Phase ordering with a global conservation law: Ostwald ripening and coalescence

Details Phase ordering with a global conservation law: Ostwald ripening and coalescence Phase ordering with a global conservation law: Ostwald ripening and coalescence

2001-09-09

arxiv.org/abs/cond-mat/0109157v2

Physics

Condensed Matter

Statistical Mechanics

20 pages, 7 figures, more details added

Scientific paper

10.1103/PhysRevE.65.046117

Globally conserved phase ordering dynamics is investigated in systems with short range correlations in the initial condition. A Ginzburg-Landau equation with a global conservation law is employed as the phase field model. The conditions are found under which the sharp-interface limit of this equation is reducible to the area-preserving motion by curvature. Numerical simulations show that, for both critical and off-critical quench, the equal time pair correlation function exhibits dynamic scaling, and the characteristic coarsening length obeys a power law in time with a 1/2 exponent. For the critical quench, our results are in excellent agreement with earlier results. For off-critical quench (Ostwald ripening) we investigate the dynamics of the size distribution function of the minority phase domains. The simulations show that, at large times, this distribution function has a self-similar form with growth exponent 1/2. The scaled distribution, however, strongly differs from the classical Wagner distribution. We attribute this difference to coalescence of domains. A new theory of Ostwald ripening is developed that takes into account binary coalescence events. The theoretical scaled distribution function agrees very well with that obtained in the simulations.

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