Fluid energy theory of membrane

Membrane science is the key strategy to solve water shortage in the future, and its essence is energy and mass transfer. Due to the complexity and variety of the internal structure of membrane, the energy transfer theory of membrane is still a black box theory. Herein, a new fluid mechanics principle is introduced to establish the energy fluid theory of membrane, which is translated into the energy formula: such as the initial total pressure difference (ΔP), the flow rate of fluid exiting the membrane (v₁ and v₂), fluid density (ρ), and energy consumption by salt resistance (NSR): { [Formula: see text] +12ρv₂³}. The theoretical framework is not only helpful for the data analysis of the energy transfer process of membranes, but also helps to allow for more in-depth and specific theoretical research. For instance, the relationship between NSR and the concentration difference (C) of salt can be expressed as NSR = aC^b (a-product constant, b-exponential constant, R²>0.99). Hence, the basic theory can not only be widely applied to a variety of membranes with complex internal structure, but also have a profound impact on the application and research of membrane science.