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A graphical performance comparison of the Philleo, the Pleau and Pigeon, and the Lu and Torquato estimates of the paste-void proximity probability density function is shown in Fig. 7. The sphere radii are lognormally distributed with a number density of 240 mm−3. The Philleo estimate terminates at s equals zero since it is already normalized for the fraction of paste within s of an air void surface. The Lu and Torquato estimate is virtually exact at the resolution of this experiment. The Philleo estimate is fairly accurate for s greater than zero, while that of Pleau and Pigeon is noticeably in error. These qualitative differences are born out in the previously reported results.
Figure 7: Estimates of the paste-void probability density function by Philleo, Pleau and Pigeon, and Lu and Torquato for lognormally distributed sphere radii with a number density of 240 mm−3. Measured values are shown as filled circles.