Hopper geometries

A fiow rate limitation is another unsteady two-phase flow mode that can occur with fine powders. Fine powders have very low permeability, and are affected by any movement of the interstitial air (air between the particles). This air movement will occur due to the natural compression and dilation of the powder bed that takes place as it flows through the cylindrical and hopper geometries as the material is compressed in the cylinder air is squeezed out, while when it dilates as it flows through the outlet, additional air must be drawn in. The air pressure gradients caused as a result of this air movement can retard discharge from a hopper, signiflcantly limiting the maximum achievable rates. 

Modify the hopper geometry. Use a different geometry that is more likely to provide mass flow (e.g., conical instead of a lectangular-to-round hopper with shallower valley angles). If the hopper is modified to have a slotted outlet, it is crucial that the feeder the hopper mates to withdraw material across the entire outlet. 

The key to implementing any corrective actions designed to reduce adverse flow-effects will be using a mathematical two-phase flow analysis to assess the effects on the bulks solids stresses and interstitial gas pressure. This analysis would need to use inputs such as key flow properties (permeability, compressibility) and equipment/process parameters (tableting rate, bin/hopper geometry, and gas pressure gradients) to assess the effect of the potential corrective actions outlined above. 

Whether core flow or mass flow is achieved is dependent on the design of the hopper (geometry and wall material) and the flow properties of the powder. For most pharmaceutical applications, the hopper design for a particular machine will be fixed thus, it is incumbent on the formulator to ensure that mass flow is achieved by modification of the powder properties. 

These angles of flow can be used to calculate the discharge opening size required on a hopper to prevent arching and rathoUng over the entrance to a feeder, predict hopper geometry required to promote gravity flow, estimate flowability and cohesiveness of different soUds. 

The design of a storage container for bulk materials is rarely taken in isolation, normally being influenced by various facets of the associated plant or the background of the manufacturer. There are three main steps to selection of storage hopper geometry (i) body configuration (ii) outlet size and shape and (iii) the transformation between the two. 

Common hopper geometries, (a) Axisymmetrical flow, (b) symmetrical plane flow, and (c) nonsymmetrical plane flow. 

For design purposes B and Qo can be plotted as a function of 0, as presented in Figure 3.12. In such a way, several options of hopper geometry can be explored. In many cases the flow rate determined above the unimpeded discharge will be well in excess of the plant requirements. For this reason feeders may be used to control discharge rate to any required value. 

If steady flow is desired, the hopper geometry should be designed such that mass flow will take place no stagnating regions should occur. In this case, the solids flow along the walls of the hopper. The wall, therefore, must be sufficiently steep and the flow channel must not have any sharp corners, abrupt transitions, or discontinuities in frictional properties at the wall. As a rule, the hopper half-angle a should not exceed with a ax determined from ... 

Intuitively, for a given hopper geometry, one would expect the stress developed in the arch to increase with the span of the arch and the weight of solids in the arch. In practice this is the case and the stress developed in the arch is related to... 

What is the powder flow function Is the powder flow function dependent on (a) the powder properties, (b) the hopper geometry, (c) both the powder properties and the hopper geometry ... 

A material s flow function, which can be determined only by shear tests, is often strongly influenced by its temperature, time of storage at rest, moisture content and particle size distribution. A hopper s flow factor is a function of the effective angle of internal friction (6), wall friction angle (< w) and hopper geometry. 

Once the hopper geometry has been chosen, the next consideration is whether or not an insert is required within the hopper. A common insert configuration is an inverted cone or pyramid as shown in Figure 2.27. Unfortunately, studies have shown that such inserts have a limited range of effectiveness and the loads acting on them are usually extremely high. The supports required to resist these loads often provide impediment to flow greater than the beneficial effect of the insert. 

The optimum hopper geometry for true mass flow, which would give a true first in first out discharge pattern, was dependant on a combination of both hopper angle and outlet size and, in this case, was the hopper of 10° angle with a 200mm slotted outlet. 

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