Krishna Rajamani
Van 't Hoff Institute for Molecular Sciences, University of Amsterdam, Science Park 904, 1098 XH Amsterdam, The Netherlands.
ACS Omega. 2019 Sep 5;4(12):15255-15264. doi: 10.1021/acsomega.9b02255. eCollection 2019 Sep 17.
The pervaporation of binary alcohol/water mixtures across polymeric membranes is modeled by combining the Maxwell-Stefan (M-S) diffusion formulation with the Flory-Huggins (F-H) description of sorption equilibrium. The combined M-S/F-H model shows that the flux of each penetrant species is coupled to the driving force of its partner penetrant. Two types of coupling contributions can be distinguished: (i) coupling arising out of correlated motions of penetrants in the polymer matrix and (ii) thermodynamic coupling. The focus of this article is on the contribution of thermodynamic coupling, which is quantified by the set of coefficients , where , the activity of species , is dependent on the volume fractions ϕ ,ϕ , of both penetrants in the polymeric membrane. Detailed analyses of published experimental data for pervaporation of ethanol/water feed mixtures of varying compositions in both hydrophobic (poly(dimethylsiloxane)) and hydrophilic (cellulose acetate, polyimide, and polyvinyl alcohol/polyacrylonitrile composite) membranes show that in all cases, the cross-coefficients Γ ( ≠ ) are negative and may attain large magnitudes in relation to the diagonal elements Γ . The net result is that the permeation fluxes of each penetrant are suppressed by its partner, resulting in mutual slowing down of permeation fluxes. If thermodynamic coupling effects are ignored, significantly higher fluxes are anticipated than those that are experimentally observed.
通过将麦克斯韦-斯蒂芬（M-S）扩散公式与弗洛里-哈金斯（F-H）吸附平衡描述相结合，对二元醇/水混合物在聚合物膜上的渗透蒸发进行建模。结合的M-S/F-H模型表明，每种渗透物的通量与其伙伴渗透物的驱动力相互耦合。可以区分两种类型的耦合贡献：（i）聚合物基质中渗透物的相关运动引起的耦合，以及（ii）热力学耦合。本文的重点是热力学耦合的贡献，其由系数集量化，其中，物种的活度取决于聚合物膜中两种渗透物的体积分数ϕ 、ϕ 。对已发表的关于不同组成的乙醇/水进料混合物在疏水（聚二甲基硅氧烷）和亲水（醋酸纤维素、聚酰亚胺和聚乙烯醇/聚丙烯腈复合材料）膜上渗透蒸发的实验数据进行详细分析表明，在所有情况下，交叉系数Γ （≠ ）均为负，并且相对于对角元素Γ 可能达到较大值。最终结果是，每种渗透物的渗透通量都受到其伙伴的抑制，导致渗透通量相互减慢。如果忽略热力学耦合效应，预计通量将比实验观察到的通量高得多。
