Modeling of multicomponent mass transfer across polymer films using a thermodynamically consistent formulation of the Maxwell-Stefan equations in terms of volume fractions
Modeling of multicomponent mass transfer across polymer films using a thermodynamically consistent formulation of the Maxwell-Stefan equations in terms of volume fractions
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DOI：
10.1016/j.polymer.2011.06.042
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发表时间：
2011-08-18
期刊：
影响因子：
4.6
通讯作者：
Paul, Donald R.
中科院分区：
文献类型：
--
作者：
Ribeiro, Claudio P., Jr.;Freeman, Benny D.;Paul, Donald R.
麦克斯韦-斯特凡 (MS) 公式相对于菲克定律在描述多组分传质方面的优势已得到广泛认可。然而，在其原始形式中，MS 方程是用摩尔分数编写的，如果其中一种组分是聚合物，则摩尔分数的定义不明确。为了克服这个问题，提出了一种以体积分数形式编写的 MS 方程的修订公式。由此产生的方程满足 Gibbs-Duhem 限制，并且与多组分 Flory-Huggins 理论完全一致，因为我们避免了有关渗透剂或聚合物链段尺寸的任何假设。该公式与 Flory-Huggins 模型相结合，得出用于模拟纯组分和二元混合物跨聚合物膜稳态传质的通用表达式。所提出的 MS 公式用于分析交联聚环氧乙烷膜对二氧化碳/乙烷混合物的分离。对于该特定系统，在 T >= 25 摄氏度时，无需输入任何多组分渗透数据，即可预测混合气体渗透系数，平均偏差小于 5%。 (C) 2011 Elsevier Ltd. 保留所有权利。
The advantages of the Maxwell-Stefan (MS) formulation over Fick's law to describe multicomponent mass transfer are well recognized. However, in its original form, the MS equations are written in terms of mole fractions, which are ill-defined if one of the components is a polymer. To overcome this problem, a revised formulation of the MS equations written in terms of volume fractions is proposed. The resulting equations satisfy the Gibbs-Duhem restriction and are fully consistent with the multicomponent Flory-Huggins theory in the sense that we avoid any assumption regarding the size of the penetrants or of the polymer segments. This formulation is combined with the Flory-Huggins model to derive general expressions for modeling steady-state mass transfer across polymer films for both pure components and binary mixtures. The proposed MS formulation is used to analyze the separation of carbon dioxide/ethane mixtures by a cross-linked poly(ethylene oxide) membrane. For this particular system, at T >= 25 degrees C, mixed-gas permeability coefficients can be predicted with an average deviation of less than 5% without any input from multicomponent permeation data. (C) 2011 Elsevier Ltd. All rights reserved.