Mass-conserving Phase-Field Numerical Simulation of Surfactant-induced Two-phase Flows*

The Cahn-Hilliard Navier-Stokes equations are employed for interface-capturing in two-phase flow simulations. This method is based on the minimization of the total energy of interfacial flows, including kinetic, potential, and free energies. When surfactants are present, additional energy terms are incorporated to account for their interactions with the bulk flow. The reduction of surface tension due to surfactant accumulation is described by a logarithmic equation of state, while non-uniform surfactant distribution induces Marangoni stress. Validation of the code involves examining drop deformation in shear flow for both clean and contaminated drops, with comparisons to Taylor's theory. The role of surfactants on the dynamics of drop oscillation, liquid thread breakup, and drop impact onto solid surfaces is numerically investigated across varying surfactant bulk concentrations. The simulations leverage adaptive mesh refinement (AMR) at the interface and utilize a Lagrange multiplier to maintain mass conservation, counteracting the adverse effects of mesh-coarsening on global conservation of phase-field variables.