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• A practical multi-interfacial tension model has been considered in the SPH framework. • Obtained results corresponded to the analytical solution of the multi-contact angles. • The model is applicable to the dynamic analysis involving two or more liquid phases. • The contribution of momentum leads to a temporal change of triple line morphology. To analyze the complex droplet transient deformation involving two immiscible phases, a practical multi-interfacial tension model has been introduced in the SPH framework. The attraction, which operates on the interface between the different phases is explicitly defined as London dispersion force using the Fowkes theoretical model, and the interfacial tension can be calculated using the sum of the attraction magnitudes corresponding to the surrounding particles. The analytical solution demonstrated good agreement with the simulated results corresponding to the macroscopic multicontact angles and nature of interphase interfacial forces. This simple model is widely applicable to the dynamic analysis of capillary forces involving two or more liquids, and we demonstrated its application to the simulation of the deformation behavior of a binary droplet that contacts a solid. The solid-liquid-liquid contact angle is not sufficient to predict the equilibrium morphology, and the momentum exchange between the two liquids should be considered. [ABSTRACT FROM AUTHOR]