Pointwise permeability

Note If a pointwise permeability value P Is measured in the units of say 10 cm /cm -sec-cm Hg/cm, then multiplying this value of Pi by 76cm Hg/atm will yield the new value of Pi in 10 cm /cm -sec-atm/cm. The new value will be higher since the pressure difference Is now measured in the lower value of atm instead of the highervalue of cm Hg. 

Other convenient units for pointwise permeability are g-moles/ cm -sec-atm/cm., applicable to both liquids and gases. The conversion for gaseous pointwise permeabihty utilizes the value of 22,414 cm (STP) per gram-mole, and a value of 76 cm Hg/atm. Thus... 

It may be observed that the units for V" are the same as for both V/A and PiPy, whereby its usage Pj refers to the overall permeability rather than the pointwise permeability. That is, strictly speaking, the comparison is as follows, in the conventions adopted for units ... 

The parameter or variable V" will have the dimensions of permeability times pressure, as previously observed in terms of moles. However, in terms of the total gas volume permeated, and using the pointwise permeability and dealing with volume fractions, then V" would have the dimensions of... 

Note that a pointwise permeability is specified, which must be divided by the membrane thickness in order to obtain the overall permeability. The foregoing units may be converted to more convenient units by multiplying V" as previously calculated, as follows ... 

If Gy = Gy- is to be the molar flux of a component /, it follows that the units for the pointwise permeability coefficient P, necessarily are... 

For a pure gas, of a single component only, commonly used units for the membrane pointwise permeability P, for a pure component i are... 

In mixtures, the pressure dimension in the permeability coefficient becomes the partial pressure pp. That is, the pointwise permeability coefficient in a mixture will have the units or dimensions of... 

Apropos of Example 2.1, a membrane cell is to have the following pointwise permeabilities to components i and / ... 

For a membrane thickness of 10 p (10 microns or 10 x 10 cm), the pointwise permeabilities convert to overall permeabilities of... 

Permeability may be expressed in different units, usually depending on whether liquids or gases are involved in the permeation, and may be on a pointwise or overall basis. 

The symbol commonly used for membrane permeability is simply P or P, denoting the permeability of (or to) a component i. The particular units of Pj are best defined merely by its usage, and may pertain either to the pointwise value or the overall value. Moreover, this use of the symbol P is to be distinguished from the usage for the fluid flowing pressure P, which may be further distinguished by Pl for the high-pressure side or reject side of the membrane, and Py for the low-pressure or permeate side, as utilized in Hoffman (2003) and in Section 19.10 of this chapter. 

The practice here is not to attempt to adapt symbols to distinguish one kind of permeability coefficient from pother (e.g., a pointwise coefficient Pj from an overall coefficient, say P-). Rather, as noted earlier, all coefficients are simply denoted P, to be further distinguished by context of usage, with the required units or dimensions and magnitude dictated by that usage. 

The membrane thickness Aw may, of course, be incorporated into the pointwise diffusion coefficient D, or the equivalent permeability coefficient P to obtain the overall coefficient. 

As previously stated, the units commonly used for pointwise membrane permeability (or mobility) are... 

The same is true in utilizing membrane calculations. As indicated by S. Y. Lee and B. S. Minhas, the observed permeabilities for the components of a mixture may be markedly less than that measured for the individual pure components. This indicates that there is a role for efficiency ratings, which may be stagewise or pointwise (as in the case of differential permeation) or an overall figure may be used. 

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