  We provide a mathematical analysis of a thermo-diffusive combustion model of
lean spray flames, for which we prove the existence of travelling waves. In the
high activation energy singular limit we show the existence of two distinct
combustion regimes with a sharp transition -- the diffusion limited regime and
the vaporisation controlled regime. The latter is specific to spray flames with
slow enough vaporisation. We give a complete characterisation of these regimes,
including explicit velocities, profiles, and upper estimate of the size of the
internal combustion layer. Our model is on the one hand simple enough to allow
for explicit asymptotic limits and on the other hand rich enough to capture
some particular aspects of spray combustion. Finally, we briefly discuss the
cases where the vaporisation is infinitely fast, or where the spray is
polydisperse.
