Modelling of Hydrodynamics and Mass Transport

Following the classical scheme, free transport of solutes and solvent in the boundary layer at the liquid-membrane interface and hindered transport of substances in the porous structure of the membrane material are described successively. 

Concentration polarization Convective transport and retention of solutes by the membrane results in an accumulation of species at wall. Local concentrations, C , are higher than in the bulk, Cb, and a back-diffusion from near the wall into the bulk liquid phase takes place. This is the so-called concentration polarization phenomenon (Fig. 12.1). A simple mass balance leads to the classical equation  

From this relation, it can be easily inferred that the phenomenon will be strongly dependent on  

The real rejection can be calculated from the observed rejection using Eqs. (12.1) to (12.3). 

As a general rule, concentration polarization will be all the more important as membrane permeability and liquid viscosity will be higher and solute diffusivity will be lower. This is the recison why its effects, ordinarily negligible for nanofiltration, appear to be of major importance during ultrafiltration. Under gel polarization conditions, i.e. in those cases where reaches a maximum gel value Cg (as an example with ultrafiltration of concentrated protein solutions). 

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