# Sound science in sampling and statistics

When I worked in the Port of Rotterdam many years ago, I wondered about the risk international commodity traders encounter because of small samples in sealed bottles. How could the quality of a cargo aboard a bulk carrier possibly be confined in a few little bottles? This question has preoccupied me since I found out that sampling and statistics are inseparable subjects in science and engineering. So much so that most disciplines teach the basics behind sampling and statistics. But not all! In fact, geostatistics is one discipline where inviolable requirements of classical statistics are routinely ignored. I shall explain why!

# Bulk Powder Density

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.
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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.

# Going Round The Bend

Bends provide a pneumatic conveying pipeline with considerable flexibility in routing. In transferring a material from point A to point B the pipeline can be routed horizontally, vertically up and vertically down, all in a single pipeline run if necessary, and so cross roads and railways lines and avoid any obstructions on route. This flexibility, however, does come at a ‘cost’ and can additionally result in specific problems with certain materials. Each bend will add to the overall resistance of the pipeline, and hence to the conveying air pressure required to achieve a given material flow rate, or to the material flow rate possible for a given air supply pressure. If the conveyed material is abrasive an ordinary steel bend could fail in a matter of hours. An abrupt change in direction, such as that caused by short radius bends, will also add to the problem of fines generation with friable materials, and ‘angel hairs’ will be generated in long radius bends with many synthetic materials.

Due to the change in direction, impact of particles against bend walls, and general turbulence, there will be a pressure drop across every bend in any pipeline. The major element of pressure drop associated with a bend, however, is that due to the re-acceleration of the particles back to their terminal velocity after exiting the bend. The situation can best be explained by means of a pressure profile in the region of a bend, such as that in Figure 1.1.

Figure 1.1 Pressure Drop Elements and Evaluation for Bends

The pressure drop that might be recorded across the bend itself is quite small, and although this technique might be appropriate fir single phase flows around bends, it is inappropriate for gas-solid flows. The particles leaving the bend will be at a lower velocity than that at entry and so they will have to be re-accelerated. The bend was the cause of the problem but the re-acceleration occurs in the straight length of pipeline following the bend, and so it is here that the associated pressure drop occurs, and not in the bend itself.

If pressure transducers are located along the length of the pipeline a steady pressure gradient will be recorded in the straight pipeline approaching the bend. A similar steady pressure gra-dient will also be recorded in the straight length of pipeline after the bend, but only after suf-ficient distance to allow for the particles to re-accelerate. The total pressure drop that can be attributed to the bend is determined in the way indicated in Figure 1.1. Typical data for wheat flour is presented in Figure 1.2.

Figure 1.2 Pressure Profile in Straight Pipeline Either Side of a Bend

The wheat flour was conveyed at a solids loading ratio of about thirty in a 53 mm bore pipe-line and the conveying line inlet air velocity was about 16 m/s. The bend had a D/d ratio of about 5:1. The pressure profile indicated by the data points clearly shows the pressure drop due to re-acceleration of the particles that occurs in the straight section of pipeline following the bend. It will be noted that the pressure gradient in the straight section of the pipeline prior to the bend was recorded at about 5.6 mbar/m, and as the pressure drop across the bend was assessed at about 0.13 bar the equivalent length of the bend for the given material and con-veying conditions comes to approximately 23 m.

Conveying conditions are also important and pressure drop will increase with increase in both conveying air velocity and solids loading ratio. Bend geometry is an important factor in terms of pressure drop and with bends having a much smaller radius, or lower D/d ratio, a significant increase in pressure drop can be expected, although articles to the contrary have been written. Is it possible that the conveyed material itself could present yet another variable in the problem? The coefficient of restitution is probably the parameter to consider here. Is it likely, therefore, that for materials having a coefficient of restitution higher than that of wheat flour, the pressure drop across the bend could be lower?

# The Design and Operation of Bin Activators

##### R. Wahl, USA

bulk solids handling Vol. 1 (1981) No. 1, pp. 43−46

This paper highlights the history and philosophy of bin activator design and details the application and operation of the highly successful vibrated bin discharger.

##### Introduction

The Bin Activator was developed almost 20 years ago in response to the basic processing need for reliable material flow from storage. At the time of its conception volumetric vibrator feeders which could meter a variety of materials with accuracies of ± 1 to 2%, were gaining greater acceptance throughout the industry. However, as with all processing units, their performance was dependent upon a continuous supply and flow of material. Existing bin discharge methods such as bin vibrators and air injection methods, could not be relied upon to provide the flow characteristics required for optimum feeder performance. As a result, a concentrated effort was mounted at that time to find a reliable way to move difficult materials from storage…..