Model of osmosis in a single-file pore.

Single-file transport of water and other small molecules through narrow pores in osmosis has drawn considerable attention in recent years due to its extensive application in biology and industry. In this work, we propose a discrete model to describe nonideal osmosis through single-file pores. Every site is assumed to be occupied by a molecule according to experiments and simulations. Hence, a dense chain can always be found, and collective hopping is the only movement method enabling the molecular chain to move. The roles of solute in osmosis are clarified in this model. Those molecules reflected at the pore entrance produce osmotic pressure, and those inside the pore contribute to the flow resistance of the molecular chain. The solute molecules that can enter the pore but cannot penetrate it may significantly reduce the osmotic flux, although they are all rejected by the pore. This conclusion can help to clarify the emerging debate about whether the reflection coefficient of the fully rejected solute can be less than 1. The design of highly efficient membrane pores may also benefit from this study.