Graham

Graham showed that the rate of diffusion of different gases through a porous diaphragm was inversely proportional to the square roots of their densities this is the basis of a method of separation of gases, and has been applied successfully to the separation of hydrogen and deuterium. 

Graham s law of diffusion This law states that the rates at which two gases diffuse are inversely proportional to their densities, i.e. 

Mark Graham has worked for 14 years with major international service and oil companies in Egypt, Dubai, Brunei, the Netherlands and the UK, prior to co-founding TRACS International. His areas of expertise include petrophysics and asset evaluation. He is Director of the training division of TRACS International and is also responsible for all TRACS projects in the FSU. 

A number of more or less equivalent derivations of the electrocapillary Eq. V-49 have been given, and these have been reviewed by Grahame [113]. Lippmann based his derivation on the supposition that the interface was analogous to a parallel-plate condenser, so that the reversible work dG, associated with changes in area and in charge, was given by... 

The treatments that are concerned in more detail with the nature of the adsorbed layer make use of the general thermodynamic framework of the derivation of the Gibbs equation (Section III-5B) but differ in the handling of the electrochemical potential and the surface excess of the ionic species [114-117]. The derivation given here is after that of Grahame and Whitney [117]. Equation III-76 gives the combined first- and second-law statements for the surface excess quantities... 

Usually one varies the head of mercury or applied gas pressure so as to bring the meniscus to a fixed reference point [118], Grahame and co-workers [119], Hansen and co-workers [120] (see also Ref. 121), and Hills and Payne [122] have given more or less elaborate descriptions of the capillary electrometer apparatus. Nowadays, the capillary electrometer is customarily used in conjunction with capacitance measurements (see below). Vos and Vos [111] describe the use of sessile drop profiles (Section II-7B) for interfacial tension measurements, thus avoiding an assumption as to the solution-Hg-glass contact angle. 

Note Some of Grahame s values for and included in this table. For a common cation, the sequence of anions in order of increasing adsorption is similar to that of the Hofmeister series in coagulation studies, and it is evident that specific adsorption properties are involved. 

Graham R A 1993 Solids under High-Pressure Shock Compression (New York Springer)... 

Fehiner F P and Graham M J 1995 Corrosion Meohanisms in Theory and Praotioe ed P Marcus and J Oudar (New York Dekker)... 

Graham R. Fleming, Department of Chemistry, The University of California, Berkeley, California, U.S.A. 

It ls not surprising chat such a relation should hold at the Limit of Knudsen diffusion, since Che Knudsen diffusion coefficients are themselves inversely proportional to the square roots of molecular weights, but the pore diameters in Graham s stucco plugs were certainly many times larger chan the gaseous mean free path lengths at the experimental conditions. 

Thus his experiments were the first to indicate the surprising result that relation (6,1) remains valid even in conditions where bulk diffusion resistance is completely dominant. Accordingly (6.1), perhaps the most important single experimental result on diffusion in porous media, will be referred to as Graham s relation. 

Though the results obtained were relatively few in number, they conformed fully to Graham s relation within the experimental accuracy. Sub sequently further evidence has been provided by the accurate experiments of... 

Che pore size distribution and Che pore geometry. Condition (iil). For isobaric diffusion in a binary mixture Che flux vectors of Che two species must satisfy Graham s relation... 

Though illustrated here by the Scott and Dullien flux relations, this is an example of a general principle which is often overlooked namely, an isobaric set of flux relations cannot, in general, be used to represent diffusion in the presence of chemical reactions. The reason for this is the existence of a relation between the species fluxes in isobaric systems (the Graham relation in the case of a binary mixture, or its extension (6.2) for multicomponent mixtures) which is inconsistent with the demands of stoichiometry. If the fluxes are to meet the constraints of stoichiometry, the pressure gradient must be left free to adjust itself accordingly. We shall return to this point in more detail in Chapter 11. 

Remick and Geankoplis also used their data to check the generalized Graham relation (6.2) and found experimental values for N wh ich... 

In this case the pressure difference across the porous medium no longer vanishes (if it did, (10.33) would be replaced by Graham s relation) but. 

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