Drop size selection in axially heated co-axial fiber capillary instability

We analyze the sphere size selection mechanism in silicon-in-silica sphere formation through the application of an external axial thermal gradient to a co-axial silicon-in-silica fiber (Gumennik et al., Nature Com., 2013). We first apply a convective/absolute stability analysis to the in-fibre capillary instability governing the sphere formation and demonstrate that the resulting wavelength selection predicts a finite but still too large wavelength. A global stability analysis is then pursued, which accounts for the spatial inhomogeneity of the base flow.