Commun. Comput. Phys., 8 (2010), pp. 249-264.


Coarsening Kinetics of a Two Phase Mixture with Highly Disparate Diffusion Mobility

G. Sheng 1*, T. Wang 2, Q. Du 3, K. G. Wang 4, Z. K. Liu 1, L. Q. Chen 1

1 Department of Materials Science and Engineering, Pennsylvania State University, University Park, PA 16802, USA.
2 Department of Materials Science and Engineering, Iowa State University, Ames, IA 50011, USA.
3 Department of Mathematics and Department of Materials Science and Engineering, Pennsylvania State University, University Park, PA 16802, USA.
4 Physics and Space Science Department, Materials Science and Nanotechnology Institute, Florida Institute of Technology, Melbourne, FL 32901, USA.

Received 16 July 2009; Accepted (in revised version) 4 November 2009
Available online 12 March 2010
doi:10.4208/cicp.160709.041109a

Abstract

The coarsening kinetics of a two-phase mixture with a large diffusional mobility disparity between the two phases is studied using a variable-mobility Cahn-Hilliard equation. The semi-implicit spectral numerical technique was employed, and a number of interpolation functions are considered for describing the change in diffusion mobility across the interface boundary from one phase to another. The coarsening rate of domain size was measured using both structure and pair correlation functions as well as the direct computation of particle sizes in real space for the case that the coarsening phase consists of dispersed particles. We discovered that the average size ($\overline{R}$) versus time (t) follows the $\overline{R}^{10/3}\propto t$ law, in contrast to the conventional LSW theory, $\overline{R}^3\propto t$, and the interface-diffusion dominated two-phase coarsening, $\overline{R}^4\propto t$.

AMS subject classifications: 65M70, 35F20, 81T80

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Key words: Coarsening kinetics, Cahn-Hilliard equation, phase-field method, computer simulation.

*Corresponding author.
Email: shengguang@psu.edu (G. Sheng), taowang@iastate.edu (T. Wang), qdu@math.psu.edu (Q. Du), kwang@fit.edu (K. G. Wang), Dr.Liu@psu.edu (Z. K. Liu), lqc3@psu.edu (L. Q. Chen)
 

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