Concentration polarization coefficient

In the following sub-section, concentration polarization coefficient (CPC) and inhibition coefficient (IC) will be introduced separately in order to show their different contribution on the overall permeance reduction. 

In order to provide a quantitative indication of the polarization level, several different concentration polarization coefficients can be found in the literature. The most used definitions are summarized in Table 14.1. The first thing to 

C = molar concentration, x = molar fraction, N=molar flux, JV =molar flux without polarization. 

Wang et alP uses a similar approach to define a concentration polarization coefficient, with the only difference that in their definition the coefficient is close to zero when the polarization is negligible. 

In order to link concentration polarization and membrane selectivity, Zhang et alP used the permeating fluxes in the definition of the coefficient. In the case where only one component is able to permeate through the membrane, this definition is very useful, because it does not depend on the particular permeation mechanism and, thus, is general. However, this approach is valid only for a binary mixture and cannot simply be generalized for a multi-component mixture. Additionally, the overall coefficient varies between zero and infinity, therefore not allowing an immediate perception of the polarization level. 

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He et al used a binary mixture-based film model to perform a theoretical analysis on the concentration polarization in a generic membrane. They defined a concentration polarization coefficient for both the two species involved in the separation as the ratio of the actual flux to the ideal one (without polarization), quantifying the polarization effect by means of the ratio of the actual fluxes of the components. Although this is a simplified approach that cannot be generalized to multi-component systems, nevertheless, under some operating conditions, the authors predicted a significant influence of the external mass transfer on the process. 

Table 14.1 The most common concentration polarization coefficients in literature...

All of the considerations made in the previous section lead to the necessity of defining a concentration polarization coefficient that could be directly connected to specific permeation quantities.Here, this approach will be direct to hydrogen permeation through Pd-based membranes. 

Since Sieverts law is valid or the deviation from it is small in most of the operating conditions under which the Pd-based membranes work, the square root difference of hydrogen partial pressure (Sieverts driving force) seems a good choice for the characteristic driving force to define the concentration polarization coefficient. 

Definition of Concentration Polarization Coefficient in the Presence of Inhibition... 

The definition of concentration polarization coefficient adopted in the previous section (eqns (14.8) to (14.10)) is general and, thus, can be conveniently applied to different situations. In particular, CPC can be also used in a situation in which permeation is affected by inhibition, as reported in eqn (14.13) in terms of both driving forces and permeances ... 

According to their definition, these coefficients - namely, concentration polarization coefficient CPC), inhibition coefficient IC) and the overall... 

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