Powders—gaseous, liquid and solid

Powders-gaseous,

liquid and solid

N. Pilpel Powders can float like a gas; flow like a liquid; or support a weight in the same way as hard-packed snow. They behave rather like gases when in the form of smoke or dust in the atmosphere; rather like liquids when poured or conveyed during manufacturing processes; and rather like solids when compressed into blocks by subjecting them to pressure.

Despite the wide occurrence of powders in naturefrom sand in the Sahara to snow on the Alps-and the enormous volumes of ground coal and mineral ores, cement, sugar, detergents, flour, and drugs employed in manufacturing industry, there is a surprising lack of general knowledge about them. The indexes of six well known school text books on physics and chemistry made no mention of powders, except for a reference to powder x-ray analysis. Basic information on powders has to be extracted from proceedings of technical conferences [l]; from specialised the monographs on, for example, measurement of particle size [2]; or from research such as Powder papers in specialist journals Technology [3]. On the other hand, a theological acquaintance assures me that there are at least 120 separate references to dust in the Bible. Powders consist of solid particles in the range of size from less than 0.1 pm to over 1000 pm. Carbon particles in smoke are about 0.2 pm in diameter; a typical pollen grain is about 20 pm; sands on the beach range from 100 to 1000 pm. Larger particles are often described as granules though strictly the term should be reserved for materials like spray-dried coffee which have actually been made by a granulation process [4]. This article describes the behaviour of powders in what I will call their ‘gaseous’, ‘liquid’. and ‘solid’ states and explain how it differs in detail from that of matter in its other physical forms. and why. Powders like gases For most people, dust and smoke imply particles which are small and light enough for them to float for some time without settling. But size is not the only criterion. The so-called dust in interstellar space contains particles as large as bricks. They remain afloat because of their weightlessness and the Earth collects many thousands of tons of them in its annual flight round the Sun. One can also form a dust cloud from coarse powders or granules simply by blowing air through Nelton

Pilpel,

B.Sc,

Ph.D.,

Was born in London Technology at Chelsea University College and years in industry before

D.Sc

in 1922 and is Reader in Pharmaceutical College, University of London. He studied at King’s College, London and worked for twelve taking up his present appointment.

Endeavour, New Series. Volume 6, No. 4,1982. (0 Pergamon Press. Printed in Great Britain) OlW-9327/82/040163-ll6 503.00.

them at sufficient speed. This is the basis of the fluidisation process which is used for, amongst other things, conveying powdered coal of about the size of garden peas through pipes to be burnt in power stations. As normally understood, however, dust usually forms a cloud only if the particles are less than about 20 pm in diameter. Provided they are not being dispersed by wind the particles gradually clump together or agglomerate due to the action of van der Waals’ forces of attraction between them. R. Whytlaw-Gray and his colleagues in the 1920s and 1930s graphically described how smoke particles about 0.2 pm in diameter agglomerate into writhing, flexible, chain-like structures about 20 pm long [5]. They expressed the agglomeration mathematically by 1 +kt n, 0 where n, is the number of particles ml-’ at the start of the experiment and n, the number after the elapse of a time t; k is a numerical term which depends on the nature and original size of the particles and on the turbulence, humidity, and temperature of the surrounding air. In cases where k turns out to be zero or very small, agglomeration does not occur and the fine particles continue to float. Particles which are sufficiently heavy gradually settle from the air in much the same way as a sediment settles from wine. The law governing sedimentation was enunciated by G. G. Stokes in the last century. It is v=p

=

d2(prp2)g

18~ where V is the velocity of the particles, equal to the distance h that they fall in time t, d is their diameter, p, is their density, p2 is the density of the air (0.0012 g ml-‘), n its viscosity (182 x 10eh poise), and g is the acceleration due to gravity (981 cm set-‘). The equation shows that big particles settle faster than small ones. In a still room a cloud of face powder (about 20 pm) takes a few seconds to settle; fine flue dust (about 1 pm) about a minute. Dust control A number of methods are used in industry for reducing the amounts of dust and smoke that are liberated into the atmosphere [6]. Contaminated gases are passed through filters on which the particles deposit. The efficiency of the filter depends on the size of its pores; it can be increased by coating it with 183

viscous or resinous substances which trap the particles by viscous or electrostatic forces. In electrostatic precipitators the dusty gas is passed through vertical tubes down the centres of which discharge electrodes are suspended. A strong electric field is applied; the particles become ionised and travel to the walls of the tubes with a velocity K1 E E, d (3) u= 127-q

from which they are collected automatically. In this expression E is the strength of the lateral field, E, is the strength of the ionising field, d is the average diameter of the particles, r) is the viscosity @f the gas or air, and K1 is a number which varies between 1.5 and 3 depending on the electrical resistivity of the particles. Cyclones work essentially by increasing the tendency of air borne particles to agglomerate and settle. The dust-laden gas is directed into a spiral path so that the particles collide with each other and with the walls of the cyclone on which they deposit. Finally, there are various types of scrubbers in which the gas is passed through a fine spray of water droplets which wash out the remaining dust. All these techniques have helped in the implementation of the 1956 Clean Air Act, at which time it was estimated that some 3 million tons of smoke and dust were being released annually into the air over Britain. Even today in every breath we breath there are over half a million particles of a size visible under the electron microscope. However, it would be misleading to give the impression that dust is always obnoxious. Farmers dust their crops with fungicides and pesticides to maintain yields. Certain pharmaceutical drugs are now formulated as dusts so that patients can inhale them directly into their lungs, where they are rapidly absorbed to produce their therapeutic effects. Typical examples are sodium chromoglycate and isoprenaline which are used for the treatment of asthma in the size range l-10 pm, with 50 per cent of the particles between 2 and 6 pm. This size range ensures that at least 70 per cent of the particles are deposited in the lungs and are not exhaled in the next breath. Patients taking drugs in this way need smaller doses than if they take them orally or by injection and this reduces the likelihood of adverse side effects which sometimes occur with larger doses. Powders like liquids Most people are familiar with the broad division of powders into those which flow easily through a hole and those which do not. But what are the factors that control this property? Clearly moisture is one of them, as anyone knows who has tried shaking salt from a cellar that has been standing in a damp kitchen for any length of time. The moisture forms a thin film over the surface of the particles and holds them together by viscous and capillary forces so that they can no longer move individually as when dry. Superficially, it might seem that a dry powder such as sand flows in much the same way as water, but closer examination reveals that this is not so. You can demonstrate the difference by sieving the sand into its different size fractions, pouring each in turn 184

into a hopper and measuring the rate at which it emerges from the bottom. You notice that the rate of flow remains practically constant irrespective of the level of sand above the hole. With a liquid the flow rate decreases as the level falls. This difference, which arises from the complex way in which pressure is transmitted through a powder, must also have been noticed by the now unknown Egyptian several thousand years ago who invented the hour glass as a *device for the measurement of time [7]. If, in the experiment, you fit the hopper with orifices of different diameters and plot the flow rates of the different size fractions of sand against their particle size, you obtain graphs like those shown in figure 1. For any particular size of hole, the flow rate increases to a maximum and then decreases; it also increases with the diameter of the hole, so that if you make it twice as large the sand flows out about six times as fast. When the sand is bigger than one-sixth of the size of the hole it blocks it because the particles form an arch, rather like the stones above a Roman gateway. Surprisingly, perhaps, very fine sand, less than 100 pm, also blocks the hole. This is because the van der Waals’ forces of attraction between the particles are now large enough to overcome their weight, which would otherwise cause them to fall through. Blocking of holes by powders can be quite spectacular. A speaker at a conference described his feelings while standing underneath the 4 ft outlet of a blocked hopper which contained several thousand tons of flour. He was wondering how to empty it. Judicious poking with a long pole, while standing well clear, eventually provided a solution. In trying to find ways of preventing hoppers and pipes from becoming blocked by powders my research group at Chelsea College has recently discovered that it is possible to make certain lowmelting powders flow more freely by cooling them to very low temperatures (81. For example, we have found that ordinary brown sugar flows twice as fast at -25°C as it does at 100”. The explanation seems to be that when low melting or sticky powders are cooled, the particles become less plastic, more elastic like small ball-bearings so that they have less tendency to clump together to cause a blockage. In these experiments we have to ensure that the powders are perfectly dry and do not absorb moisture from the atmosphere. The experiments have been done only on a small scale and more work is needed to decide whether the results could be exploited commercially; for example, in hot countries where powders with low melting points frequently cause problems during transportation. A better tried method for improving flow is to exercise control over the size distribution of the powders’ particles. I can illustrate the method by referring to the middle graph in figure 1. Suppose we are dealing with a sand which contains three different sizes of particles-80 pm, 500 pm, and 800 pm-and we want to get it to flow as fast as practicable through the 0.9 cm hole. The graph shows that the flow rates of these fractions are respectively zero (or anyway less than 400 g min-‘), about 850 g min-‘, and about 650 g min-I. If we mix the three sizes

l!x

200

Particle

Figure 1 diameters

Rates of flow

XXI

1000

diameter,

of sand through

2000

pm

holes of different

together in different proportions and measure their flow rates we can plot the results on the triangular diagram shown in figure 2. In this diagram the apices represent 100 per cent of each of the sizes; the point A represents a mixture of 30 per cent of 80 pm and 70 per cent of 500 pm sizes; the point B represents a mixture of 60 per cent of the 80 ,um, 10 per cent of the 500 pm, and 30 per cent of the 800 pm sizes. We then draw contour lines to enclose mixtures which have approximately equal rates of flow, in the same way as one draws contour lines on a topographical map. We see that mixtures in the shaded section of the diagram flow faster than the rest and we therefore add or subtract appropriate amounts of the different sizes to the particular batch of sand that we are dealing with to make its composition fall somewhere within this shaded region. For example, if the batch originally had a composition at point C of 50 per cent of 80 ,um, 20 per cent of 500 Frn, and 30 per cent of 800 pm particles and therefore flowed at a rate of 650 to 700 g min-‘, we would add about 20 per cent of the 500 pm particles to it so as to move its composition along the dotted line to the point D

and thus increase its flow rate to between 750 and 800 g min-‘. (It would be impracticable to move the composition further to the point E, where the flow rate is over 800 g mini as we would then have to discard most of the 80 pm and 800 pm material). In the last 25 years a lot of work has been done on the flow properties of powders: their behaviour in with that of liquids is pretty well comparison understood. There are mathematical expressions available for predicting the flow rates of single size fractions of powders and of powders which contain a range of sizes between about 100 pm and 5 cm. that is of the size of coke. The terms in these expressions allow for the shapes, sizes, roughness, and densities of the particles; there are also terms which allow for the shapes and dimensions of the hoppers or pipes from which they are flowing [9]. As already noted, however, there are many powders which, because they are smaller than 100 pm, or because they have very irregular shapes, or because they are damp or inherently sticky, will not flow through holes in the conventional sense. They include materials like mustard, cornflour, iron oxide, garden lime, pollen, cocoa, and a wide variety of organic chemicals and pharmaceutical drugs. Powders of this kind are generally described as cohesive; they behave as much like solids as like liquids. What are the laws that govern the ways in which cohesive powders behave?

Powders like solids In order to answer this question we pack the powder in a carefully controlled way into two different types of container or cell, illustrated schematically in figures 3 and 4. The tensile cell is a shallow metal cylinder 9 cm in diameter and 1 cm deep which is split vertically in half. One half is fixed to the base, the other is mounted on ball bearings so that it can be pulled to the left by a motor until the bed of powder splits in a vertical plane. The force needed to do this depends on how tightly the powder has been packed, that is on its packing density, pr,. This is

Plane

spu

Less thm 400 g mm-l

A

of

TellSIOn

400.6COgmw-’

6.

650-700

Plan

Elevation g nun-’

Figure 2 Triangular diagram showing rates at which mixtures of three different sizes of sand flow through a hole 0.9 cm in diameter

Figure

3

Tensile

cell

Elevation

Figure

4

Ptan

Shear cell

185

defined as its bulk density divided by the actual density of the particles, both of which can be measured. Calling A the cross-sectional area of the split face and F the breaking force required, the tensile strength of the powder at the particular packing density or, is

The shear cell consists of a cylindrical metal base and a lid which form an annulus into which the powder is packed to the same packing density pr,, to form a ring with an inner radius of 4 cm and an outer radius of 6 cm. A known load uN is placed on the lid which is held stationary while the base of the cell is slowly rotated until the bed of powder shears in the horizontal plane. The torque exerted on the lid is measured and this gives the shear strength of the powder at failure (5) TFl e 0.0025 Q NmP2 As with T, the value of rr, depends on the packing density of the powder; it also depends on the load oN being applied via the lid. By plotting graphs of rr against oN we obtain the curves shown in figure 5, each relating to a particular packing density of the powder. These intersect the ordinate at points C,. C2, C3 . . . which are defined as the cohesion of the powder at the particular pF3. . If we packing densities I+, , PF2’ extrapolate the curves to the left they intersect the abscissa on the negative side at the points T,, TZ, T3 . . which are the tensile strengths of the powder at these same packing densities. These curves are known as yield loci. They show the combinations of loading, packing density, and shearing force under which the bed of powder fails. Thus if no load is being applied ( oN = 0 ) the sample which has been packed to a density of pr, fails when the shearing force pr = C,. If the load on it is oNr, it fails when the shearing force is rr,. The sample also fails if a negative load or pull of - (SN = T, is applied to it and no shearing force is needed, since at T, the value Of TF = 0. By packing a large number of different cohesive powders+ement, dried egg. mustard, flue dust, precipitated chalk etc-to different densities and anlysing the shapes of their yield loci, researchers at the U.K. Department of Industry Laboratory at Warren Spring showed that they could all be fitted to a single equation (F+

=

“N;

T

(6)

This is known as the Warren Spring Equation [lo]; n is a number which varies between 1 for slightly cohesive powders and 7 for very cohesive powders. The other symbols have already been defined. It is interesting to notice that the equation predicts that the shear strength of the powder should continue to increase indefinitely as the load oN applied to the lid of the shear cell is increased. However, what happens in practice is that when oN is increased beyond the the packing density of the powder point ONE,, or2 and its subsequent changes from pri to behaviour is then along the yield locus labelled pr2 186

~~ Nm-* I

(4)

N mP2

T, =+

in figure 5. The limiting shear strength is reached when the powder has been so tightly packed that

N m-* Figure

5

Yield loci

T, Nm-’

Nm-’ Figure

6

Replotted

yield

loci

there are no spaces between the particles and its packing density equals unity. Its shear and tensile strengths are then those of the solid of which it is composed. Instead of plotting yield loci as in figure 5 it is often more convenient to move them so that they TF pass through the origin of the axes by plotting against ( (TN + T) instead of against oN. ( oN + T) is called the compound load. We find that with many powders, though not all, it is then possible to draw a single line with a slope of tan a through the origin of the axes and the ends of the yield loci (figure 6). Since n relates to the ends of the yield loci where the powder is exhibiting its maximum strength at any particular value of pr, then providing a remains independent of pF (in contrast to C and T) it appears to be a fundamental property of the powder. It is called the angle of internal friction of the powder, and it is a measure of the frictional and cohesive forces between the particles which prevent them from flowing like a liquid, though with the differences that I have already described. It has been of interest to explore the relationships that exist between the quantity n (or sometimes more conveniently T at a specified value of pr) and

IO Ii

i \ ‘1 \ ‘\ “&

.\ \

Lactose .N.\

‘\

‘\

z*

Drug formulation

‘N.\ ‘I*-

Calcium

I I I 20 50 IO Particle diameter, pm Figure

7

Tan A versus

particle

carbonate

I 40

size

other properties of a powder such as the size and shape of its particles, its temperature, moisture content, or presence in it of other ingredients or additives. Considerable care has to be taken in preparing samples for testing to ensure that the results will be meaningful. The first step is to mill the powder and sieve out all particles larger than about 50 Frn, because large particles tend to break in shear and tensile tests thus changing the original constitution of the sample and invalidating the results. The remainder is classified into narrow size fractions for using, example, a Microplex aerodynamic classifier. The sample is then carefully

Figure

8

Different

shaped

particles

(X 1~OOO)

dried and the measurements are carried out at a controlled relative humidity. Figure 7 shows typical graphs of tan n plotted against average particle size for lactose, calcium carbonate, and a pharmaceutical formulation used in the treatment of asthma. For many powders in the size range 1 to 40 pm the relation tan n = K2 + K3 log d (7) applies, where K2 and K3 are constants for each powder and d is their average particle diameter [ll]. This expression agrees with the general observation that the finer a powder the more cohesive it is because of the van der Waals’ and frictional forces between the particles. However, in the range that we are considering it is difficult entirely to separate the effects of particle size and shape. In most powders the particles span a range of shapes (figure 8), and when, as for example with magnetic iron oxide, they are needle shaped it is difficult exactly to specify their size. (As a first approximation one takes the diameter as the average of length, breadth, and width). It is not possible to classify powders smaller than 40 pm into different shape fractions, though sometimes one can produce a batch all of the same shape by carefully controlled crystallisation or precipitation from solution. Nevertheless it seems that just as the quantities a and T decrease as the particles are made larger (figure 7) so they also decrease as they are made rounder and smoother, presumably because this reduces the friction between them. It appears that the term K3 in equation 7 is related to the shape of the particles, while the term K2 depends on their hardness and elasticity, which are essentially determined by the chemical nature of the powder. It was stated earlier that powders become sticky and more cohesive when wetted. However, if you add increasing amounts of water or an oil or something soft like soap or petroleum jelly to a powder and measure the change produced in A or in Tat a particular packing density, you find that the cohesiveness of the powder first decreases sharply but then increases. A simple calculation shows that the minimum in the curve corresponds to water or the other additive forming a layer one or two molecules thick over the surface of the particles, reducing the friction between them and thus acting as a lubricant. But when the coating is thicker it starts to bind the particles together by viscous and capillary forces and the powder becomes cohesive. Water, oils, fats, and gums are widely employed for making powders sticky so that they will behave less like flowing liquids and more like plastic solids. Typical examples are pastry, putty, icing for cakes, potters’ clay, and damp sand for building children’s castles by the sea. Besides coating the particles, we have also been investigating what happens to A or T when we mix two or more powders together in different proportions. This is often done in industry; for example, in the manufacture of cosmetic face powder. Are the values for the mixtures proportionally intermediate between those of thkir constituents? The answer generally is no. Table 1 shows values of tan A for mixtures of two different batches of calcium carbonate and for mixtures of calcium carbonate and lactose. When these sorts of 187

results are plotted against composition, one obtains graphs which exhibit maxima or minima or points of inflexion. A possible explanation is that as the composition is changed so changes occur in the packing arrangement of the particles, but this has not been proved. TABLE 1:

Percent CaCO, (10 @rn) 100 75 50 25 0

VALUES

by weight

OF TAN A FOR MIXTURES

Percent

CaCO, (25 pm)

tan A

CaC03 (4 pm)

0 25 50 75 100

0.95 1 .oo 0.93 0.91 0.50

0 25 50 75 100

by weight

Lactose (4 pm) 100 75 50 25 0

tan A

References 1.15 0.95 0.89 0.91 1.05

Effects of temperature

I will conclude with some additional remarks on the effects of temperature on the properties of cohesive powders. We saw earlier that cooling certain powders causes them to flow more easily through holes. In general, heating powders produces the reverse effect. When you actually measure their tensile strengths or angles of internal friction over a range of temperatures [8] you find that in most cases they increase as the temperature is raised until, at a

188

temperature of about %oth of the melting point (both expressed in OK) there is a sudden decrease. Up to this temperature near their melting points the powders are becoming more cohesive. This fact is made use of in industry for the compaction of metal and other powders to form blocks or solids of different shape-oal briquettes, ‘leads’ for pencils, insulators, toys, and light weight building materials.

PI Society

of Chemical Industry Monograph No 14. ‘Powders in Industry’ 1961. PI Allen, T. ‘Particle Size Measurement’ (2nd ed.) Chapman & Hall, London 1975. 131Powder Technology. Elsevier Sequoia, S. A. Lausanne. Pilpel, N. Endeavour, 30, 77, 1971. R. and Patterson, H. S. ‘Smoke: A Study of ;s; Whytlaw-Gray, Aerial Disperse Systems.’ Arnold, London. 1932. [61 Green, H. L. and Lane, W. R. ‘Particulate Clouds, Dusts, Smokes and Mists.’ E. & F. N. Spon. London, 1957. [71 Balmer, R. T. Endeavour (New Series), 3, 118, 1979. PI Pilpel, N. and Britten, J. R. Powder Technology, 22, 33, 1979. [91 Brown, R. L. and Richards, J. C. ‘Principles of Powder Mechanics’. Pergamon Press, Oxford. 1970. [lOI Ashton, M. D., Cheng, D. C. H., Farley, R., and Valentin, F. H. H. Rheologica Acta, 4, 206, 1965. [Ill Kocova, S. and Pilpel, N. Powder Technology, 5, 329, 19711 72; and 8, 33, 1973.