  Harnessing fluidic instabilities to produce structures with robust and
regular properties has recently emerged as a new fabrication paradigm. This is
exemplified in the work of Gumennik et al. [Nat. Comm. 4:2216, DOI:
10.1038/ncomms3216, (2013)], in which the authors fabricate silicon spheres by
feeding a silicon-in-silica co-axial fiber into a flame. Following the
localized melting of the silicon, a capillary instability of the silicon-silica
interface induces the formation of uniform silicon spheres. Here, we try to
unravel the physical mechanisms at play in selecting the size of these
particles, which was notably observed by Gumennik et al. to vary monotonically
with the speed at which the fiber is fed into the flame. Using a simplified
model derived from standard long-wavelength approximations, we show that linear
stability analysis strikingly fails at predicting the selected particle size.
Nonetheless, nonlinear simulations of the simplified model do recover the
particle size observed in experiments, without any adjustable parameters. This
shows that the formation of the silicon spheres in this system is an
intrinsically nonlinear process that has little in common with the loss of
stability of the underlying base flow solution.
