Evolution of surfactant-laden viscous capillary-gravity waves – Initial Value Problem and Direct Numerical Simulations

The effect of surfactants on the fluid-fluid interfaces ranges from the small scales of bubbles [Tagawa, 2014] to the large scales of breaking waves [Erinin et. al., 2023]. In the present study, we investigate the effect of surfactants on the evolution of small-amplitude viscous waves by solving an Initial Value Problem (IVP). The solution of viscous wave IVP shows the presence of continuous modes along with the normal modes [Farsoiya, 2019]. To validate the solution of the initial value problem, we perform Direct Numerical Simulations (DNS) of small surfactant-laden waves and validate the results of the initial value problem. We extend the analysis to study the effect of surfactants on finite amplitude waves. The DNS are performed using the hybrid scheme of Volume of Fluid and Phase-Field interface representation that simulates insoluble surfactant transport [Farsoiya et. al., 2024]. However, the resolution requirements increase with the increase in surface Péclet number and become prohibitive. In the present work, we improved the numerical scheme and validated the method for infinite Péclet number i.e. strictly advective transport of surfactants.