基于均匀化的流体饱和变形多孔介质中离子迁移的双尺度模拟
Homogenization based two-scale modelling of ionic transport in fluid saturated deformable porous media
摘要：
研究了双组分电解质饱和变形多孔介质的均匀化问题。与微观尺度相关的模型描述了介质的稳定状态，同时反映了基本的物理现象，即在小的外部静电场和缓慢流动的假设下，在稀牛顿溶剂中的电化学相互作用。均匀化被应用到一个线性化的微观模型，其中的热力学平衡表示的参考状态。由于量纲分析，缩放的粘度和介电常数被引入，使极限模型保留与孔径和双电层厚度相关联的特征长度。均质化模型由两个弱耦合部分组成：电解质的流动可以用两种离子的全局压力和流动电位来求解，而不依赖于随后计算的作用于孔壁上的流体应力的固相变形。双尺度模型已在SfePy有限元软件中实现。数值结果表明，均匀化系数的微观结构孔隙率的依赖性。借助于均匀化的校正结果，可以从宏观解重构局部代表性单元中的微观响应。
英文摘要：
The paper deals with the homogenization of deformable porous media saturated by two-component electrolytes. The model relevant to the microscopic scale describes steady states of the medium while reflecting essential physical phenomena, namely electrochemical interactions in a dilute Newtonian solvent under assumptions of a small external electrostatic field and slow flow. The homogenization is applied to a linearized micromodel, whereby the thermodynamic equilibrium represents the reference state. Due to the dimensional analysis, scaling of the viscosity and electric permitivity is introduced, so that the limit model retains the characteristic length associated with the pore size and the electric double layer thickness. The homogenized model consists of two weakly coupled parts: the flow of the electrolyte can be solved in terms of a global pressure and streaming potentials of the two ions, independently of then the solid phase deformations which is computed afterwards for the fluid stress acting on pore walls. The two-scale model has been implemented in the SfePy finite element software. The numerical results show dependence of the homogenized coefficients on the microstructure porosity. By virtue of the corrector result of the homogenization, microscopic responses in a local representative cell can be reconstructed from the macroscopic solutions.
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