The effect of the granule velocity on the dilute-dense flow transition in granular system

Abstract

The effect of granule velocity on the dilute-dense flow transition in granular system is studied both experimentally and by numerical simulations. Our experiments show that high granule velocity above the exit results in a decrease of critical exit size in dilute-dense flow transition if the inflow rate is fixed. When the granular flow becomes the dense flow, the effect of the granule velocity is counteracted by a high density region above the exit, and the outflow rate is almost irrelative with the granule velocity. Similar results are also obtained by molecular dynamics simulations for corresponding two-dimensional systems. With simulation calculations, the space distributions of the density and speed are also obtained. The distributions show that the density and the thickness of the granule accumulation above the exit vary with the incoming granule velocity, and the variation plays a key role in determining the final granular flow state.

Phase Transition and Critical Phenomenon Occurring in Granular Matter*

“…In the granular flow, the two granular states exhibit as two different flow states; i.e., dilute flow state and dense flow state. [8−10] In a previous study, [8] we have investigated the granular flow in a channel with a specific bottleneck by both experiments and simulations. We found that there is a crucial relationship between the local flow rate and the local packing fraction in a selected choke area under the fixed particle number condition, which can define the granular flow state clearly.…”

“…To take into account all kinds of granular flow state (including the dense flow state), a soft sphere approach is used to simulate the collision between granules. The detailed interactions form between granules or side wall are the same as those we used in the previous work, [8,13] but in addition to the gravity and the collision between granules or side wall, a normal distributed random force (𝑓 ) is considered to apply to each granules at every time step ∆𝑡. The average of this normal distributed random force is zero in both 𝑥 and 𝑦 directions ( f𝑥 = f𝑦 = 0), and the standard deviation is 𝐹 r .…”

“…The calculation of these quantities can be performed by statistical analysis for all the granules in the selected area. [8,13] Figure 2 shows the distribution of the packing fraction and the speed (absolute value of the velocity) of the granules over the entire channel for a fixed granule number of 700, which belongs to a moderate dense flow state, without random force field. We can clearly see that this system is extremely non-uniform and the physical quantities in different places can vary seriously.…”

“…2 shows the distribution of the packing fraction and the velocity of granule over the entire channel, it is not very helpful to explain to the sudden change in the flow rate observed in the experiments. In the previous work, [8] we have pointed out that the key area for determining the outflow rate is the fan-shaped area above the exit (the thickness of the fan-shaped area is set to 𝑑 = 4𝑑 0 = 8.0 mm, see Fig. 1), and the discontinuous change in outflow rate observed by the experiment can result in the change of the flow state in this area.…”

“…The inset is the pressure-volume relationship in the analysis of the gas-liquid phase transition in statistical physics (quoted from Ref. [8]).…”