Particle size selection in capillary instability of locally heated coaxial fiber

Harnessing fluidic instabilities to produce structures with robust and regular properties has recently emerged as a new fabrication paradigm. This approach is exemplified in the work of Gumennik et al. [Nat. Commun. 4, 2216 (2103)], in which the authors fabricated silicon spheres by feeding a silicon-in-silica coaxial fiber into a flame. Following the localized melting of the silicon, a capillary instability of the silicon-silica interface induced the formation of uniform silicon spheres. Here we investigate 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 result demonstrates 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.