Dynamics of osmotic flows

The paper presents a theoretical model that allows the dynamic description of osmotic flows through a semi-permeable interface. To depict the out-of-equilibrium transfer, the interface is represented by an energy barrier that colloids have to overcome to be transmitted to the other side of the membrane. This energy barrier thus represents the selectivity of the membrane. Furthermore, this energy barrier induces additional force terms in the momentum and the mass balances on the fluid and the colloids phases. Based on a two- fluid model, these forces can reproduce the physics of the osmotic flow without the use of the semi-empirical laws of non-equilibrium thermodynamics. It is shown that a decrease in local pressure near the interface initiates osmosis. When these balance equations are solved in a transient mode, the dynamic of the osmotic flow can be described. The paper illustrates these potentialities by showing the dynamic of an osmosis process occurring in the absence of transmembrane pressure and both the dynamic of the reverse osmosis with a constant flow through the membrane. A simulation reproducing the dynamic of the Abb\'e Nollet experiment is presented. The role played by the colloid-membrane interactions on the osmotic flow mechanism and on the counter osmotic pressure is analyzed and discussed in great details.