Direct numerical simulations of interfacial flows with surfactant-induced complexities involving surface viscous stresses are performed within the framework of the Level Contour Reconstruction Method (LCRM); this hybrid front-tracking/level-set approach leverages the advantages of both methods. In addition to interface-confined surfactant transport that results in surface diffusion and Marangoni stresses, the interface, endowed with shear and dilatational viscosities; these act to resist deformation arising from velocity gradients in the plane of the two-dimensional manifold of the interface, and interfacial compressibility effects, respectively. By adopting the Boussinesq-Scriven constitutive model, We provide a mathematical formulation of these effects that accurately captures the interfacial mechanics, which is then implemented within the LCRM-based code by exploiting the benefits inherent to the underlying front-tracking/level-sets hybrid approach. We validate our numerical predictions against a number of benchmark cases that involve drops undergoing deformation when subjected to a flow field or when rising under the action of buoyancy. The results of these validation studies highlight the importance of adopting a rigorous approach in modelling the interfacial dynamics. We also present results that demonstrate the effects of surface viscous stresses on interfacial deformation in unsteady parametric surface waves and atomisation events.
Panda et al. (Mon,) studied this question.