The nature of the edge flame formed downstream of a splitter plate initially separating two co-flows of fuel vapor and droplets and an oxidant is investigated. The way in which both the presence of a spray of fuel droplets and the different diffusivities of the fuel vapor and the oxidant influence the combustion in the mixing layer formed is examined. The spray is described using the sectional approach and for simplicity a mono-sectional model is utilized. The steady state behavior of the system is described using a diffusional-thermal model and the governing non-linear equations are solved numerically. The results illustrate how the initial droplet load, the vaporization Damkohler number and the Lewis numbers of the fuel vapor and oxidant determine the intensity and location of the edge flame and its trailing diffusion flame. These parameters are also shown to possess critical values for the onset of flame oscillations. In particular, altering the oxidant Lewis number (by, say, changing the diluent in which it is supplied) can effectively dampen undesirable spray induced oscillations.