Modified Kedem–Katchalsky equations for osmosis through nano-pore

• Published in: Desalination Vol. 399; pp. 47 - 52
• Main Authors: Shu, Liangsuo, Liu, Xiaokang, Li, Yingjie, Yang, Baoxue, Huang, Suyi, Lin, Yixin, Jin, Shiping
• Format: Journal Article
• Language: English
• Published: Elsevier B.V 01.12.2016
• Subjects: Aquaporin; Coefficients; Desalination; K–K equations; Mathematical analysis; Mathematical models; Membranes; Nanostructure; Osmosis; Osmotic pressure coefficient; Primary filtration coefficient; Reflection coefficient; Secondary selectivity rate; Primary filtration coefficient; Osmotic pressure coefficient; Reflection coefficient; Secondary selectivity rate; K–K equations; Aquaporin
• ISSN: 0011-9164; 1873-4464
• DOI: 10.1016/j.desal.2016.08.011

Kedem–Katchalsky (K–K) equations provide an important model in analyzing the osmosis in both biological systems and membrane technology, including reverse osmosis for desalination. However, some experiments have shown that it is not able to accurately describe the osmosis through nano-pores. The most significant problem is that the two reflection coefficients in two of the K–K equations are not equal to one another. In this work, three new parameters, osmotic pressure coefficient, primary filtration coefficient and secondary selectivity rate, were introduced to replace the reflection coefficient in the K–K equations. Using an analytical method based on molecular dynamics, the quantitative relationship between osmotic pressure coefficient and the molecule size was obtained. This quantitative relationship was verified by comparing the theoretical results with the reported experimental data of aquaporin osmosis. The theoretical predictions agreed well with experimental results, showing high accuracy of this model. This work is expected to pave the way for a better understanding of osmosis in bio-systems and to inspire new ideas in designing new membranes with better performance. •Modified Kedem–Katchalsky equations for osmosis through nano-pore are proposed.•Osmotic pressure coefficient of a solute was found to be chiefly affected by the entrance of the pore.•The passing rate of a solute can be affected by both the entrance and the selectivity filter in the pore.