A Mathematical Model for Flash Sintering

Ian J. Hewitt, Andrew Alfred Lacey, Richard I. Todd

Research output: Contribution to journalArticlepeer-review

29 Citations (Scopus)
59 Downloads (Pure)


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.
Original languageEnglish
Pages (from-to)77-89
Number of pages13
JournalMathematical Modelling of Natural Phenomena
Issue number6
Publication statusPublished - 2 Oct 2015


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