Stability of the Ignited State in Packed-Bed Reactor

The ignited state is associated with a thin reaction zone and a steep temperature gradient ahead of the front. The stability of this front is analyzed for small radial and azimuthal perturbations. The near-equidiffusional assumption is made, and the deviation of the Lewis number from unity is considered as the bifurcation parameter. The analysis shows that the planar front becomes unstable at Lewis numbers above unity after a Hopf bifurcation. The oscillatory front collapses into hot spots or rings which oscillate around the axial axis. For Lewis numbers less than one, a steady-state cellular front structure is found.