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Particle Dynamics

Strictly speaking, the Lu and Torquato equations are meant for equilibrium systems in which the spheres are allowed to mix and interact before coming into some equilibrium state. The mixing does not alter the size distribution of the spheres, only the locations of the spheres. From this description, air voids in concrete should also exhibit statistics of an equilibrium system, although the effect of gravity and the presence of the aggregates may not be ignored.

This computer experiment uses a parking approach to the final placement of the air voids. Once placed, the spheres do not move, nor do they interact with one another. The spatial statistics of both an equilibrium and a parked system can be quantified using an n-point correlation function, as was used by Lu and Torquato [41]. Although the spatial statistics of an equilibrium system and a parked system differ, they are similar at low air contents. Therefore, if the results of the computer experiment for monosized parked spheres agree with the exact Lu and Torquato results for monosized spheres, the spatial statistics, over the range of air contents tested, must be sufficiently similar between the equilibrium and the parked systems that the results are indistinguishable. This would suggest that the results for parked lognormally distributed air void radii are also a valid approximation for an equilibrium distribution of air void radii.