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

Journal Article · Fri May 15 00:00:00 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), Vol. 45:10; ISSN 1050-2947
• Country of Publication: United States
• Language: English

Related Subjects

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