Reduced model for capillary breakup with thermal gradients: Predictions and computational validation

TL;DR

This paper validates a simplified model predicting silicon droplet sizes during capillary breakup under thermal gradients by comparing it with detailed 3D simulations, demonstrating its accuracy and utility for experimental design.

Contribution

The paper provides the first quantitative validation of a reduced capillary breakup model against detailed simulations using consistent physical parameters and temperature profiles.

Findings

Excellent agreement between the reduced model and 3D simulations across various feed speeds.

The local capillary number at breakup remains nearly constant regardless of feed speed.

The reduced model is computationally efficient and useful for experimental planning.

Abstract

It was recently demonstrated that feeding a silicon-in-silica coaxial fibre into a flame$\mathord{-}$imparting a steep silica viscosity gradient$\mathord{-}$results in the formation of silicon spheres whose size is controlled by the feed speed [Gumennik et al., Nat.Commun. 4, 2216 (2013)]. A reduced model to predict the droplet size from the feed speed was then derived by Mowlavi et al. [Phys. Rev. Fluids. 4, 064003 (2019)], but large experimental uncertainties in the parameter values and temperature profile made quantitative validation of the model impossible. Here, we validate the reduced model against fully-resolved three-dimensional axisymmetric Stokes simulations using the exact same physical parameters and temperature profile. We obtain excellent quantitative agreement for a wide range of experimentally relevant feed speeds. Surprisingly, we also observe that the local capillary number at the breakup location remains almost constant across all feed speeds. Owing to its low computational cost, the reduced model is therefore a useful tool for designing future experiments.