Lineal-path function for random heterogeneous materials. II. Effect of polydispersivity

Journal Article · Fri May 15 04:00:00 EDT 1992 · Physical Review A. General Physics; (United States)

DOI:https://doi.org/10.1103/PhysRevA.45.7292· OSTI ID:7237768

Lu, B ^[1]; Torquato, S ^[2]

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1. Department of Mechanical and Aerospace Engineering, North Carolina State University, Raleigh, North Carolina 27695-7910 (United States)
2. Department of Mechanical and Aerospace Engineering, North Carolina State University, Raleigh, North Carolina 27695-7910 (United States) Department of Chemical Engineering, North Carolina State University, Raleigh, North Carolina 27695-7910 (United States)

The lineal-path function {ital L}({ital z}) for two-phase heterogeneous media gives the probability of finding a line segment of length {ital z} wholly in one of the phases, say phase 1, when randomly thrown into the sample. The function {ital L}({ital z}) is equivalent to the area fraction of phase 1 measured from the projected image of a slab of the material of thickness {ital z} onto a plane. The lineal-path function is of interest in stereology and is an important morphological descriptor in determining the transport properties of heterogeneous media. We develop a means to represent and compute {ital L}({ital z}) for distributions of {ital D}-dimensional spheres with a polydispersivity in size, thereby extending an earlier analysis by us for monodispersed-sphere systems. Exact analytical expressions for {ital L}({ital z}) in the case of fully penetrable polydispersed spheres for arbitrary dimensionality are obtained. In the instance of totally impenetrable polydispersed spheres, we develop accurate approximations for the lineal-path function that apply over a wide range of volume fractions. The lineal-path function was found to be quite sensitive to polydispersivity for {ital D}{ge}2. We demonstrate how the measurement of the lineal-path function can yield the particle-size distribution of the particulate system, thus establishing a method to obtain the latter quantity.

• DOE Contract Number: FG05-86ER13482
• OSTI ID: 7237768
• Journal Information: Physical Review A. General Physics; (United States), Journal Name: Physical Review A. General Physics; (United States) Vol. 45:10; ISSN 1050-2947; ISSN PLRAA
• Country of Publication: United States
• Language: English

Related Subjects

36 MATERIALS SCIENCE
360602* -- Other Materials-- Structure & Phase Studies
665000 -- Physics of Condensed Matter-- (1992-)
75 CONDENSED MATTER PHYSICS
SUPERCONDUCTIVITY AND SUPERFLUIDITY
CONFIGURATION
CRYSTAL STRUCTURE
DISPERSIONS
DISTRIBUTION FUNCTIONS
FILTRATION
FUNCTIONS
MECHANICS
MICROSTRUCTURE
MORPHOLOGY
RANDOMNESS
SCALING
SEPARATION PROCESSES
SIZE
SPHERICAL CONFIGURATION
STATISTICAL MECHANICS