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Self-similarity and coarsening of three dimensional particles on a one or two dimensional matrix

Jorge Vinals·W. W. Mullins
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Abstract

We examine the validity of the hypothesis of self-similarity in systems coarsening under the driving force of interface energy reduction in which three dimensional particles are intersected by a one or two dimensional diffusion matrix. In both cases, solute fluxes onto the surface of the particles, assumed spherical, depend on both particle radius and inter-particle distance. We argue that overall mass conservation requires independent scalings for particle sizes and inter-particle distances under magnification of the structure, and predict power law growth for the average particle size in the case of a one dimensional matrix (3D/1D), and a weak breakdown of self-similarity in the two dimensional case (3D/2D). Numerical calculations confirm our predictions regarding self-similarity and power law growth of average particle size with an exponent 1/7 for the 3D/1D case, and provide evidence for the existence of logarithmic factors in the laws of boundary motion for the 3D/2D case. The latter indicate a weak breakdown of self-similarity.

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Jorge Vinals, W. W. Mullins. 1997-07-06. Self-similarity and coarsening of three dimensional particles on a one or two dimensional matrix. https://doi.org/10.1063/1.366751

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