2019/04/11 by T.G. Myers, Myers, Timothy G., Matthew G. Hennessy +3 · 1 citation
Earth and Planetary Sciences · Engineering · Materials Science · #80A22 #Computational Physics (physics.comp-ph) #FOS: Physical sciences #Material Dynamics and Properties #Mesoscale and Nanoscale Physics (cond-mat.mes-hall) #Phase Change Materials Research #nanoparticles nucleation surface interactions
paper · pdf · doi:10.48550/arxiv.1904.05698
openalex publication_date 2019/04/11 · openalex created_date 2022/07/29 · openalex updated_date 2026/07/28
In this paper we formulate a Stefan problem appropriate when the\nthermophysical properties are distinct in each phase and the phase-change\ntemperature is size or velocity dependent. Thermophysical properties invariably\ntake different values in different material phases but this is often ignored\nfor mathematical simplicity. Size and velocity dependent phase change\ntemperatures are often found at very short length scales, such as nanoparticle\nmelting or dendrite formation; velocity dependence occurs in the solidification\nof supercooled melts. To illustrate the method we show how the governing\nequations may be applied to a standard one-dimensional problem and also the\nmelting of a spherically symmetric nanoparticle. Errors which have propagated\nthrough the literature are highlighted. By writing the system in\nnon-dimensional form we are able to study the large Stefan number formulation\nand an energy-conserving one-phase reduction. The results from the various\nsimplifications and assumptions are compared with those from a finite\ndifference numerical scheme. Finally, we briefly discuss the failure of\nFourier's law at very small length and time-scales and provide an alternative\nformulation which takes into account the finite time of travel of heat carriers\n(phonons) and the mean free distance between collisions.\n