Unusual damping behaviour in nonlinear shape oscillations of surfactant-laden drops

Drop shape oscillations have received considerable attention in the literature since the earliest works of Lord Rayleigh, Sir Horace Lamb, and Chandrasekhar. It is widely understood that surfactants lower the restoring force due to surface tension and enhance the damping of such oscillations. As we show here, for the first time, via three-dimensional direct numerical simulations, however, however, the nonlinearity in the coupled surfactant-laden Marangoni stress, diminishes the damping of such oscillations over a range of system parameters. We also demonstrate via a scaling analysis the dependence of the oscillatory dynamics on the surfactant elasticity parameter in which we contrast the surfactant-free and surfactant-laden cases. This analysis captures the trends obtained from the numerical predictions.