Concentration Polarization (β Modulus) Calculator
Determine boundary layer solute accumulation factor ($\beta = C_m / C_b$), film mass transfer coefficient ($k$), and surface scaling potential.
Cross-Flow Velocity & Flux
Polarization Factor & Wall Concentration
Recommended Tools & Equipment
Tested hardware and components for high reliability
Film Theory & Concentration Polarization
As permeate water flows perpendicularly through an RO membrane sheet, rejected salt ions are left behind at the membrane surface. Because fluid velocity approaches zero right at the solid membrane wall, rejected ions must diffuse backward into the bulk crossflow against the convective drag of incoming water.
The Polarization Modulus ($eta$)
The ratio of solute concentration at the active membrane wall ($C_m$) to the bulk stream concentration ($C_b$) is governed by the film theory equation: $$\beta = \frac{C_m}{C_b} = \exp\left(\frac{J_w}{k}\right)$$ Where $J_w$ is permeate flux and $k$ is the mass transfer coefficient. Elevated $\beta$ values increase local osmotic pressure, lower net driving pressure, reduce salt rejection, and precipitate mineral scale directly onto the membrane.