In this thesis, I have worked on direct numerical simulations to elucidate the physics of vortex- surface interaction in turbulent multiphase jets for industrial mixing applications. The thesis topic focuses on understanding physics of interface breakup and coalescence, which exemplify situations wherein the interface undergoes topological transitions, e.g. filament breakup into drops, and merg- ing of drops/bubbles due to coalescence, accounting for surfactant-induced effects. These transitions involve the development of singularities where interfacial distances vanish and velocity fields diverge, requiring highly-specialised numerical techniques.