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

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 (R) versus time (t) follows the R 10/3 ∝t law, in contrast to the conventional LSW theory, R 3 ∝ t, and the interface-diffusion dominated two-phase coarsening, R 4 ∝ t.

Non-integer temporal exponents in trans-interface diffusion-controlled coarsening

“…1 of a paper by Seidman et al [84] as experimental evidence supporting the results of their computer simulations, using the knowledge that diffusion in the ordered c 0 precipitates in a ternary Ni-5.2Al-14.2Cr (at.%) alloy is much slower than in the matrix. Similar to their predecessors, Sheng et al [54] attributed their findings to interface diffusion-controlled coarsening. Inspired by the simulations of Sheng et al, Dai and Du [85] mathematically examined the implications of a dimensionless mobility M* = 1 ?…”

“…In fact, doubts have been raised recently [87][88][89] about the assertions that interface diffusion control governs late-stage coarsening with mobilities of the type M* = 1-u 2 , even in the sharp interface limit. What then to make of the claim that the computational results of Sheng et al [54], and by implication those of Dai and Du [55,85], are supported by the temporal exponent n = 3.3 taken from the data reported by Seidman et al [84] in Fig. 1 of their paper?…”

“…Sheng et al [54] explored the impact of several different concentration-dependent mobilities, including those mentioned above, and concluded that temporal exponents of n & 3.35 are characteristic of late-stage coarsening whenever the mobility in the precipitate phase is much smaller than that in the matrix phase, actually approaching zero. They cited the data reported in Fig.…”

“…In this context, it should be noted that concentration-dependent atomic mobilities have been incorporated into theories of late-stage spinodal decomposition (well into the coarsening regime) [47][48][49][50][51][52][53], and that phase field simulations of c 0 precipitate coarsening have used similar assumptions [54,55]. These works show that with suitably chosen functions for the mobility of solute, particularly functions that represent extremely slow diffusion in the precipitate phase, the temporal exponent n actually increases from 3 to as much as 4, with the irony that the kinetics in these papers is attributed to interface diffusion control.…”

Three-dimensional coarsening dynamics of a conserved, nematic liquid crystal-isotropic fluid mixture

“…The same model, which stems from that considered in [35], has been used in the two-dimensional study of Mata et al [26] and the current work is a follow-up report on our findings for the corresponding three-dimensional system. Similar phase field models have been used extensively in phase separation [14,25,19,4,1,2,21,22,5,35,37,36,3,38,13,39,12,30,17,33].…”