Permeability Constants, Units, and Dimensions

By considering the flux of gas through porous membranes, a the volume V measured at a pressure jp, passing through the membrane in time t, in relation to the equation governing the flow (19,20), one can define permeability constants of various types, and having various dimensions. The equation of flow for an incompressible fluid in a pore system may be written  

In these expressions we can call and Pq permeabilities . As such they will be functions of the membrane thickness, pore type and size, and of the nature of the gas. By multiplying each of these permeabilities by I, the membrane thickness, one gets permeability coefficients and PqI which are dependent only upon pore type and size, and the nature of the gas. Finally, multiplying each permeability coefficient by the viscosity one obtains the specific permeability Pj Itj or PqIti, which should depend only on the pore tyjie and size. 

In considering the equation of flow of rarefied gases another set of permeability constants is obtained. The Knudsen equation, for a capillary system, may be written 

The various constants defined above have, it will be seen, different dimensions. It is important therefore to specify accurately what constants are being employed. When, as is usually done, the permeability constant is formally defined as the number of unit volumes passing in unit time through unit cube having unit pressure difference between its faces, its dimensions are cm. sec. g.-, which are those of the permeability coefficient of Table 1, for Poiseuille flow. The dimensions of the diffusion constant D defined by Pick s law 

The numerical measure of the permeability constant is dependent upon the units in which it is expressed. The literature shows a lack of uniformity with respect to units. It is specially important to state the thickness of the membrane used. In some systems it may also be an advantage to give other membrane properties such as porosity, defined by the 

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