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. Our quasi-steady linear stability analysis of volatile bicomponent sessile drops comprising ethanol-water mixtures placed on heated substrates demonstrates that evaporation is highly unstable with several competing modes. Whilst the analysis qualitatively agrees with experiments, presence of multiple competing modes indicates that the quasi-steady analysis may not be suitable for volatile bicomponent sessile droplet systems. To understand the roles of these modes better, we perform a transient growth analysis. Here, we apply small disturbances to the binary system base state, giving perturbed stability equations that evolve with time. Perturbations are introduced into the system at an early time instance. These are solved alongside the base state to find the linear stability growth characteristics, in order to compare to the dispersion curves obtained from the quasi-steady state stability analysis. Similar to findings from our quasi-steady analysis, our results show drop interfacial instabilities occur predominantly at the contact line.