Bounds on the effective properties of polydispersed suspensions of spheres: An evaluation of two relevant morphological parameters

Journal Article · Tue May 15 04:00:00 EDT 1990 · Journal of Applied Physics; (USA)

DOI:https://doi.org/10.1063/1.345169· OSTI ID:6938390

Thovert, J F ^[1]; Kim, I C; Torquato, S ^[2]; Acrivos, A ^[3]

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1. Laboratoire d'Aerothermique du C. N. R. S., 4 ter, route des Gardes, 92190 Meudon, (France)
2. Department of Mechanical and Aerospace Engineering, North Carolina State University, Raleigh, North Carolina 27695-7910 (USA)
3. The Levich Institute, T202, City College of New York, Convent Avenue at 140 Street, New York, New York 10031 (USA)

Expressions for the two microstructural parameters that appear in the variational third-order bounds (G. W. Milton, Phys. Rev. Lett. {bold 46}, 542 (1981)) for the effective conductivity and elastic moduli of composite media are derived analytically to first order in the sphere concentration {ital c} for random well-mixed dispersions of impenetrable spheres with an arbitrary size distribution. These relations lead to rigorous bounds on the effective properties which are exactly valid to order {ital c}{sup 2} for such models. The apparent {ital linear} behavior of the microstructural parameters up to moderately high {ital c} enables one to apply the bounds beyond second-order in {ital c}, however. Employing these results, the effect of polydispersivity on the effective properties is examined. It is worth noting that, under some conditions, polydispersivity can actually lead to a slight decrease of the shear modulus, whereas, for highly conducting particles, polydispersivity always increases the effective conductivity.

• DOE Contract Number: FG05-86ER13482
• OSTI ID: 6938390
• Journal Information: Journal of Applied Physics; (USA), Journal Name: Journal of Applied Physics; (USA) Vol. 67:10; ISSN 0021-8979; ISSN JAPIA
• Country of Publication: United States
• Language: English

Related Subjects

656002* -- Condensed Matter Physics-- General Techniques in Condensed Matter-- (1987-)
75 CONDENSED MATTER PHYSICS
SUPERCONDUCTIVITY AND SUPERFLUIDITY
COMPOSITE MATERIALS
CRYSTAL STRUCTURE
DISPERSIONS
ELASTICITY
MATERIALS
MECHANICAL PROPERTIES
MICROSPHERES
MICROSTRUCTURE
PHYSICAL PROPERTIES
SUSPENSIONS
TENSILE PROPERTIES
THERMAL CONDUCTIVITY
THERMODYNAMIC PROPERTIES
VARIATIONAL METHODS