Random close packing (RCP) of equal spheres : structure and implications for use as a model porous medium.
The structure of the Finney Random Close Packing (RCP) of equal spheres
has been analysed, together with the influence which such structure
exerts over the capillary pressure characteristics of geometrically
similar sphere packings.
The analysis is centred on the simplicial, or Delaunay cell, which is an
irregular tetrahedron with apices defined by four immediate neighbour
sphere-centres. In terms of using RCP as a model porous medium, an
individual simplicial cell is equivalent to an individual pore. A number
of measured pore-size distribution parameters are presented for the
Finney packing, from which it is shown from first principles that
drainage-imbibition hysteresis is not an intrinsic property of the
The nature and degree of randomness which characterises the Finney
packing is evaluated on two levels. First, by classifying edgelengths as
either short or long, seven mutually exclusive cell classes are defined.
Using the binomial theorem it is shown that cells (pores) are not random
on the level of the individual cell. There are less of the extreme cells
(with 6 long edges, or with 6 short edges) and more of the bland cells
(with 3 short and 3 long edges) in the Finney packing than predicted on
the basis of simple random expectations. Second, the distribution of
cell classes within the packing is shown to be essentially homogeneously
random. Evidence for extremely slight cell class clustering is found.
The drainage and imbibition processes within the packing are simulated
using pore-level algorithms. The algorithms utilise both the Haines'
insphere approximation and the MS-P approximation for critical drainage
meniscus curvature, and the cell cavity insphere radius approximation for
critical imbibition meniscus curvature. Good agreement with experimental
data is obtained, and the results confirm that drainage-imbibition
hysteresis is a direct consequence of the connectivity between cells
(pores), and is not an intrinsic property of the individual pore.
Finally, the drainage and imbibition algorithms are adapted to emulate
percolation theory models. The results prove that the classical bond
problem of percolation theory does not adequately describe the drainage
process for RCP, and that the classical site problem does not adequately
describe the imbibition process for RCP.