Next: Paste-Void Proximity Distribution Up: Spacing Equations Previous: Pleau and Pigeon
The paste-void and the void-void spacing distributions have application both inside the the field of cementitious materials [24,25,26,27,28,29] and outside the field[30,31,32]. Using various approximation techniques, the problems of the paste-void and the void-void spacing distributions have been solved for systems composed of monosized spheres [33,34,35,36,37,38,39]. These approximations have been compared to results of Monte Carlo simulations [36,37] and they are in agreement. One method of approximation relies upon n-point correlation functions, and Torquato, Lu, and Rubenstein [36] have obtained exact expansions for monosized spheres. Lu and Torquato [40] developed a means to map these correlation functions to systems of polydispersed sphere radii, thereby making it possible to extend the approximations for monosized spheres. These approximations for polydispersed sphere radii are given in Lu and Torquato [41], and are used here as estimates for both the paste-void and the void-void spacing distribution.
The results of Lu and Torquato [41] for both the paste-void and the void-void proximity calculations require the following defined quantities:
The value of B depends upon the exact way the system is constructed. For the calculations performed here, B=0. Also, there was an error in the published value for g in Ref. [41], which has been corrected here.
Since Lu and Torquato were studying systems composed of a matrix containing solid spheres they use the terms "void" and "particle" to represent the matrix and the spheres, respectively. Therefore, the authors' "void exclusion probability" is used here to estimate the paste-void proximity distribution, and their "particle exclusion probability" is used here to estimate the void-void proximity distribution.