Dynamical surface fluctuations of a contaminated microbubble

We investigate the dynamical surface fluctuations of a surfactant-laden and surface viscous microbubble. Particular cases of a free system and that of micrometric particles where a time-dependent periodic forcing force is exerted at its poles are examined as well as more general forcing mechanisms such as magnetic, electric or acoustic fields. Assuming a small-amplitude approximation in the surface fluctuations, the effect of bulk viscosity is neglected and assuming the forcing are point particles, analytical expressions are derived for the dynamic fluctuations of the interface. The damping effect of surface viscosity and soluto-Marangoni fields on surface fluctuations is studied with the modified wave dispersion. This is a first step in characterising the interfacial fluctuations of a microbubble more systematically, under different levels of surface contamination.