The structure of a curved premixed flame tip under the influence of external heat loss, fuel spray, and preferential diffusion is investigated using large activation energy asymptotics. Two flame structures, normal and inverted Bunsen flames, are considered. Two spray modes, completely and partially prevaporized burning modes, are identified. Five parameters are used in the analysis, including the droplet size, amount of liquid-fuel loading, external heat loss, stretch, and Lewis number (Le). The internal heat transfer resulting from droplets gasifying provides internal heat loss and heat gain for rich and lean sprays, respectively. Stretch is negative for a normal Bunsen flame but positive for an inverted Bunsen flame. Stretch strengthens (or weakens) the burning intensity of the Le >1 (or Le <1) normal Bunsen flame but decreases (or increases) the burning intensity of the Le >1 (or Le <1) inverted Bunsen flame. The burning intensity of a flame tip weakens when the curved flame experiences a larger amount of external heat loss and intensifies (or weakens) when the lean (or rich) spray has a smaller droplet size or a larger amount of liquid loading. For a lean methanol-spray normal Bunsen flame with Le >1 or a rich methanol-spray inverted Bunsen flame with Le <1, closed tip solutions are obtained. Conversely, stretch weakens the burning intensities of lean methanol-spray inverted Bunsen flames with Le > 1, or rich methanol-spray normal Bunsen flames with Le <1, eventually leading to tip opening. The opening becomes wider when the external heat loss increases, the droplet size decreases (or increases), or liquid loading increases (or decreases) for the rich (or lean) sprays. Note that for a lean methanol-spray normal (or inverted) Bunsen flame with Le > 1, if liquid loading is large enough and droplet size is sufficiently small, there. is a flame transition from a normal (or inverted) Bunsen flame through a planar flame to an inverted (or normal) Bunsen flame. Finally, the critical value of droplet size, at which there exists a planar flame rather than a normal (or inverted) Bunsen flame, increases with increasing liquid loading or decreasing external heat loss. (C) 2015 Elsevier Ltd. All rights reserved.