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# Alternative Attiogbe Equation

Studying the results of the monosized air voids experiment, there may remain confusion as to which Attiogbe equation to use. Here, an explicit form for G was used while Attiogbe has previously used the equation

where, Φα1 [is] the specific surface of the air voids for G =1," [19]. It was this equation that Attiogbe has used to compare systems with different air voids distributions.

It can be argued that Eqn. 42 is completely incorrect based upon Attiogbe's own calculations. Equation 42 shows that G is directly proportional to α. By comparison, the equation derived by Attiogbe for the air void distribution in Eqn. 11 can also be expressed as a function of α:

Although this equation for G is a function of α, it is not proportional to α.

Another argument for why the application of Eqn. 42 is erroneous can be demonstrated from the experimental data for monosized air voids. This experiment was reported in two parts: constant number density and constant diameter. For the constant diameter portion of the data, the sphere diameter distribution remains constant. Since α1 refers to the system of 150 µm diameter spheres when G=1, the ratio ( α / α1 ) remains constant throughout the 150 µm diameter experiment. Therefore, for a system of 150 µm diameter spheres at a number density of 20 mm-3, the correct numerator for G, based upon Eqn. 10, is 8. Since the volume fraction of paste within t of an air void surface must be independent of how one conducts an experiment, the corresponding numerator for G in the constant number density data with a diameter of 150 µm and a number density of 20 mm−3 must also be 8, based upon Eqn. 10. By similar arguments for experiments conducted for other sphere diameters, the numerator for the constant number density experiment should be 8, based upon Eqn. 10.

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