A Mathematical Model for Flash Sintering

被引:30
作者
Hewitt, I. J. [1 ]
Lacey, A. A. [2 ,3 ]
Todd, R. I. [4 ]
机构
[1] Univ Oxford, Inst Math, Oxford OX1 3LB, England
[2] Heriot Watt Univ, Maxwell Inst Math Sci, Edinburgh EH14 4AS, Midlothian, Scotland
[3] Heriot Watt Univ, Dept Math, Sch Math & Comp Sci, Edinburgh EH14 4AS, Midlothian, Scotland
[4] Univ Oxford, Dept Mat, Oxford OX1 3PH, England
关键词
flash sintering; non-local problems; non-linear heat equations; blow-up; THERMISTOR PROBLEM; THERMAL RUNAWAY; BLOW-UP; EQUATIONS; ZIRCONIA; PROFILES;
D O I
10.1051/mmnp/201510607
中图分类号
Q [生物科学];
学科分类号
07 ; 0710 ; 09 ;
摘要
A mathematical model is presented for the Joule heating that occurs in a ceramic powder compact during the process of flash sintering. The ceramic is assumed to have an electrical conductivity that increases with temperature, and this leads to the possibility of runaway heating that could facilitate and explain the rapid sintering seen in experiments. We consider reduced models that are sufficiently simple to enable concrete conclusions to be drawn about the mathematical nature of their solutions. In particular we discuss how different local and non-local reaction terms, which arise from specified experimental conditions of fixed voltage and current, lead to thermal runaway or to stable conditions. We identify incipient thermal runaway as a necessary condition for the flash event, and hence identify the conditions under which this is likely to occur.
引用
收藏
页码:77 / 89
页数:13
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