The influence of particle size on the flow of initially fluidised powders
Introduction
An important feature of granular material is its mobility or the degree to which it is capable of moving freely from its source. This is exploited in industrial processes as a mechanism by which solid material can be transported from one place to another. It is also important in many environmental flows, such as the pyroclastic flows produced by some explosive volcanic eruptions, where large, dangerous and destructive currents of material can travel up to several tens of kilometres [1].
The extent and behaviour of granular flows depends to a large extent on the role of friction within them. In systems where there is no gas flow when a stream of cohesionless particles is poured onto a horizontal surface, it is well known that a wedge-shaped pile forms with a surface angle equal to the internal angle of friction [2]. The behaviour of the particles is dominated by inter-particle friction and movement is confined to a thin layer close to the top of the pile [3]. When particles are introduced into a system and gas is passed vertically through them at a high enough rate that the drag it exerts on the particles balances their weight, then the effects of friction become negligible. As a result, rather than a pile, a thin and mobile current is formed in which nearly all the particles participate [4], [5].
In many situations, the friction between the particles that subsequently form a current are negligible because of a gas flow passed through them or because they are in free fall, but the current that is formed moves into an environment where this is no longer the case. When this happens, it is not known the extent to which the initial conditions affect the subsequent motion of a granular current: once the air flow through the particles ceases, does friction immediately dominate the motion of the current irrespective of initial conditions, or do the initial conditions largely determine the subsequent motion of the particles? The picture is complicated by the presence of physical mechanisms other than the effects of gas flow through the particles. The nature of the contact between particles will be particularly important: the bulk behaviour of particles can depend on whether the particles can move relative to one another, the length of time that the particles are in contact with each other, and whether the particles can slide relative to each other. Instantaneous collisions between particles that generate a ‘granular temperature' and the subsequent stress can be important in many granular flows by influencing the motion of the flow [6] and the segregation between particles of different sizes. In the relatively small and slow flows examined here, this is unlikely to be significant [4].
Particle size is important when determining the behaviour of powders, particularly when they are interacting with a fluid. We shall use the well-known Geldart classification of fluidised particles [7], which describes the effect of particle size on the behaviour of fluidised beds for classifying and labelling the different particles used in the experiments. It distinguishes between fine particles (group A, typically with a diameter between 30 and 100 μm for glass or sand particles in a gas) and larger groups B and D particles when they are fluidised. When group A powders are fluidised then between the minimum fluidisation velocity, Umf, and a higher critical velocity, Umb, bubbles do not form in the bed, which instead expands. Should the gas supply be interrupted then the bed collapses at a constant rate [8].
Many practical flows contain particles of a wide range of sizes and can straddle the Geldart group boundaries; in some cases, the size range of particles can vary from tens of micrometres up to the order of a metre. This can lead to a variety of behaviour owing to the different responses of the mixture components to the gas flow depending on how they arrange themselves: that is the extent to which they are segregated and the pattern which they form, which can in turn depend on the motion of the current.
This investigation addresses the question of the extent to which initially passing a gas through a bed of particles before it is released onto a horizontal surface affects the subsequent behaviour of a current of particles. Measurements are made of the flow of particles released from a fluidised column along a channel. The mobility of the particles is characterised by measuring the distance travelled by the particles after release. In particular, the effects of particle size and the mixture of particle sizes are examined. Section 2 describes the experimental arrangement. The behaviour of single-sized particles is then described in Section 3 and then that of mixtures in Section 4, firstly when there is no initial gas flow and then when there is. Conclusions are drawn in Section 5.
Section snippets
Apparatus
The experiments were carried out in the apparatus shown in Fig. 1. The bed was 8 cm in width and constructed from perspex and fibreboard. The particles were initially retained behind a sliding gate which was opened manually at the beginning of an experiment. This part of the apparatus has a porous floor (10 mm thick Porvair Vyon ‘D’ porous plastic board) through which gas was passed. The sliding gate was held in runners and soft sealed, which allowed uniform fluidisation before the gate was
The behaviour of flows of single-sized particles
The behaviour of flows of single-sized particles is described in [10], [11]. The shapes of the deposits for different degrees of initial fluidisation are shown in Fig. 4. When no gas is introduced into the system, then the ultimate shape is a good approximation to the expected wedge with an angle equal to that of repose except for a little run-out caused by the inertia of the flow. At high gas velocities, all the powders have a similar ultimate profile with a long shallow wedge form, similar to
Flows when there is no initial gas flow
When there is no initial aeration, then the composition of a current can have a strong effect on its mobility, as shown by the run-out distances in Fig. 7. All the beds of single-sized particles have similar run-outs, but mixtures can have significantly greater mobilities. This effect is most pronounced when there is a moderate proportion of fine particles (α = 0.2–0.4). The maximum run-out in the mobility depends strongly on the diameter of the coarse component of the mixture: there is no
Conclusion
The mobility of currents of particles is significantly increased when they are initially aerated, suggesting that the initial condition of a bed of particles, especially with respect to the operation of friction between the particles, has an important effect for subsequent transport. The importance of particle size and size distribution on the mobility of particles currents is clear. Fine particles are more mobile than larger particles and respond more strongly to the initial gas flow through
Acknowledgements
O.R. was supported by an E.U. Marie Curie Fellowship and RSJS gratefully acknowledges a Royal Society-Wolfson Merit Award. The authors thank Prof. C. Campbell for his idea on the reason for the decrease in mobility of group A particles above Umf.
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