Local volume fraction fluctuations in random media

Journal Article · Sat Feb 01 04:00:00 EST 1997 · Journal of Chemical Physics

DOI:https://doi.org/10.1063/1.473414· OSTI ID:450269

Quintanilla, J; Torquato, S ^[1]

---

1. Princeton Materials Institute and Department of Civil Engineering Operations Research, Princeton, New Jersey 08544 (United States)

Although the volume fraction is a constant for a statistically homogeneous random medium, on a spatially local level it fluctuates. We study the full distribution of volume fraction within an observation window of finite size for models of random media. A formula due to Lu and Torquato for the standard deviation or {open_quotes}coarseness{close_quotes} associated with the {ital local} volume fraction {xi} is extended for the nth moment of {xi} for any n. The distribution function F{sub L} of the local volume fraction of five different model microstructures is evaluated using analytical and computer-simulation methods for a wide range of window sizes and overall volume fractions. On the line, we examine a system of fully penetrable rods and a system of totally impenetrable rods formed by random sequential addition (RSA). In the plane, we study RSA totally impenetrable disks and fully penetrable aligned squares. In three dimensions, we study fully penetrable aligned cubes. In the case of fully penetrable rods, we will also simplify and numerically invert a prior analytical result for the Laplace transform of F{sub L}. In all of these models, we show that, for sufficiently large window sizes, F{sub L} can be reasonably approximated by the normal distribution. {copyright} {ital 1997 American Institute of Physics.}

• DOE Contract Number: FG02-92ER14275
• OSTI ID: 450269
• Journal Information: Journal of Chemical Physics, Journal Name: Journal of Chemical Physics Journal Issue: 7 Vol. 106; ISSN JCPSA6; ISSN 0021-9606
• Country of Publication: United States
• Language: English

Related Subjects

36 MATERIALS SCIENCE
COLLOIDS
COMPOSITE MATERIALS
CRACKS
DISPERSIONS
FLUCTUATIONS
GAUSS FUNCTION
HETEROGENEOUS EFFECTS
MICROSTRUCTURE
PHASE STUDIES
POROUS MATERIALS
RANDOMNESS
VOLUME