| The mechanisms of flow-induced spontaneous segregation and pattern formation of multi-component granular materials are the hotspots and difficult problems in powder science and engineering. We studied the granular avalanche, dense flow, jamming, hysteretic transition between the "continuous flow" and "discrete avalanche", the mechanisms of spontaneous segregation and pattern formation of binary granular materials in quasi-2D diveces, the results suggest:1. In quasi-two dimensional vertical Hele-Shaw cell, flow rate Q and the properties of granular materials （the size ratio of big and small particle: φ=dL/dS, and the difference of the angle of repose between big and small ingredients:δ=θL-θS） have great effect on the flow process and heap formation of the binary granular materials. Granular mixtures tend to mixed when the flow rate Q increases and the the size ratio of big and small ingredient decreases （φ<1.4） because of the weakness of effect of size segregation. Reduce the flow rate Q, under the conditions that δ<0, the system will show complete segregation. If δ>0and the system exhibits intermittent avalanche, the system will form spontaneous stratification. In the striped patterns, we notice the angle of interface between the big and small ingredient behaves linearly with the flow rate Q. The relation between the wavelength A of the layers and the flow rate Q is λ∞Q2/3.2. It was found that the granular materials show discrete avalanche or continuous flow depends on the rotating speed of drum. We show that, upon varying the cylinder rotating speed Ω, the system undergoes a hysteresis cycle between discrete avalanche and continuous flow regime. According to the jamming transition and metastable nature of granular heap, we speculate that the different flow regimes and jamming style may lead to different stress and density distribution, and different structure of the force net in the granular heap. This memory effect of granular heap may explain that the existence of two different critical transition rotating speed Ω+and Ω△Ω=（Ω+Ω）>0 which corresponding to the speed up and slowing down of the rotating drum respectively.3. In quasi-two dimensional rotating drum, a binary granular mixture must obtain moon pattern firstly in order to evolve into regular petal pattern in continuous flow. The mechanisms of petals pattern formation express as follow:moon pattern are formed due to the spontaneous segregation; the formation of zigzag structure of moon pattern due to the flow instability and the fluctuation of two gradients’concentration; this structure evolves into an incipient stripe due to "wave-breaking" mechanism; the coupling of the memory effect and the differences of dynamic angle of repose causing the incipient stripe growing and coarsening into a regular petal patterns eventually. The expression of the petal number of the patterns （N） is: Here T is the angle of material occupied in the rotating drum. A and B are the parameter related to the properties of granular ingredients. C accounts for the situation that the regular petal pattern may have some mixed region. The parameter φ is the concentration ratio of small component versus big component. As in this study, the bi-dispersed glass bead mixture has A=4.76, B=0.15, and C=0.9. While the mixture of glass bead and steel bead has A=9.13, B=0.06and C=0.7. When the drum boundary conditions and mixtures are determined, the number of petals has exponentially relation with the order parameter that is rotating speed Ω. |
PDF Full Text Request