Experimental evidence points to a rich variety of physical scenarios that arise when a
laminar flame propagates through a pre-mixture of evaporating liquid fuel and a gaseous
oxidant. In this paper new results of time-dependent numerical simulations of rich
off-stoichiometric spray flame propagation in a two-dimensional channel are presented. A
constant density model is adopted, thereby eliminating the Darrieus-Landau instability. It
is demonstrated that there exists a narrow band of vaporization Damkohler numbers (the
ratio of a characteristic flow time to a characteristic evaporation time) for which the
flame propagation is oscillatory. For values outside this range steady state propagation
is attained but with a curved (cellular) flame front. The critical range for the
non-steady propagation is also found to be a function of the Lewis number of the deficient
reactant.