Modified Kedem-Katchalsky equations for osmosis through nano-pore

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.