Lineal-path function for random heterogeneous materials. II. Effect of polydispersivity
- Department of Mechanical and Aerospace Engineering, North Carolina State University, Raleigh, North Carolina 27695-7910 (United States)
- 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
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SUPERCONDUCTIVITY AND SUPERFLUIDITY
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665000 - Physics of Condensed Matter- (1992-)