Transient growth stability analysis of evaporating sessile drops comprising binary mixtures

The evaporation and spreading dynamics of a binary mixture sessile drop are complex due to the interplay of thermal and solutal Marangoni stresses alongside the hydrodynamic transport, evaporation, mass diffusion and capillary stress of the drop. Under the assumption of an ideal binary mixture and linear surface tension dependence on temperature and concentration, we recently investigated the quasi-steady linear stability of volatile bicomponent sessile drops with high wettability comprising ethanol-water deposited on heated substrates.  The stress singularity at the contact line is avoided by including a precursor film. Our analysis shows several competing modes for bicomponent drops – indicating that the quasi-steady analysis may not be suitable. To understand the roles of these modes better, we have developed a transient growth analysis. This linear stability analysis applies small disturbances to the binary system, giving perturbed stability equations that evolve with time. These are solved alongside the base state to find the linear stability growth characteristics.