(b) Probability of clogging with N particles left in the hopper. For these data g / F 0 = 10 − 2 this matches the blue diamonds in Figs. For w / d = 1.8, 1.6, and 1.25, the data are taken from simulation runs with 1454, 1697, and 1579 trials respectively. The lines are the best fit to the Gompertz hazard rate (integrated over the next 50 droplets). (a) Hazard rate: probability of clogging as the next 50 droplets flow out, as a function of the number of particles N left in the hopper. Additionally, an analysis of the number of particles left in the hopper when clogging occurs provides evidence for a hydrostatic pressure effect that is relevant for the clogging of soft particles, but less so for the harder (glass) or frictional (silicone rubber) particles.
In contrast, for the silicone rubber particles with larger frictional interactions, arches have more particles than the low friction cases. For particles with low or no friction, the average number of particles in a clogging arch depends only on the ratio between hopper exit width and the mean particle diameter. Results from both simulations and experiments demonstrate that clogging is easier for reduced gravitational force or stiffer particles. Our simulation mimics the experiments using purely two-dimensional soft particles with viscous interactions but no friction. The hopper chamber has an adjustable exit width and tilt angle (the latter to control the magnitude of gravitational forcing). The experiments utilize spheres made with hydrogel, silicone rubber, and glass. We study the outflow of soft particles through quasi-two-dimensional hoppers with both experiments and simulations.
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