Multi-scale analysis for solidification of phase change materials (PCMs): Experiments and modeling

Abstract

We present a multi-scale solidification framework for pure substances using laboratory experiments and mathematical modeling. The multi-scale phenomena of solidification are experimentally captured by the state-of-the-art thermal control chamber and optical devices. In particular, the transient temperature over five solidification stages is observed under various cooling rates, while the nucleation site and crystal evolution are photographed and further processed via image analysis. A unified mathematical model is also developed to quantitatively examine the solidification process at three scales: (i) the supercooling, freezing, and subcooling stages with a time-dependent boundary at the macroscale are analytically solved by Duhamel’s theorem and perturbation method; (ii) the two-dimensional (2D) dendritic growth at the mesoscale is computed by the Allen-Cahn equation through phase field modeling; and (iii) the heterogeneous nucleation at the microscale is numerically simulated. The results demonstrated that the experimental data and modeling were in close agreement with the freezing curve, nucleation temperature, nucleation time, 2D crystal evolution, and freezing time.