Concentration polarization (CP) is the accumulation of rejected solutes near the membrane surface that results in the formation of a ‘polarized layer.’ This phenomenon increases the osmotic pressure at the membrane surface, resulting in flux decline from a decreased effective driving force across the membrane. The effect of CP on membrane performance can be approximated with the use of film theory as detailed below [1].

Note: is generally reported between 0 and 100%, but it should be a value between 0 and 1 for this calculation. Details on determining can be found __here__.

Note: Details for calculating can be found below. The most widely used equation in a cross-flow system is equation 1.1. for laminar flow. Please note that, generally, the value is around 100 L m^{-2} h^{-1} for a cross-flow velocity of 0.8-1.6 L min^{-1}. **Turbulent condition is defined for Re > 10**^{4} and laminar condition for Re < 10^{4}

With , , , , and assuming

With , , , and assuming

- [1] Baker, R. W. Membrane Technology and Applications; John Wiley & Sons, Ltd.: New York, 2012
- [2] Imbrogno, A., & Schäfer, A. I. (2019). Comparative study of nanofiltration membrane characterization devices of different dimension and configuration (cross flow and dead end). Journal of Membrane Science, 585, 67-80.
- [3] G. Schock, A. Miquel, Mass transfer and pressure loss in spiral wound modules, Desalination, 64 (1987) 339-352.