Flow of solids
The gravity flow of particulate solids such as ceramic powders, plastic pellets, and ores in the form of separate particles, with the particles in contact and the voids between them filled with gas, usually air.
Particulate solids are a two-phase, solid-gas system. They are compressible; their bulk density changes during flow. Since the volume of the particles changes little during this process, it is the size of the voids that is mostly affected. Changes in the size of the voids can cause changes in gas pressure and result in gas-pressure gradients across a flowing solid which tend to reduce the rate of gravity discharge. When the solid is made up of large particles, that is, its permeability is high, when the required flow rates are low, the gas-pressure gradients are not significant; the gaseous phase can be ignored and the solid treated as a one-phase, solid-only system.
A bin (silo, bunker) generally consists of a vertical cylinder and a converging hopper. From the standpoint of flow, there are three types of bins: mass-flow, funnel-flow, and expanded-flow.
Mass flow occurs when the hopper walls are sufficiently steep and smooth to cause flow of all the solid, without stagnant regions, whenever any solid is withdrawn. The range of hopper slope and friction angles leading to mass flow is shown in the illustration. Funnel flow will occur unless both the conditions for mass flow shown there are satisfied.
funnel flow. (c) Range of φ and θp leading to mass flow and funnel flow.">
Bounds on mass flow and funnel flow. (a) Geometry of a transition hopper, showing slope angles θc and θp. (b) Range of kinematic angle of friction (φ′) and θc leading to mass flow and funnel flow. (c) Range of φ and θp leading to mass flow and funnel flow.
Mass-flow bins have advantages. Flow is uniform, and feed density is practically independent of the head of solid in the bin. Segregation is minimized because, while a solid may segregate at the point of charge into the bin, continuity of flow enforces remixing of the fractions within the hopper. Mass-flow bins have a first-in-first-out flow sequence, thus ensuring uniform residence time and deaeration of the stored solid.
Funnel flow occurs when the hopper walls are not sufficiently steep and smooth to force material to slide along the walls or when the outlet of a mass-flow bin is not fully effective.
In a funnel-flow bin, solid flows toward the outlet through a channel that forms within stagnant material. The diameter of that channel approximates the largest dimension of the effective outlet. As the level of solid within the channel drops, layers slough off the top of the stagnant mass and fall into the channel. This erratic behavior is detrimental with cohesive solids since the falling material packs on impact, thereby increasing the chance of material developing a stable arch across the hopper so that a complete stoppage of flow results. A channel, especially a narrow, high-velocity channel, may empty out completely, forming what is known as a rathole, and powder charged into the bin then flushes through. Powders flowing at a high rate in a funnel-flow bin may remain fluidized because of the short residence time in the bin, and flush on exiting the bin. A rotary valve is often used under these conditions to contain the material, but a uniform flow rate cannot be ensured because of the erratic flow to the valve.
Funnel-flow bins are more prone to cause arching of cohesive solids than mass-flow bins, and they therefore require larger outlets for dependable flow. These bins also cause segregation of solids and are unsuitable for solids which degrade with time in the stagnant regions. Cleanout of a funnel-flow bin is often uncertain because solids in the stagnant regions may pack and cake.
Expanded-flow bins are formed by attaching a mass-flow hopper to the bottom of a funnel-flow bin. The outlet usually requires a smaller feeder than would be the case for a funnel-flow bin. The mass-flow hopper should expand the flow channel to a dimension sufficient to prevent ratholing.
