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 Concentration polarization

Basics

  Definition

 • Concentration  Polarization

 • Resistance in Series Model

 • Cake Layer Compaction

 • Dynamic Membrane

 • Back Transport

   - Brownian diffusion

   - Shear induced

   - Inertial lift

   - Effect on cake layer

 • Critical Flux

    - Concept

    - Measurement

 • TMP vs Flux

 • Flux vs Fouling

 • Constant Flux vs Constant Pressure

 • Fouling Roadmap

   - Constant flux mode

   - Constant pressure

   - Sudden TMP rise

 • Temperature effect on flux

 • Permeability effect on membrane performance

 

Effect of membrane surface property on membrane performance

 • Zeta potential

 • Contact Angle

 • Surface roughness

 • Pore size and its  distribution

 • Internal pore connectivity

 • Limitation of theory

 

Reference

 

 

   When liquid permeates through membrane, particles (or solutes) are rejected by membrane and form a layer with high particle/solute concentration near the membrane surface. Due to the high particle concentration in the layer, particles tend to diffuse back to the bulk as long as they are not fixed in gel/cake layer. The concentration profile settles at the equilibrium between convective particle transport to membrane surface and diffusive particle back transport to the bulk solution as illustrated in Fig. 1. This is so called concentration polarization phenomenon that fundamentally limits the membrane performance (Porter, 1972).

 

   The flux, J, can be calculated by balancing the convective particle transport toward membrane and the diffusive particle back transport as shown in equation (1).

 

                                             ----------------------------------------- (1)

 where

     J     =  water flux at steady state (m/s)

     C    =  particle concentration (mg/L)

     x     =  distance from membrane surface (m)

     Deff =  effective diffusion coefficient (m2/s)

 

  The minus sign in above equation is used to reflect the negative concentration gradient along the x-axis. The effective diffusion coefficient, Deff, conceptually includes the effects from thermodynamic diffusion, shear induced diffusion, and all other hydrodynamic forces that moves particles away from membrane surface. The particle back transport velocity is discussed in detail here.

 

   The equation (1) can be integrated using the boundary conditions at steady state, i.e. (x=0, C=CG) and (x=d, C=CB), where d is a boundary layer thickness (m),  CG and CB are particle concentration in gel layer and in bulk, respectively.

 

                                      ----------------------------------------- (2)

 

According to this equation, steady state flux, JSS, increases when boundary layer thickness, d, decreases and the effective diffusion coefficient, Deff, increases. The thinner boundary layer and higher Deff can be achieved in a given condition by increasing cross-flow velocity on membrane surface in general (Bian, 2000).

 

                                Fig. 1. Concentration polarization model

 

 

Ó 2011 by S. Yoon. All rights reserved.