Eck C, Knabner P (2002)
Publication Type: Book chapter / Article in edited volumes
Publication year: 2002
Publisher: Springer
Edited Volumes: Multiscale Problems in Science and Technology
City/Town: Berlin, Heidelberg
Pages Range: 175-187
ISBN: 978-3-540-43584-6
DOI: 10.1007/978-3-642-56200-6_7
In many liquid-solid phase transitions, a specific dendritic microstructure of the phase interface is observed. In this contribution we present two-scale models capable to describe the evolution of equiaxed microstructure. The models are based either on a sharp interface model or on a phase field model for phase transitions in binary alloys. In both cases, a formal asymptotic expansion in terms of a scale parameter ε for the microstructure is carried out, with solute diffusivity scaling proportional to ε2. In the limit ε→0 we obtain a two scale-model consisting of a macroscopic heat transport equation and, at each point of the macroscopic domain, of a local cell problem modeling the microsegregation and the evolution of the microstructure.
APA:
Eck, C., & Knabner, P. (2002). Two-Scale Models for Liquid-Solid Phase Transitions in Binary Material with Equiaxed Microstructure. In Nenad Antonić, C. J. van Duijn, Willi Jäger, Andro Mikelić (Eds.), Multiscale Problems in Science and Technology. (pp. 175-187). Berlin, Heidelberg: Springer.
MLA:
Eck, Christof, and Peter Knabner. "Two-Scale Models for Liquid-Solid Phase Transitions in Binary Material with Equiaxed Microstructure." Multiscale Problems in Science and Technology. Ed. Nenad Antonić, C. J. van Duijn, Willi Jäger, Andro Mikelić, Berlin, Heidelberg: Springer, 2002. 175-187.
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