Diffuse-interface modeling of two-phase flows with a Boussinesq-Scriven interface

• Extension of the diffuse-interface method for computational interfacial rheology. • Application to two-phase flows with a Boussinesq-Scriven interface. • Convergence tests and 2D droplet deformation and coalescence examples. In this study, the diffuse-interface method is employed to model a Boussinesq-Scriven interface that incorporates surface viscosity alongside surface tension. This method differs from the sharp-interface approach in its continuous treatment of the additional surface stress in the momentum conservation equation. The finite element formulation and numerical results are presented. Convergence tests are carried out by using the method of manufactured solution, and optimal convergence rates are observed in both time and space. For a two-dimensional droplet deformation problem, the results show that the diffuse-interface method converges to the sharp-interface method as the diffuse-interface thickness decreases. The present formulation is also applied to a two-dimensional droplet coalescence problem to investigate the effect of surface viscosity.