Sinking dynamics and splitting of a granular droplet

Abstract

Recent experimental results have shown that binary granular materials fluidized by combined vibration and gas flow exhibit Rayleigh-Taylor-like instabilities that manifest themselves in rising plumes, rising bubbles, and the sinking and splitting of granular droplets. This work explores the physics behind the splitting of a granular droplet that is composed of smaller and denser particles in a bed of larger and lighter particles. During its sinking motion, a granular droplet undergoes a series of binary splits resembling the fragmentation of a liquid droplet falling in a miscible fluid. However, different physical mechanisms cause a granular droplet to split. By applying particle image velocimetry and numerical simulations, we demonstrate that the droplet of high-density particles causes the formation of an immobilized zone underneath the droplet. This zone obstructs the downwards motion of the droplet and causes the droplet to spread and ultimately to split. The resulting fragments sink at inclined trajectories around the immobilized zone until another splitting event is initiated. The occurrence of consecutive splitting events is explained by the reformation of an immobilized zone underneath the droplet fragments. Our investigations identified three requirements for a granular droplet to split: (1) frictional interparticle contacts, (2) a higher density of the particles composing the granular droplet compared to the bulk particles, and (3) a minimal granular droplet diameter.

Multifluid model simulations of gravitational instabilities in fluidized binary granular materials

“…36 Overall, turning off the Schaeffer model 16 in MFM simulations has the equivalent effects as turning off particle friction in discrete particle simulations. Therefore, Figure 6 shows that particle friction contacts are necessary for granular droplet splitting, consistent with the conclusion of the discrete particle simulation study of Metzger et al 8 Comparing Figures 6 to 4, it can be seen that with the Schaeffer model 16 turned off, the droplet sinking occurs much faster than MFM simulations with the Schaeffer model 16 turned on, confirming the inference that the accuracy of the used frictional solids stress model is one of the reasons that lead to the discrepancy of the necessary time for droplet sinking in simulations.…”

“…Figures 3–5 demonstrate that MFM simulations can capture the granular droplet splitting instability, although the related solidification has been regarded as a persistent challenge in MFM simulations of gas–solid fluidization 9,10 . In a recent discrete particle simulation study, 8 particle properties, including the coefficient of friction, particle diameter and particle density, were varied to explore the particle requirements for granular droplet splitting to occur. The results from this recent study show that both frictional inter‐particle contacts and a higher density of the particles composing the granular droplet as compared to the bulk particles are necessary for granular droplet splitting.…”

“…However, possibly due to the use of a gas–solids drag law and the modeling approach for vibration (see later), using the same median particle size in simulations can produce obvious gas bubbles in the bed if the same vibration conditions as in experiments are used, although it has been found that using the same median particle size in simulations can predict U mf quite similar to experimental values: the predicted U mf of solids with ρ s,l = 2500 kg/m 3 and diameter d s,l = 1.70 mm is 0.80 m/s, which is within 10% of the U mf of the light particles, 0.87 m/s, with ρ s,l = 2500 kg/m 3 and diameter d s,l = 1.70 ± 0.15 mm in experiments; and the predicted U mf of solids with ρ s,h = 6000 kg/m 3 and diameter d s,h = 1.10 mm is 0.92 m/s, which is within 10% of the U mf of the heavy particles, 0.95 m/s, with ρ s,h = 6000 kg/m 3 and diameter d s,h = 1.10 ± 0.10 mm in experiments. The recent discrete particle simulation study of granular droplet splitting 8 also indicated that simulations are more prone to gas bubbles than experiments with the use of vibration. Therefore, to avoid the effects of gas bubbles on the dynamics, we decided to slightly tune the particle size in simulations to make both sets of particles have the same U mf .…”

“…As mentioned earlier, the U mf of both sets of particles in experiments is slightly different. Even so, the effects of gas bubbles are not obvious in The recent discrete particle simulation study of granular droplet splitting 8 also indicated that simulations are more prone to gas bubbles than experiments with the use of vibration. Therefore, to avoid the effects of gas bubbles on the dynamics, we decided to slightly tune the particle size in simulations to make both sets of particles have the same U mf .…”

“…Of particular interest is the granular droplet splitting instability. A recent particle‐image‐velocimetry experiment and discrete particle simulation study 8 revealed that the granular droplet made of heavier particles causes the formation of a local solidification zone underneath the droplet, which then results in the granular droplet spreading and ultimately splitting. Continuum models of gas–solid flows, however, have been shown to struggle to capture local solidification and the related fluid–solid transitions 9,10 .…”