Sintering of viscous droplets under surface tension

Abstract

We conduct experiments to investigate the sintering of high-viscosity liquid droplets. Free-standing cylinders of spherical glass beads are heated above their glass transition temperature, causing them to densify under surface tension. We determine the evolving volume of the bead pack at high spatial and temporal resolution. We use these data to test a range of existing models. We extend the models to account for the time-dependent droplet viscosity that results from non-isothermal conditions, and to account for non-zero final porosity. We also present a method to account for the initial distribution of radii of the pores interstitial to the liquid spheres, which allows the models to be used with no fitting parameters. We find a good agreement between the models and the data for times less than the capillary relaxation timescale. For longer times, we find an increasing discrepancy between the data and the model as the Darcy outgassing time-scale approaches the sintering timescale. We conclude that the decreasing permeability of the sintering system inhibits late-stage densification. Finally, we determine the residual, trapped gas volume fraction at equilibrium using X-ray computed tomography and compare this with theoretical values for the critical gas volume fraction in systems of overlapping spheres.