An investigation of spherical micro/nanoparticle melting using asymptotic matchings in a weak formulation
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Institute for Advanced Study, Shenzhen University, Nanshan District Shenzhen, Guangdong, China
Submission date: 2023-02-15
Final revision date: 2023-03-22
Acceptance date: 2023-03-29
Online publication date: 2023-05-19
Publication date: 2023-07-31
Corresponding author
Yue Chan   

Institute for Advanced Study, Shenzhen University, China
Journal of Theoretical and Applied Mechanics 2023;61(3):419-426
In this paper, we investigate the speed of moving boundaries for melting micro/nanoparticles in the initial and final stages using asymptotic matchings in a weak formulation of the prob- lem. We find that such a speed is initially proportional to the flux across the moving bound- ary, however a blowup occurs in a finite time when the surface tension is considered, both numerically and theoretically, by assuming linear relations between thermal conductivities and diffusivities, which paves the way to tackle the related two and higher phase change problems. Last but not least, we verify our theoretical outcomes using a quasi-stationary approximation approach.
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