Ion transport through deformable porous media: derivation of the macroscopic equations using upscaling
Ion transport through deformable porous media: derivation of the macroscopic equations using upscaling
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DOI：
10.1007/s40314-016-0321-0
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发表时间：
2017-09-01
影响因子：
2.6
通讯作者：
Mikelic, Andro
中科院分区：
文献类型：
--
作者：
Allaire, Gregoire;Bernard, Olivier;Mikelic, Andro
我们研究了均匀化（或放大）的多组分电解质在稀牛顿溶剂中通过可变形多孔介质的运输。考虑了流动与结构变形之间的孔隙尺度相互作用（用线性化弹性方程建模）。经过仔细的无量纲化过程，我们首先考虑所谓的平衡解，在没有外力的情况下，速度和扩散通量消失，静电势是泊松-玻尔兹曼方程的解。当运动由一个小的静电场和小的流体动力和弹性力，我们使用奥布莱恩的论点推导出一个线性模型。然后，我们执行这些线性化方程的一个合适的选择的时间尺度的均匀化。事实证明，多孔介质的变形是弱耦合的电动力学系统的意义上，它不影响电动力学，虽然后者产生的渗透压项的力学方程。因此，有效张量满足Onsager性质，即对称正定。
We study the homogenization (or upscaling) of the transport of a multicomponent electrolyte in a dilute Newtonian solvent through a deformable porous medium. The pore scale interaction between the flow and the structure deformation (modeled by linearized elasticity equations) is taken into account. After a careful adimensionalization process, we first consider so-called equilibrium solutions, in the absence of external forces, for which the velocity and diffusive fluxes vanish and the electrostatic potential is the solution of a Poisson-Boltzmann equation. When the motion is governed by a small static electric field and small hydrodynamic and elastic forces, we use O'Brien's argument to deduce a linearized model. Then we perform the homogenization of these linearized equations for a suitable choice of time scale. It turns out that the deformation of the porous medium is weakly coupled to the electrokinetics system in the sense that it does not influence electrokinetics although the latter one yields an osmotic pressure term in the mechanical equations. As a consequence, the effective tensor satisfies Onsager properties, namely is symmetric positive definite.