Chord-length distribution function for two-phase random media
Journal Article
·
· Physical Review E; (United States)
- Princeton Materials Institute and Department of Civil Engineering Operations Research, Princeton University, Princeton, New Jersey 08544 (United States)
- Department of Mechanical and Aerospace Engineering, North Carolina State University, Raleigh, North Carolina 27695 (United States)
A statistical correlation function of basic importance in the study of two-phase random media (such as suspensions, porous media, and composites) is the chord-length distribution function [ital p]([ital z]). We show that [ital p]([ital z]) is related to another fundamentally important morphological descriptor studied by us previously, namely, the lineal-path function [ital L]([ital z]), which gives the probability of finding a line segment of length [ital z] wholly in one of the phases when randomly thrown into the sample. We derive exact series representations of the chord-length distribution function for media comprised of spheres with a polydispersivity in size for arbitrary space dimension [ital D]. For the special case of spatially uncorrelated spheres (i.e., fully penetrable spheres), we determine exactly [ital p]([ital z]) and the mean chord length [ital l][sub [ital C]], the first moment of [ital p]([ital z]). We also obtain corresponding formulas for the case of impenetrable (i.e., spatially correlated) polydispersed spheres.
- DOE Contract Number:
- FG02-92ER14275
- OSTI ID:
- 6705641
- Journal Information:
- Physical Review E; (United States), Journal Name: Physical Review E; (United States) Vol. 47:4; ISSN PLEEE8; ISSN 1063-651X
- Country of Publication:
- United States
- Language:
- English
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