Pattern formation on a bubble: Capillary waves on surfactant-laden interfaces*

On a surface-tension-driven liquid interface, the behaviour of the capillary wave is often a bellweather of the overall motion of the system. Consequently, understanding how capillary waves behave is crucial in various interfacial flows at the edge of instability, such as capillary-driven breakup, liquid bridges and pattern formation phenomena. Examining the dynamics of the capillary waves on a surfactant-laden interface, the role of critical wavenumber (at which the capillary wave transitions from the dispersive underdamped regime to the non-dispersive overdamped regime) is explored in the context of the onset behaviour of pattern formation instabilities observed experimentally. Moreover, we look at the effect of the convective-diffusive transport of insoluble surfactants along the interface on the critical wavenumber and the overall dynamics of the capillary waves.