Direct numerical simulation of interfacial waves with surface rheological effects

The interfacial mechanics of complex fluid interfaces are governed by the interplay between surface viscoelasticity, Marangoni stresses, and the solubility and diffusivity of surfactants. Among these, surface rheological effects remain relatively underexplored. Surfactant-laden interfaces, such as those covered with hexadecanol, can form highly viscous membranes that exert a two-dimensional in-plane friction as interfacial particles move relative to one another. This generates viscous dissipation along the interface. In this work, we develop a numerical method to incorporate surface viscous effects into three-dimensional multiphase flow simulations. Our approach employs a hybrid level-set/front-tracking technique within a one-fluid formulation: the interface is represented by Eulerian level-set functions and tracked using Lagrangian elements. Surface viscosity is modelled via the Boussinesq–Scriven constitutive law, which captures the interfacial stresses due to both shear and dilatational viscous tractions. The numerical framework is validated against benchmark cases and applied to study parametric surface waves. We demonstrate the influence of both shear and dilatational surface viscosity on the dynamics of square Faraday waves.