A DYNAMIC MODEL OF POLYELECTROLYTE GELS
A DYNAMIC MODEL OF POLYELECTROLYTE GELS
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DOI：
10.1137/110855296
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发表时间：
2013-01-01
影响因子：
1.9
通讯作者：
Calderer, Maria-Carme
中科院分区：
文献类型：
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作者：
Mori, Yoichiro;Chen, Haoran;Calderer, Maria-Carme
我们推导了聚电解质凝胶的机械和电化学耦合效应的模型。我们假设浸泡在流体域中的凝胶是固体聚合物组分和流体的不可混溶和不可压缩的混合物。随着凝胶的膨胀和下沉，凝胶-流体界面可以移动。我们的模型由聚合物和凝胶流体组分的质量和线性动量平衡的偏微分方程组、周围流体区域的Navier-Stokes方程和整个区域的离子浓度的Poisson-Nernst-Planck方程组成。此外，还补充了一类新颖而通用的边界条件，这些边界条件表示了移动的凝胶-流体界面上的质量和线性动量平衡。我们的边界条件包括早期研究中提出的渗透率边界条件。根据热力学第二定律，我们的模型的一个显著特征是它满足自由能量耗散恒等式。我们还利用边界层分析表明，在我们的模型中采用电中和极限，自然地产生了建立良好的平衡的Donnan条件。
We derive a model of the coupled mechanical and electrochemical effects of polyelectrolyte gels. We assume that the gel, which is immersed in a fluid domain, is an immiscible and incompressible mixture of a solid polymeric component and the fluid. As the gel swells and deswells, the gel-fluid interface can move. Our model consists of a system of partial differential equations for mass and linear momentum balance of the polymer and fluid components of the gel, the Navier-Stokes equations in the surrounding fluid domain, and the Poisson-Nernst-Planck equations for the ionic concentrations on the whole domain. These are supplemented by a novel and general class of boundary conditions expressing mass and linear momentum balance across the moving gel-fluid interface. Our boundary conditions include the permeability boundary conditions proposed in earlier studies. A salient feature of our model is that it satisfies a free energy dissipation identity, in accordance with the second law of thermodynamics. We also show, using boundary layer analysis, that the well-established Donnan condition for equilibrium arises naturally as a consequence of taking the electroneutral limit in our model.