Self-propagating High temperature Synthesis (SHS) in the high activation energy regime

TL;DR

This paper rigorously derives the limiting behavior of self-propagating high temperature synthesis (SHS) in the high activation energy regime, revealing a connection to the Stefan problem and explaining pulsating wave phenomena.

Contribution

It provides a precise mathematical limit of SHS in the high activation energy regime, linking it to the Stefan problem and clarifying pulsating wave observations.

Findings

Limit of SHS described by Stefan problem for supercooled water.

Connection between high activation energy limit and pulsating wave phenomena.

Open questions remain on convergence proofs.

Abstract

We derive the precise limit of SHS in the high activation energy scaling suggested by B.J. Matkowksy-G.I. Sivashinsky in 1978 and by A. Bayliss-B.J. Matkowksy-A.P. Aldushin in 2002. In the time-increasing case the limit turns out to be the Stefan problem for supercooled water with spatially inhomogeneous coefficients. Although the present paper leaves open mathematical questions concerning the convergence, our precise form of the limit problem suggest a strikingly simple explanation for the numerically observed pulsating waves.