Concentration Polarization Calculator

Concentration polarization modulus, Cm/Cf

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].

  • unitless
  • L m-2 h-1
  • L m-2 h-1

  • unitless
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 > 104 and laminar condition for Re < 104

1. Feed-side mass transfer coefficient, , in thin rectangular channel in cross-flow

With , , , , and assuming

2. Feed-side mass transfer coefficient, , in circular stirred cell

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.