2025 AIChE Annual Meeting
(646d) Oscillations of Slightly Viscous Liquid Drops Covered with a Monolayer of Insoluble Surfactant.
A fundamental understanding of the oscillations of surfactant-laden drops in air is crucial for applications including the measurement of interfacial properties, liquid atomization, inkjet printing, atmospheric sciences, and drop impact. In this study, the small-amplitude oscillations of a free drop of an incompressible Newtonian liquid covered with a monolayer of an insoluble surfactant are analyzed. Here, the free boundary problem comprised of the Navier-Stokes system governing liquid motion within the drop and the convection-diffusion equation governing surfactant transport along the liquid-gas interface are solved analytically using linear stability analysis and computationally using a finite element-based sharp-interface simulation technique. The presence of surfactant lowers surface tension and thereby reduces the oscillation frequency. On the other hand, its presence generates surface tension gradients and thus enhances damping rate. Special attention is devoted to the variation of the damping rate D with the surfactant strength parameter B. An approximate analytical solution in the limit of small viscosity (M) is examined to elucidate the key role played by a certain dimensionless number involving the ratio B/M. The roles of vorticity and energy dissipation in the dynamics are also explored, and insights gained from them are used to explain the variation of D as a function of the initial surfactant loading.