Coarsening kinetics from a variable-mobility Cahn-Hilliard equation: Application of a semi-implicit Fourier spectral method

Abstract

An efficient semi-implicit Fourier spectral method is implemented to solve the Cahn-Hilliard equation with a variable mobility. The method is orders of magnitude more efficient than the conventional forward Euler finite-difference method, thus allowing us to simulate large systems for longer times. We studied the coarsening kinetics of interconnected two-phase mixtures using a Cahn-Hilliard equation with its mobility depending on local compositions. In particular, we compared the kinetics of bulk-diffusion-dominated and interface-diffusion-dominated coarsening in two-phase systems. Results are compared with existing theories and previous computer simulations.

Computation of multiphase systems with phase field models

“…As time increases, the maximum value of the structure function increases and shifts to lower k, indicating an increase in the real-space average length scale. This is consistent with the results reported in [25]. In Figure 6 we plot the cubic of the average domain size versus time.…”

“…In Figure 6 we plot the cubic of the average domain size versus time. The straight line behavior confirms the expected cubic growth law [25].…”

“…This is the case of interface diffusion controlled coarsening that is characterized by much slower dynamics but with similar morphological patterns. These results are analogous to the ones reported in [25]. But here, with the unconditionally stable scheme, we are able use a large time step (∆t = 0.01) to follow the very slow coarsening dynamics.…”

“…Eyre [23] considers a discretization of this type for the one-dimensional Cahn-Hilliard equation with constant mobility, Smereka [24] uses it in the context of interface motion by surface diffusion while Zhu, Chen, Shen, and Tikare [25] use it for the mobility term but not for the nonlinear one, resulting in a conditionally stable method.…”

Nucleation, Growth, and Aggregation of Mineral Phases: Mechanisms and Kinetic Controls

“…The growth of these fluctuations is diffusion controlled, based on the local compositional gradients. Annealing of spinodal fluctuations eventually gives rise to coarsening and phase separation, and the appearance of exsolution structures in solid solutions (Yund et al, 1974;Zhu et al, 1999). Talanquer and Oxtoby (1994) developed a DFT approach for heterogeneous nucleation of droplets with sharp interfaces and compared this with a CNT estimate of nucleation rate.…”