Morphology and topology of interfaces during coarsening via nonconserved and conserved dynamics

Large-scale simulations in three-dimensions were performed with the phase-field method on a parallel computing platform to model coarsening of two-phase mixtures. Simulations included symmetric mixtures evolving via nonconserved dynamics (model A) governed by the Allen-Cahn equation and symmetric and asymmetric mixtures with volume fractions of 22%, 30%, 36%, and 40% evolving via conserved dynamics (model B) governed by the Cahn-Hilliard equation. Symmetric mixtures with the two different dynamics were compared. The volume fraction dependency was investigated in mixtures evolving via conserved dynamics.;The scaled morphology and topology were studied using the interfacial shape distribution and the genus, respectively. The interfacial shape distribution and the genus were scaled by a characteristic length. For symmetric mixtures evolving via both dynamics and 36% and 40% mixtures evolving via conserved dynamics, time-invariant scaled morphologies were found. Each bicontinuous mixture has a unique scaled interfacial shape distribution. The probability flux that governs the interfacial shape distributions was calculated for the two symmetric mixtures to investigate the time-evolution of interfacial patches. However, all these mixtures have similar topology, yielding a universal value in the scaled genus. Additionally, these bicontinuous mixtures are different from the topology of Schoen's G surface that has been considered previously as a good model for such bicontinuous mixtures.;The presence of a range of volume fractions where interfacial structures remain bicontinuous in the late-stage coarsening is of great interest. It has been assumed that symmetric mixtures have a bicontinuous structure and asymmetric mixtures have a droplet or clustered structure in the late-stage coarsening regardless of the dimensionality. This assumption is based upon experimental results from thick films that can be considered as two-dimensions and 2D simulations. We find that mixtures can remain bicontinuous down to volume fraction of 36% in 3D. The differences between the behavior of 2D and 3D systems are attributed to different percolation limits in different dimensions and the occurrence of pinching off the minority phase only in three-dimensions.