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Transport processes in fractals

1986; Elsevier BV; Volume: 114; Issue: 1 Linguagem: Inglês

10.1016/0021-9797(86)90258-4

1095-7103

F. Gilbert, P. M. Adler,

Composite Material Mechanics

The rotation tensor of spheres arranged in a Leibniz packing with small gaps between them is calculated in the lubrication approximation. Numerical data show that nondiagonal components of the tensor are constant, while diagonal components do not seem to reach any asymptotic regime when the number of generations increases. An explicit but approximate formula is then derived for this tensor which is in excellent agreement with the exact numerical results. The asymptotic behavior of the diagonal components is analyzed with the aid of the so-called exponent of some Leibniz subpackings.