J. Phys. I France
Volume 6, Numéro 4, April 1996
Page(s) 557 - 574
DOI: 10.1051/jp1:1996229
J. Phys. I France 6 (1996) 557-574

Sintering of Mass Fractals by Surface Diffusion or by Viscous Flow: Numerical and Scaling Approaches in d = 2

Nathalie Olivi-Tran, Romain Thouy and Rémi Jullien

Laboratoire de Science des Matériaux Vitreux, Université Montpellier II, Place Eugène Bataillon 34095 Montpellier, France

(Received 2 November 1995, received in final form 19 December 1995, accepted 21 December 1995)

Numerical methods are used to model two kinds of sintering processes, by Surface Diffusion (SD) or by Viscous Flow (VF), and are applied to deterministic and random two-dimensional "mass fractals" with various fractal dimensions. In the SD case the relevant partial differential equation is discretized and the evolution of the contour is numerically studied. In the case of viscous flow, a recently introduced approximate "dressing" method is used. In both cases it is shown that the geometrical characteristics which are the perimeter length L, the size $\xi$ and the lower cut-off a, vary as some powers of time $t\,(L\sim t^{-\alpha},\,\xi\sim t^{-\beta},\,a\sim t^{\gamma})$. The exponents $\alpha, \beta, \gamma$, and their dependence on the fractal dimension D, are estimated from scaling arguments and are found to be different in the SD and VF cases. The SD case is particular in the sense that $\beta\simeq 0$ (no shrinkage) and that, if the initial fractal is too large, it breaks into separate pieces.

© Les Editions de Physique 1996

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