Osmosis and reverse osmosis in fine-porous charged diaphragms and membranes
Osmosis and reverse osmosis in fine-porous charged diaphragms and membranes
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DOI：
10.1016/0001-8686(95)00246-m
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发表时间：
1995-09
影响因子：
15.6
通讯作者：
A. Yaroshchuk
中科院分区：
文献类型：
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作者：
A. Yaroshchuk
细孔带电膜和隔膜中的渗透和反渗透理论以演绎方式提出，并考虑了几个结构良好的层次。分析从不可逆热力学的不连续版本开始，其中膜被认为是一个绝对的黑匣子，不需要任何有关其内部结构的信息。然而，作为通用性的权衡，热力学力必须很小。从对各种现象学系数的数量级的相当明显的假设出发，得出了许多定性结论。在电解质混合物的情况下，这些结论出奇地多且重要，包括反射系数大于1和强负渗透的预测。这两种异常现象都得到了实验结果的证实。下一步是引入“均匀黑”盒，即宏观上均质的膜，其内部结构未明确。这允许采用不可逆热力学的连续版本，从而允许放弃小热力学力的限制。在二元电解质的情况下，对于表观渗透压和反渗透的问题获得求积的一般解，并且对于渗透问题获得非常准确的求积的近似解。将一些理论预测与孔径为 8 nm 的径迹蚀刻膜中二元电解质反渗透的实验数据进行了比较。在电解质混合物的情况下，在反渗透的极限情况下以足够大的佩克莱特数进行半定量渐近分析，并且在混合物中一种主要电解质的特定情况下，获得精确的求积解。这些分析使得预测许多重要的规律成为可能，这些规律与跨各种带电多孔膜的压力驱动传输或三元电解质混合物的实验数据有关。理论与实验之间具有良好的定性一致性。下一步是在一般毛细管模型范围内指定唯象系数。这使得盒子呈灰色但不透明，因为毛细管横截面的形状以及表面力的性质尚未指定。根据离子分布和扩散系数导出的唯象系数的一般表达式使得可以对孔隙内离子分布不均匀性的影响进行定性分析。最后，引入毛细管空间电荷模型，使分析完全机械化。考虑了多种方法来近似描述细孔中双电层重叠扩散部分的结构。由于微观非均质性的定性影响似乎不依赖于孔隙几何形状的细节，因此对狭缝状毛细管进行了示例数值计算，其中泊松-玻尔兹曼方程的求积有通解。引入了导电凝胶中更通用的孔隙模型，试图从不可逆热力学角度定量描述阳离子交换膜的完整表征结果。
The theory of osmosis and reverse osmosis in fine-porous charged membranes and diaphragms is presented in a deductive way with several well-structured levels of consideration. The analysis starts from the discontinuous version of irreversible thermodynamics where the membrane is considered as an absolutely black box without any information needed about its internal structure. As a trade-off for generality, however, the thermodynamic forces must be small. A number of qualitative conclusions is drawn proceeding from rather evident assumptions about the order of magnitude of various phenomenological coefficients. In the case of electrolyte mixtures those conclusions turn out surprisingly numerous and non-trivial including predictions of reflection coefficients larger than unity and strong negative osmosis. Both those anomalous phenomena are confirmed by experimental findings. The next step is the introduction of a ‘uniformly black’ box, namely a macroscopically homogeneous membrane with otherwise unspecified internal structure. That permits to employ the continuous version of irreversible thermodynamics thus allowing to drop the restriction of small thermodynamic forces. In the case of binary electrolytes general solutions in quadratures are obtained for the problems of apparent osmotic pressure and of reverse osmosis, and a very accurate approximate solution in quadratures is obtained for the problem of osmosis. Some of the theoretical predictions are compared with experimental data on the reverse osmosis of binary electrolytes in track-etched membranes with the pore size of 8 nm. In the case of electrolyte mixtures a semi-quantitative asymptotic analysis is performed in the limiting case of reverse osmosis at sufficiently large Péclet numbers, and in the particular case of one dominant electrolyte in the mixture an exact solution in quadratures is obtained. Those analyses make possible to predict a number of non-trivial regularities that are confronted with experimental data on the pressure-driven transport or ternary electrolyte mixtures across various charged porous membranes. A good qualitative agreement between the theory and experiments is recorded. The next step is the specification of phenomenological coefficients within the scope of a general capillary model. That makes the box grey but not transparent, yet, as the shape of capillary cross-section as well as the nature of surface forces are not specified. General expressions for phenomenological coefficients derived in terms of ion distribution and diffusion coefficients make possible a qualitative analysis of the effect of inhomogeneity of ion distribution inside pores. Finally, the capillary space charge model is introduced making the analysis completely mechanistic. Several approaches are considered to the approximate description of the structure of overlapped diffuse parts of double electric layers in fine pores. Since qualitative effects of microscopic heterogeneity appear to be not dependent on the details of the pore geometry sample numerical calculations are performed for slit-like capillaries where there is a general solution of Poisson-Boltzmann equation in quadratures. A more general model of pores in an electrically conducting gel is introduced in an attempt to quantitatively describe the results of complete characterization of cation-exchange membranes in terms of irreversible thermodynamics.