# Particle size selection in capillary instability of locally heated co-axial fiber

## TL;DR

This paper investigates the physical mechanisms behind particle size selection in capillary instability during the localized heating of co-axial fibers, revealing the nonlinear nature of the process through simulations.

## Contribution

It demonstrates that linear stability analysis fails to predict particle size, while nonlinear simulations accurately recover experimental results, highlighting the nonlinear dynamics involved.

## Key findings

- Linear stability analysis does not predict particle size.
- Nonlinear simulations match experimental particle sizes.
- Particle formation is an intrinsically nonlinear process.

## Abstract

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.