Diaphragms tortuosity

The diffusion coefficient is written as Dcff(DABs/r) because, in fact, diffusion occurs through a porous diaphragm whose porceity and tortuosity affect the observed flux based on the geometrical cross-sectional area, luregrarion of Eq- (2.3-28) under the assumption of constant fluid density relates the flux to the composition difference at any time ... 

Detailed investigations by MacMullin et al.72 show that the value of Kx/r for many porous beds is 3.666 0.098. Since the tortuosity of a porous asbestos diaphragm is —1.5 and Kx varies in the range of 5-5.5, the model describing the porous beds is applicable for the separators used in diaphragm chlor-alkali cells. 

S.3. Diaphragm Resistance. The calculation of the resistance across a separator, such as an asbestos or a polymeric diaphragm, is identical to the method employed to determine the resistance of an electrolyte between two parallel plates. However, the distance between the two faces of a separator is not equal to its thickness, as the liquid path in the separator is tortuous and the area is restricted by the finite porosity. Therefore, the 1/A term in the parallel plate configuration should be modified to read as [tortuosity x length]/[porosity x area] or as the ratio of tortuosity to porosity, which is called the MacMullin number. The MacMullin number, characterizing a... 

This approach will yield a conservative measure of the tortuosity/porosity ratio for a given diaphragm. 

Since x/L — r,the tortuosity factor is the ratio of the effective length of micropores to the thickness of the diaphragm mat. 

There are two major ways in which this analysis can be questioned. First, the diffusion coefficient used here is an effective value altered by the tortuosity in the diaphragm. Theoreticians occasionally assert that different solutes will have different tortuosities, so that the diffusion coefficients measured will apply only to that particular diaphragm cell and will not be generally usable. Experimentalists have cheerfully ignored these assertions by writing... 

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