Coarsening model

Figure C2.11.6. The classic two-particle sintering model illustrating material transport and neck growtli at tire particle contacts resulting in coarsening (left) and densification (right) during sintering. Surface diffusion (a), evaporation-condensation (b), and volume diffusion (c) contribute to coarsening, while volume diffusion (d), grain boundary diffusion (e), solution-precipitation (f), and dislocation motion (g) contribute to densification.

Fig. 3. The two-sphere model illustratiag material transport paths I—VII duriag sintering where (a) represents coarsening (b), the two spheres before...

The phase separation process at late times t is usually governed by a law of the type R t) oc f, where R t) is the characteristic domain size at time t, and n an exponent which depends on the universality class of the model and on the conservation laws in the dynamics. At the presence of amphiphiles, however, the situation is somewhat complicated by the fact that the amphiphiles aggregate at the interfaces and reduce the interfacial tension during the coarsening process, i.e., the interfacial tension depends on the time. This leads to a pronounced slowing down at late times. In order to quantify this effect, Laradji et al. [217,222] have proposed the scaling ansatz... 

H.-J. Diepers, C. Beckermann, I. Steinbach. Modeling of convection-influenced coarsening of a binary alloy mush using the phase-field method. In ... 

By integrating Equations (3) and (4), neglecting the A term, with random initial conditions, mounds similar to those of the simulation can be obtained (Fig. 3). These mounds also coarsen in time. However, there has not been direct test of this equation as a description of multilayer growth. In particular, Eq. (4) was derived by fitting to Monte-Carlo data in the submonolayer regime. In this paper we show that certain aspects of multilayer growth by the Monte-Carlo model are well represented by Eq. (3) and (4). 

ILL. Golubovic, Interfacial coarsening in MBE growth models without slope selection, preprint (1996). 

Source-Limited Coarsening. During source-limited coarsening, the interfaces surrounding the particles behave as poor sources and sinks, and the coarsening rate then depends upon the rate at which the diffusion fluxes between the particles can be created or destroyed (accommodated) at the particle interfaces. In a simple model, the same assumptions can be made about the source action at the particles as those that led to Eq. 13.24. The rate of particle growth can then be written... 

The mean-field theory has a number of shortcomings, including the approximations of a mean concentration around all particles and the establishment of spherically symmetric diffusion fields around every particle, similar to those that would exist around a single particle in a large medium. The larger the particles total volume fraction and the more closely they are crowded, the less realistic these approximations are. No account is taken in the classical model of such volume-fraction effects. Ratke and Voorhees provide a review of this topic and discuss extensions to the classical coarsening theory [8]. 

The average foam dispersity in the experiments performed varied within the limits of aVL = 6.10"2-3.5.10 1 mm the degree of polydispersity significantly increased in the process of foam coarsening. It can be seen that curves 1 and 2 fit well at expansion ratio n > 300. At low expansion ratio (20 < n < 40) the difference between rjr (n) and rjrn(n) grows to 15% but if the longitudinal curvature is accounted for then this difference is about 7%. This means that the difference in size of the individual bubbles in a polydisperse foam does not influence strongly the course of the ra lrn (n) dependence as compared to the monodisperse model system. 

CG residues and three atomistic, and so on. In addition, they also increased the temperature of each replica, such that while the fully atomistic model was simulated at 298 K, the fully CG model was simulated at 700 K. However, despite the small size of the system, the small difference between the CG and atomistic models (OPLSUA Vi. OPLSAA) and the use of incremental coarsening, the acceptance ratio of the swap moves was still very low, running between 2.5% and 5.8%. Applications of this method to larger systems, or using a greater difference between the atomistic and CG models therefore looks problematic. 

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