptotics and simulation.
引用
收藏
页码:1413 / 1438
页数:26
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