The first two things to consider about bulk density are the nature of the bulk material and establish the purpose for which the measurement is to be made. This is because the bulk density of a powder is strongly dependent upon both the nature of the particles and the manner is which the sample is prepared and measured. This is considerably more important for some powders compared to others. The density of fine powders is very sensitive to the amount of gas that is trapped in the voids and to the stresses acting on the bed of material. On the other hand, the density attained by firm, coarse particles depends much more on the conditions of formation of the bulk and to the geometry of the measuring container. This is because air can escape from the coarse bulk easily, the contact structure of large grains can sustain relatively large forces before yielding and a wall contact surface constrains the way in which the large particles can nest together.
The dimensions of the contact structure in a bed of fine particles is heavily dependent on the amount of air in the voids, because it is more difficult for the gas to escape through the tortuous paths of the narrow void gaps. As a consequence, forces acting on the bed due to the overpressure of the weight of particles are partly supported by the gas pressure and the bed is compressed. In extreme conditions of dilatation the residual forces between particles is ineffective in resisting their relative movement and the mass behaves as a fluid. At the other end of the scale, when the bulk has settled to a dense condition and the void pressure is ambient, the contact between fine particles in close proximity incurs molecular attractive forces that assume high prominence. Shear is also opposed by the resistance to expansion of the bed in these compacted conditions, because the increasing void volume creates a partial vacuum as the low permeability of the bed prevents ambient gas from easily meeting the demand.
To understand these influencing factors in more detail it is necessary first to consider the mechanics of particulate structures. An excellent review of the packing characteristics of particulate solids is described in a Chapman & Hall book by W.A.Gray on The packing of solid particles. The next step is to consider the effect of the void gas on flow behaviour. This is usually air, as there is rarely interest in the density of a bulk material in vacuum conditions, although this special state does remove many complications. An informative paper by Bruff and Jenike, – A silo for ground anthracite in Powder Technology 1, 1967/68, pp 252 – 256, illustrates well the significance of void air content and the effect that this can have on flow.
The importance of the reason for interest in bulk density is that, even under static conditions, this value may be stable or transient depending upon the state of the bulk material. The best way to consider this is to consider the effect of a powder settling from a condition of quiescent fluidisation. Air will permeate from the voids according to many factors, such as the viscosity of the gas, the permeability of the pore structure and the geometry of the powder bed. Ultimately, the pressure in the voids will come to equilibrium with the ambient surrounds and then the density will reflect the loads acting on the assembly of particles. A bed of fine particles will compact with loading as the packing order of the particles is disturbed. Coarse particles are more easily re-shuffled by vibration than direct loading as the relatively small number of particle to particle contact points can readily form a load path but are vulnerable to dislocation by erratic disturbances.
The main point is that density measurements should reflect the conditions of interest for the application. e.g dilated settlement for filling and small scale storage, compacted state for large scale storage, pressings and tableting. Agitated dilatation correlates with active conveying methods such as screw, scraper conveying and chute transfer. Fluidised bulk measurement is needed to relate to dilute phase pneumatic conveying. It is interesting to note that there are about twenty British Standards for density measurement, ranging from the density of feathers and down for filling pillows to various specialised mineral commodities.
For cheap, general purpose use, a one litre measuring cylinder from any large chemist or home brewing supply shop will suffice. This should be filled with about 750 cc, of material and shaken vigorously, then set down to rest. When the contents have settled to a stable condition, the volume and weight will determine what may be called the loose settled state of density.
Raising and dropping the cylinder 20 times from a height of about 25mm onto a hard surface will normally give a consistent value of tapped density. This will align with the lightest condition of material that is transported by road, rail or in-plant movement.
Heavier compaction may be measured in a small, shallow, circular cell that is subjected to increasing step loads and the volume reduction measured by a dial gauge. A plot of the load/compaction curve is a powerful characterisation method and allows the density at significant stress levels to be quantified. Janssen’s formula may be used to determine the pressures acting in a silo
At the dilute end of the scale, a fluidising cylinder may be used to determine the expanded state and the settling rate of fine powders. A deep bed will illustrate the effect of diminishing porosity. For this test the ambient temperature should be similar to the conditions of use and be noted because the viscosity of a gas increases with temperature. This feature tends to explain why products from kilns and driers are more prone to behave in a fluid manner than when in a cold condition.
A large container is required to measure the density of very coarse particles. This is to avoid bias caused by the effect of a confining surface on the nesting structure of particles that extends up to 5 or 6 particle diameters from each wall.
Generally no expensive equipment is needed to measure bulk density but a thorough appreciation of bulk material behaviour is necessary to avoid drawing false assumptions or conclusions. This is particularly true when assessing the effect of bulk density on flow behaviour or bulk strength, where a powerful correlation can be developed from a proper understanding of the fundamentals of powder technology. The shear strength of a powder is dependent upon both the stresses acting on the bulk and the ‘state’ of the material. This later condition is a feature of the stress history of the bulk, but may be generally characterised by its bulk density. The isotropy of the material and stresses must also be taken into account for a thorough understanding, but this aspect warrants later detailed explanation.
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