Dripping-onto-droplet capillary breakup

TL;DR

This study combines experiments, simulations, and theory to analyze capillary breakup in dripping-onto-droplet scenarios, revealing flow regimes, scaling laws, and potential rheometric applications.

Contribution

It introduces a comprehensive mixed approach to characterize filament breakup dynamics and identifies flow regimes affected by gravity, with a new diagram correlating breakup time and flow parameters.

Findings

Identified three flow regimes: capillary-inertial, capillary-viscous, and mixed.

Developed a diagram linking filament breakup time with dimensionless parameters.

Showed DoD can measure extensional relaxation time of polymer solutions.

Abstract

This experimental, numerical, and theoretical study investigates the capillary thinning and breakup of Newtonian filaments formed following the coalescence of a millimetric-nozzle-generated pendant drop with a lower droplet cap contained in a millimetric cylinder in ambient air, i.e., dripping-onto-droplet capillary breakup (DoD). Our mixed approach combines filament breakup experiments recorded with a high-speed camera and three-dimensional numerical simulations based on a variational multiscale framework for multiphase fluid flows. The results are analysed by considering the dynamics of fluid filament thinning, energy transfers, and scaling laws. Three flow regimes are highlighted: capillary-inertial, capillary-viscous, and mixed capillary-inertial-viscous. All regimes are affected by gravity. The findings are summarised in a two-dimensional diagram that correlates the filament breakup time with different flow regimes using the important dimensionless parameters of the problem, e.g., the Ohnesorge number (which relates the viscous stress to inertial and capillary stresses) and the Bond number (which balances the gravitational stress with the capillary one). This diagram can be used to quantify both the liquid viscosity and the liquid-gas surface tension (for Newtonian fluids). Lastly, we demonstrate that DoD can also be used as a rheometric test, giving access to the extensional relaxation time of polymer solutions (for viscoelastic fluids).