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.
Highlights
The sintering of high-viscosity droplets to form a denser, connected mass is important in a range of industrial and natural scenarios, including the fabrication of ceramics [1], metals and glass, the welding of volcanic ash [2] and the vitrification of Iron Age fortification walls [3,4]
We focus on what is commonly called ‘viscous sintering’—the sintering of two or more viscous droplets in the regime where interfacial tension drives fluid flow—which constitutes a viscous end-member of droplet coalescence problems
We show that viscous sintering can be modelled using a modified version of the original Mackenzie & Shuttleworth [6] theory
Summary
The sintering of high-viscosity droplets to form a denser, connected mass is important in a range of industrial and natural scenarios, including the fabrication of ceramics [1], metals and glass, the welding of volcanic ash [2] and the vitrification of Iron Age fortification walls [3,4]. We test the commonly used [2,7,8,19,24] exponential approximation of the vented bubble model (equations (2.19) and (2.22)) as described in §2d, where we note the implicit assumption that bubble radius is independent of time Despite this assumption, which must, in reality, be violated, the results of fitting for the timescale λb for both the φ → 0 and φ → φf conditions are very close to each other (figure 5g,h) and almost indistinguishable from those of the small φ approximation, resulting in average best-fit radii in excellent agreement with ai and a coefficient of determination of 0.995 (table 1). The agreement between the exponential approximation and data is slightly closer than for the vented bubble models, astb approaches unity
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