SURFACES OF HARD-SPHERE SYSTEMS
DOI:
https://doi.org/10.5566/ias.1134Keywords:
biofilm, fracture surface, hard spheres, porous layer, surfaceAbstract
In various situations surfaces appear that are formed by systems of hard spheres. Examples are porous layers as surfaces of sand heaps and biofilms or fracture surfaces of concrete. The present paper considers models where a statistically homogeneous system of hard spheres with random radii is intersected by a plane and the surface is formed by the spheres with centers close to this plane. Formulae are derived for various characteristics of such surfaces: for the porosity profile, i.e. the local porosity in dependence on the distance from the section plane and for the geometry of the sphere caps that look above the section plane.
It turns out that these characteristics only depend on the first-order characteristics of the sphere system, its sphere density and the sphere radius distribution.
Comparison with empirically studied biofilms shows that the model is realistic.
References
Bezrukov A, Bargiel M, Stoyan D (2002). Statistical analysis of simulated random packings of spheres. Part. Part. Syst. Charact. 19, 111-118
Bondreau BP, Jorgensen, BB (2001). The Benthic Boundary Layer: Transport Processes and Bio-Geochemistry. Oxford University Press, Oxford.
Chiu SN, Stoyan D, Kendall WS, Mecke J (2013). Stochastic Geometry and its Applications. 3rd Edition, Wiley.
Hahn U, Micheletti A, Pohlink R, Stoyan D, Wendrock H (1000). Stereological analysis and modeling of gradient structures. J. Microscopy 195, 113 - 124.
Hahn U, Stoyan D (1998). Unbiased stereological estimation of the surface area of gradient surface processes. Adv. Appl. Prob. 30, 904 - 920.
Hansen JP, Macdonald IR (1986). Theory of Simple Liquids. Academic Press, New York.
Khalili A, Morad MR, Matyka M, Liu B, Malekmohammadi R, Weise J, Kuypers MMM (2013). Porosity variation below a fluid--porous interface. Chemical Engineering Science
Lewandowski Z (2000). Notes on biofim porosity.
Water Resources 34, 2620 - 2024.
Mecke J and Stoyan D (1980). Stereological problems for spherical particles. Math. Nachr. 96, 311 - 317.
Stroeven P (1982). Structural modelling of plain and fibre
reinforced concrete. J. Comp. 1982, April, 129 - 139.
Stroeven P (2000). A stereological approach to roughness of
fracture surfaces and tortuosity of transport paths in concrete.
Cement & Concrete Composites 22, 331 - 341.
Zhang TC, Bishop PL (1994). Density, porosity, and pore structure of biofilms. Water Resources 28, 2267 - 2277.
