Powder flow
Michael E. Aulton
Chapter contents
Particle properties and bulk flow
Process conditions: hopper design
Characterization of powder flow
Determinations based on bulk density
Improvement of powder flowability
Alteration of particle size and size distribution
Alteration of particle shape or texture
Formulation additives: flow activators
Key points
Introduction
Powders are generally considered to be composed of solid particles of the same or different chemical compositions having equivalent diameters less than 1000 µm. Granules are groups of particles formed into granules and individual larger particles which may have overall dimensions greater than 1000 µm (Chapter 28). As far as powder flow is concerned, these will be discussed together and the word ‘powder’ is used here to describe either system.
The largest pharmaceutical use of powders is to produce tablets and capsules. Together with mixing and compaction properties, the flowability of a powder is of critical importance in the production of pharmaceutical dosage forms. Some of the reasons for producing free-flowing pharmaceutical powders include:
There are many industrial processes that require powders to be moved from one location to another and this is achieved by many different methods, such as gravity feeding, mechanically assisted feeding, pneumatic transfer, fluidization in gases and liquids and hydraulic transfer. In each of these examples, powders are required to flow and, as with other operations described earlier, the efficiency with which they do so is dependent on both process design and particle properties.
Particle properties
Adhesion and cohesion
The presence of molecular forces produces a tendency for solid particles to stick to themselves and to other surfaces. Adhesion and cohesion can be considered as two aspects of the same phenomenon. Cohesion occurs between like surfaces, such as the same component particles in a bulk solid, whereas adhesion occurs between two different objects, for example between two different particles, or between a particle and, say, a hopper wall.
Adhesive and cohesive forces acting between particles in a powder bed are composed mainly from short-range non-specific van der Waals forces which increase as particle size decreases and vary with changes in relative humidity. Other attractive forces contributing to interparticulate adhesion and cohesion may be produced by surface tensional forces between adsorbed liquid layers at the particle surfaces and by electrostatic forces arising from contact or frictional charging. These may have short duration but increase adhesion and cohesion through improving interparticulate contacts and hence increasing the quantity of van der Waals interactions. Cohesion provides a useful method of characterizing the drag or frictional forces acting within a powder bed to prevent powder flow.
Angle of repose
Angle of repose is a simple measure of powder flow but it is based on scientific principles. An object, such as a particle, will begin to slide when the angle of inclination is large enough to overcome frictional forces. Conversely, an object in motion will stop sliding when the angle of inclination is below that required to overcome adhesion/cohesion. This balance of forces causes a powder poured from a container on to a horizontal surface to form a heap. Initially the particles stack until the approach angle for subsequent particles joining the stack is large enough to overcome friction. They then slip and roll over each other until the gravitational forces balance the interparticulate forces. The sides of the heap formed in this way make an angle with the horizontal which is called the angle of repose and is a characteristic of the internal friction or cohesion of the particles.
The value of the angle of repose will be high if a powder is cohesive and low if a powder is non-cohesive. If the powder is very cohesive, the heap may be characterized by more than one angle of repose. Initially, the interparticulate cohesion causes a very steep cone to form but, on the addition of further powder, this tall stack may suddenly collapse, causing air to be entrained between particles and partially fluidizing the bed, thus making it more mobile. The resulting heap has two angles of repose: a large angle remaining from the initial heap and a shallower angle formed by the powder flooding from the initial heap (Fig. 12.1).
Particle properties and bulk flow
In the discussion concerning adhesion/cohesion it is clear that an equilibrium exists between forces responsible for promoting powder flow and those preventing powder flow, i.e. at equilibrium:
(12.1)
that is:
(12.2)
Some of these forces are modified or controlled by external factors related to particle properties, such as size, shape and density.
Particle size effects
Because adhesion and cohesion are phenomena that occur at surfaces, particle size will influence the flowability of a powder. In general, fine particles with very high surface-to-mass ratios are more adhesive/cohesive than coarser particles which are influenced more by gravitational forces. Particles larger than 250 µm are usually relatively free flowing but as the size falls below 100 µm, powders become more adhesive/cohesive and flow problems are likely to occur. Powders having a particle size less than 10 µm are usually extremely adhesive/cohesive and resist flow under gravity. An important exception to this reduction in flowability is when the very small particles become adhered/cohered to larger ones and the flowability of the powder as a whole then become controlled by the larger particles. This phenomenon is important in the concept of ordered mixing (Chapter 11) and formulation of dry powder inhalers (Chapter 37).
Particle shape
Powders with similar particle sizes but dissimilar shapes can have markedly different flow properties owing to differences in interparticulate contact areas. For example, a group of spheres has minimum interparticulate contact and generally optimal flow properties, whereas a group of particle flakes or dendritic particles has a very high surface-to-volume ratio and poorer flow properties. Irregular shaped particles may experience mechanical interlocking in addition to adhesional and cohesional forces.
Particle density (true density)
Because powders normally flow under the influence of gravity, higher density particles are generally less adhesive/cohesive than less dense particles of the same size and shape.
Packing geometry
A set of particles can be filled into a volume of space to produce a powder bed which is in static equilibrium owing to the interaction of gravitational and adhesive/cohesive forces. By slight vibration of the bed, particles can be mobilized so that if the vibration is stopped, the bed is once more in static equilibrium but occupies a different spatial volume than before. The change in bulk volume has been produced by rearrangement of the packing geometry of the particles. In general, such geometric rearrangements result in a transition from loosely packed particles to more tightly packed ones, so that the equilibrium balance moves from left to right in Equations 12.1 and 12.2 and adhesion/cohesion increases. This also means that more tightly packed powders require a higher driving force to produce powder flow than more loosely packed particles of the same powder.
Characterization of packing geometry by porosity and bulk density
A set of monosized spherical particles can be arranged in many different geometric configurations. At one extreme, when the spheres form a cubic arrangement, the particles are most loosely packed and have a porosity of 48% (Fig. 12.2a). At the other extreme, when the spheres form a rhombohedral arrangement, they are most densely packed and have a porosity of only 26% (Fig. 12.2b). The porosity used to characterize packing geometry is linked to the bulk density of the powder. Bulk density, ρB, is a characteristic of a powder rather than individual particles and is given by the mass, M, of powder occupying a known volume, V, according to the relationship:
(12.3)
The bulk density of a powder is always less than the true density of its component particles because the powder contains intraparticular pores or interparticulate air-filled voids. Thus whereas a powder can only possess a single true density, it can have many different bulk densities, depending on the way in which the particles are packed and the bed porosity. However, a high bulk density value does not necessarily imply a close-packed low-porosity bed, as bulk density is directly proportional to true density.
(12.4)
or:
(12.5)
The constant of proportionality, k, is known as the packing fraction or fractional solids content. For example, the packing fraction for dense, randomly packed spheres is approximately 0.65, whereas the packing fraction for a set of dense, randomly packed discs is 0.83. Also:
(12.6)
where e is the fractional voidage of the powder bed, which is usually expressed as a percentage and termed the bed porosity. Another way of expressing fractional voidage is to use the ratio of particle volume Vp to bulk powder volume VB, i.e.:
(12.7)
A simple ratio of void volume Vv
