Interfacial transport phenomena in two-phase flows with insoluble surfactants, e.g., interfacial heat and mass transfer and boiling, are frequent in nature and industry. Multiple examples can be found in thermal energy technology, and the so-called unit operations of chemical engineering. Surfactants modify the hydrodynamics and transport processes of two-phase flows. Indeed, this work introduces a novel unstructured conservative level-set (UCLS) method [1, 2, 3, 4] for interfacial transport processes in two-phase flows with insoluble surfactant and Marangoni effects on collocated unstructured meshes. This method enforces the mass conservation of insoluble surfactants at the interface. Surface tension is coupled to the surfactant concentration through the Langmuir equation of state, together with a consistent linearized form. Furthermore, a transport equation is solved at the interface for the evolution of insoluble surfactant. The transport equations are discretized within a three-dimensional finite-volume framework on collocated and unstructured meshes, and pressure–velocity coupling is handled via the fractional-step projection method. Convective transport is resolved with unstructured TVD flux-limiters to reduce numerical diffusion and suppress spurious oscillations, whereas diffusive terms are discretized with a central-difference scheme including non-orthogonal corrections. Verification and validation are carried out using gravity-driven rising bubbles. The validated solver is then employed to investigate the influence of insoluble surfactants, parameterized by the Marangoni number, on the bubble dynamics on unconfined domain and vertical pipes, with Eotvos number Eo ≥ 3 and Morton number Mo ≤ 10−4. The results highlight how surfactant-induced surface-tension gradients alter interfacial shear, thereby modifying the drag coefficient (CD) and the interfacial mass-transfer rate (Sherwood number, Sh), providing physical insight relevant to bubbly flows, and data to develop or improve correlations for CD and Sh.