The mechanisms of free surface segregation

Pmvder Technology,

The Mechanisms J. A. DRAHUN* Deportment (Received

36 (1983)

39

39 - 53

of Free Surface

Segregation

and J_ BRIDG\VATER**

of Engineering August 11, 1982;

Science,

Oxford

University.

in revised form February

SUhlAlARY

When a heap is formed by pouring, free surface segregation is the process by which free flowing particles sepamte. Experiments were conducted in an appamtus in which all variables could be controlled and the results could be expressed in dimensionless form. Data were obtained principally for small quantities of a tracer component in a closesized bulk material_ Both diameter and density had a significant effect on the spatial probability distribution of the tracers. Those larger than the bulk or less dense would float down to the bottom of the free surface. whereas those smaher than the bulk or more dense would sink into the heap close to the pouring point. Improvement in distribution could be achieved by balancing the effects of size and density. Increase in the velocity of impact onto the surface affected the influence of size but not of density. The spatial distribution of the tracer in the feed material was also significant.

INTRODUCTION When a cohesionless material is discharged onto a free surface, it is found that differing particles become sepamted. Such effects can give rise to problems in the design of bunkers. affecting both the structural design of the bunker and the variation of the quality of the solid discharged with time. If a fluid is being pnssed through the bed to effect. for csamplc, Prcscut nddrcsrrs: *I.C.L blond Division. P.O. Box 7. Wiuniugtou. Northwich. Cheshire CWS 4DJ (Ct. Britnin). +*Depnrtmcnt of Chcmicnl Engineering, Birnriughun~ University, P-0. Box 363. Birmiughnnr Bl5 2TT (Gt. Britain); (to whom corrcspoudence should bc addressed.) 0032.0581/83/S3.00

Oxford

(Gt. Britain)

7, 1993)

drying, fluid maldistribution can influence the processing time. Even more significant effects can appear if chemical reaction is occurring, since fluid maldistribution can promote hot spot formation as indicated by Stanek and Szekely [I]. The present work arose since conflicting evidence on the effect of particle properties on free surface segregation was to be found in the literature_ The prior literature will be assessed following presentation of evidence accumulat.ed here.

EQUIPMENT

AND

ESPERIhlENTXL

PROCEDURE

A detailed description of the esperimental equipment has been given previously 121 and onlv the key features are reiterated. The equipment design permits the slope length. solids flow rate and solids f311 height. to be varied independently. Most of the work was conducted with binary systems with one component being present in small quantities (Fig. 1). The major component is placed in the bunker A and is then fed by the conveyor belt B into the perspes bos C in which the surface slope is formed. The speed of the conveyor belt may be v3ried. Minor components may be introduced manu3lly onto the top of the material on the conveyor. the clearance of the conveyor from the bottom of the bunker generally being such that 3 nearly full monolayer esist.ed nnd the minor component thus also rested on the belt. However. thick layers could also be used with the minor component being added at the top or the bottom of the layer by 3 mu-row st.nndpipe. The purpose of avoiding uncontrolled segregation in the solids supply to the free surface was thus achieved. The vertical position of the box C was controlled by the motor D. It ~3s. thus possible 0 Elscvirr ScquoinlPrinted

in The Ncthcrlauds

bed. The solids between the plates were withdrawn by a vacuum gun and the misture analysed, sieving being most commonly employed. 6. From a knowledge of the masses of a component found in the various boxes, the frequency distribution, or spatial probability distribution 4, is calculated.

PREVIOUS FINDINGS [21

Here we shall now consider a rectangular bed. Some of the key geometric variables are shown in Fig. 2. 5, the mean position of a tracer, can be shown using dimensional analysis [2] to be given by

s

-=f 1

Fig. 1. The inclined plane. A. feed hopper for bulk material; B. conveyor; C, box; D, motor for Iowering bos; E, inclined plane; F, hinge for settin& free surface horizontal

during analysis.

the distance from the conveyor to the free surface at a predetermined value_ A roughened surface E was set into the box aL about the angle of repose. The box C thus provides a means of studying a section of a poured heap; if the box has parallel vertical faces, a rectangular heap is being modelled. If these faces diverge, it should be possible to model a conical heap. The general procedure was as follows: 1. A thin bed of particles was deposited on the inclined slope by the conveyor_ 2_ The solids flow was continued with tracers being added at intervals, 200 - 500 tracer particles normally being used. 3 - Tracer addition ceased and then sufficient bulk material was added to be certain that the tracers had reached final positions. 4- The bunker and conveyor assembly was removed and the box C rotated about hinges F’ so that the free surface now became horito maintain

4 PP ‘hi Y db Pb

3

-_,---.F,j-

where I is the projected slope length ( a more convenient length scale than the actual slope length L used previously), d, is the diameter of the minor component and db that of the main component. pP, pb are the true solid densities of the minor and main components and y is the free-fall height onto the top of the surface. Equation (1) applies to spherical materials and it is supposed that the surface friction is constant, implying that the angle of repose is also constant. The previously reported experiments showed that data were reproducible and that the group c/Z was not dependent on the group

zontaI, the purpose being to avoid bulk mo-

tion and segregation during analysis. 5. Plates were pushed into the slots set in the perspex walls thereby isolating sections of the

Fig. 2. The inclined plane. Schematic diagram and notation_

d,,/l. this being established for slope lengths 1 differing by a factor of 4 and d, = 2.05 and 4.00 mm, the material being glass beads. Conveyor speeds of either 0.4 or 4.6 cm/s with a monolayer of feed had no effect on the results. Rendering tracer particles rough by the adherence of powdered copper, or smooth by spraying with PTFE, had no influence on the findings_ We thus have

(2) The bulk material built up under the conveyor and then suddenly avalanched down the surface, sometimes petering out part way down the slope and sometimes reaching the far end of the slope. Avalanches disturbed the material down to a depth of about 7 particle diameters, but displacements of greater than db were only observed in the first four layers. The success of eqn. (2) suggests that the distribution of avalanche size is in proportion to the slope length. Particles denser or smaller than the main material sank below the surface, the mechanism being that of interparticle percolation 133 at a very low normal stress_ Particles larger or lighter than the main material rose to the surface by a mechanism termed particle migration identified during studies on mixture behaviour in failure zones [4]. The two classes of particle have been termed ‘sinkers’ and ‘floaters’. RESULTS

Here detailed consideration is given to the effect of some of the independent variables

Fig_ 3_ Distributiops

on free surface segregation. First of all, the effects of particle properties will be csamined for y/l = 0 with a particle monolayer on the feed conveyor_ In all the present studies. data were obtained with I = 43.4 cm. Size The results for a number of differentiy sized tracers but same density as the bulk arc shown in Fig. 3. The vertical asis (I denotes the spatial frequency distribution of stated tracer. The bulk material is 3.00 mm glass_ Tracers iarger than the bulk, 5.10 mm (*) and 5.31 mm (0) glass, arc floaters, whereas tracers smaller than the bulk. 2.05 mm (0) and 3.26 mm (X) glass, predominate at the conveyor end and are sinkers. For bulk tracers (z) an approximately even distribution is obtained. The relationship between c/Z and d,.ld,, is shown in Fig. 4. Similar results were obtained for 2 different bulk material, in this case 4.9s mm acrylic resin. and the relationship between s;‘l and d,; d, is inciuded in Fig_ 4_ It is evident that a linear relationship esists between .?/l and d,/ cl,, and that results are not affected by changing the bulk material. If d,Jd, was greater than about l-5, virtually 211 floaters ended at the side w;alls_ Most of the movement towards the side walls occurred during avalanches_ A likely explanation for this is that the velocity of particles in an avalanche varied across the avalanche front; the particles at the centre moved faster t.han those at the walls, giving rise to a transverse velocity gradient- and tracers moved into these to areas of lowest velocit>y_ Moreover, since the tracers would be larger than the

of tracers differing from the bulk in size. Bulk: 3.00 mm &~SSbeads. Pp/& = 1.0. Tracers: G. = l-O);+ (dp/db = ~-~Sk=‘~ (d,fd,, = 1-16).

glass (dp/db = 0.51); x, (dp/db = 0.8~); 0, (d,/d,

42

Fig_ 4_ Relationship between 511 and dp{db for p,,/p,, = 1.0.0, bulk, 4.00 mm glass beads, db = 4.00 mm, p,, = 2950 kglmq angle of repose 22” (measured after an avalanche); 0, bulk, 4.98 mm acrylic resin beads, d,, = 4-98 mm, P,, = 1190 kg/m3, angle of repose 19.5’ (measured after an avalanche).

Fig. 5. Distributions of tracers differing from the b=lk in density_ Bulk: 4.00 mm glass beads. dp/db = 1.0. Tracers: 0, acrylic resin (&,/pb = O-40); 0,dehin (pJp,-, = O-47); X, steel (pP/&, = 2.64); 0, brass (pp\pb = 2.84).

roughness of the surface, rolling would readily occur_ This effect was particularly prevalent with 2.05 mm glass as bulk, in which diameter ratios of 2 to 3 were tried. With the two other bulk materials, values of dp/db did not exceed 1.5 and no more than 1% cf floaters reached the side walls. Density A number of different tracer particles of the same size as bulk particles were studied with two different bulk materials. For 4.00 mm glass, some results are shown in Fig. 5. Experiments were also conducted with 4.98 mm acrylic resin beads. The division by density into two groups is at least as dramatic as that by size- The denser tracers collect at the conveyor end, whereas the lighter float to the far end- The relationship between S/Z and pp/pb for both bulk materials (Fig_ 6) shows

linear behaviour for pP/pb < l-2_ At large density ratios, the distribution becomes independent of density ratio.

Shape The effect of tracer particle shape was investigated, the diameter of the tracer particle being taken as that determined from the sphere of equivalent volume. Exact matching of diameter ratios and density ratios with spherical phaterials proved difficult, but results for 0.7 < pp/pb < l-7 showed generally the same behaviour. In one case, however, a detailed comparison was possible_ Results for celon chip, a cylindrical material with a length to diameter ratio of 1.42 (dp/db = 0.53, pp/pb = 1.0) can be compared with those for 2.05 mm glass in 4.00 mm glass (dp/db = 0.51, pD/pb = 1.0). For the former, S/Z = 0.92,

0 0

Fig.

6.

Relationship

betsvecn S/l and &.,I&_ d,ldb

= 1.0. 0, bulk:

-2.00 mm glass beads; a, bulk: a.98 mm r-in

beads.

whereas for the latter S/Z = C-90_ The results suggest that any effect of shape is small. The exception among the non-spherical tracers occurred when using metal washers with an outer diameter about three times t.hat of the bulk. Size and density (dp/db = O-55, pp/pb = 6.51) both suggest that the tracer should remain at the conveyor end; however, it is in fact concentrated at the far end with S/Z = O-16_ The reason is that washers lie flat on the free surface and are consequently unable to percolate into avalanches Thus, the extremes of shape have an effect on the tracer distributions_ Particles of roughly equal dimensions behave as spheres. Particles in the form of plates, and probably of needles, may behave in a different fashion.

Variation of both size and density Both size and density are of major importance in free surface segregation and thus it

Fig_ 7. Distributions drJdb = 0.78, &,jpb x. dp\db = 3.48.

may be possible to produce an even distribution by combining suitable density and diameter ratios_ Figure 7 shows an esample for a tracer species with d,Jd, = 0.78, ppjpb = O-43_ The distribution is more even; the effects of size and density have almost cancelled out. The practical utilisat.ion of such behaviour would be dependent on controlling some of the other variables discussed belowSuitable systems were not available to develop a specification of the relationship between chat yielded a uniform disd,& and &Pb tribution- None the less, this behaviour is of possible direct practical importance. ..A number of different sizes of steel tracers were studied in 2.05 mm glass as bulk. The results, three of which are shown in Fig. 7, show little change in the distribut.ion with size ratio. Density ratio is an unimportant parameter when size ratio is the predominant. cause of segregation, an effect found to be generally true from studies in other systems.

of tracers differing from the bulk in size and density. Bulk: 4.00 mm glass beads. Tracer: 0, = O-43. Bulk: 2-05 glass beads. ‘i?racers: steel, p,&, = 2.64: l. dddb = 1.93; 9 dp/db = 2.33,;

44 ------5Ocmdrop;onIy

I

--------_A,

6 t

tracers dropped

do b s -_=, pa

-r F

1

05 i/t Fig.

8.

The influence

of free-fall height y on the mean

tracer

position

S/I.

02 q CM-%

\ \

= Oh 0

\

\ 'x

I__-'-x__9= -x-_9_.cL.n-=-

1 1

05

g. Distributions of tracer glass (dp[db = 0.51, pp/pb = l-00) glass beads as bulk; 0, y = 0 cm; 0, y = 3 cm; X, y = 9 cm.

Fig.

Free-fall Height The influence of free-fall height on the mean position of tracers is illustrated in Fig_ EL For the highest value of y *“, this group being chosen as a measure of the free-fall velocity it was not practicable to discharge (%Y)“‘, both the 1 lk and the tracer from that position and only the tracer was so handled. When using this technique, it is seen that labelled bulk particles pass down the surface_ Smaller particles with pp/pb = 1 move down with respect to this labelled material and larger particles with pP/pb = 1 move up with respect to this labelled material. This behaviour is compatible qualitatively with the observations at lower free-fall height with both components being discharged from the same height (Fig. 9). A bi-modal distribution may be found with some small particles near the conveyor end and with others at the far end.

at different

free-fall heights in 4-00 mm diameter

As free-fall height increases, large tracers have increased momentum and thus are more likely to break through the free surface and enter areas which are unaffected by avalanches- Conversely, for small tracers, the increased momentum causes these to bounce off the free surface, thus preventing them from resting in hollows on the free surface and hence preventing them from percolating. Furthermore, the bouncing carries the particles down the slope. If the d@nsity is varied for dJdb = 1, pp/pb < 1, the tracer particles may now be reflected to the far end rather than travelling in avalanches For pp/pb > 1, it might be deduced that the tracer particle will be yet more likely to be trapped at the conveyor end. The insensitivity of the distribution to the density ratio when this ratio is large has already been noted (Fig. 6); the insensitivity to free-fall height is

45

thought to be related. This is discussed below_

further

Multiple bulk layer feeding Instead of the usual monolayer of material on the conveyor, several layers were discharged and tracers initially located at a level most removed from their natural final location Thus, sinkers were located on the top layer and floaters in the bottom layer. It was observed that the thickness of bulk material in avalanches increased with the number of layers discharged from the conveyorThe behaviour of a floater by virtue of density, 3.99 mm acrylic resin, as a function of b, the number of bulk layers, is shown in Fig. lo_ For all thicknesses, the tracers floated only slowly. The majority of particles were unable to rise enough to be affected by avalanching- Observation revealed that for the largest values of b only about 1% of particles rose to the free surface itself, but this number

increased as b decreased, reaching about 10% of the total for b equal to 2. Results of similar nature were obtained for floaters by virtue of size but, for the range of variables studied, the proportion of particles that rose to the free surface during the experiments was greaterThe relationship between Z/l and b is seen in Fig. 11. Results for a typical sinker, 3-96 mm steel, are shown in Fig. 10. The distributions are notable for similarity rather than differenceSinking behaviour is still eshibited, but the distributions are centred further down the slope_ Similar results are found for sinkers controlled by size. The relationships for SiZ to b are shown in Fig. 11; the variation in the distributions of these sinkers with b is relatively small_ Xn explanation for the linear relationship between s/l and b at low b is that. the rate at which sinkers percolate to regions where they are unaffected by avalanches is proportional

OXI-

030 q

c

021 I-

Fig.

--per with the thickness of the feed on the conveyor b_ Buik: 1.00 variation of the distribution of t..__ Tracers {acrylic resin. d,/d,, = 1.00, ppl& = O-40) in bottom laxer; X. b = 3; 4 b = 4; .z. b = 6. (steel. d,/d,, = 0.99. pblpp = 2.61) in top layer;A, b = 2; yT b = 4 ;4 b = 6.

10. The

mm glass beads. ‘Tracers

Fig.

4.00

11. The relationship between mean mm glass beads. 0, tracer 2.05 mm

tracer position glass beads.

SII and

the thickness

of the feed

on the conveyor

b_ Bulk:

46

Fig_ 12. 22.4

Distributions wt.%“c; g. B 44.8

of varying concentrations of 2.05 mm (B) glass in mixtures wt.%; X. B 72.7 w+%; 0. results for low concentration of B.

with

3.00

mm

dia_ glass_ 0, B

Fig. 1% Ditributions of glass of different diameters loaded in separate bunkers_0, 2.05 mm dia.; q* 1.00 mm dia.; two layers of the former fed on the top of four layers of the latter; 0, results for low concentration of small particles_

to the number of layers in motion on the slope beneath them. This view is compatible with the observation that the number of layers taking part in avalanches appeared to increase with b. There must be a limit for the number of layers that can be involved in avalanching and, consequently, increasing b beyond the limit does not increase the avalanche thickness and S/Z becomes constant_

Tracer concentration In most experiments, the weight of tracers did not exceed 1% of the bulk material_ A few experiments were carried out where the proportion of tracer was significant compared with that of the bulk. The materials used were 2.05 mm and 4.00 mm glass, which could be

conveniently separated by sieving. The quantities of each component in a compartment were weighed rather than counted_ Monolayer feed was used first and the components were loaded in the main bunker in alternate layers, the sizes of the layers being proportional to the relative proportions of the components. Figure 12 shows the distributions obtained at three different proportions of species A and B. It is evident that for both components the distribution moves towards the centre as the proportion of that component increases since, in the limit, the distribution will be even _ Experiments were also carried out with layers of 2-05 mm glass on top of layers of 4.00 mm glass. Practical difficulties prevented the number of layers of the smaller sized glass

being more than two, and the results for four layers of the larger glass used are shown in Fig. 13_ The sinker is disposed more centrally and the floater is disposed both at the conveyor end and the far end compared with Fig. 12. The importance of the inlet structure of the feed is evident.

Divergent

walls

Esperiments of a preliminary nature with the bos of parallel vertical sides replaced by one with divergent walls were carried out, the purpose being to simulate the behaviour on a conical heap. The dimensionless approach found previously [2] could not be repeated exactly since the conveyor width then entered the dimensional analysis. On studying the effects of size and density, the general effects were similar [5]_ The most noticeable difference was a generally decreased frequency of avalanching but with the principal particles being partly convected, particularly for glass beads, down the surface by a process that may be termed ‘shimmering’ in which up to half the particle surface moved down the surface together with a displacement of 1 or 2 particle diameters_ There was no evidence that this alternative method of motion affected the qualitative effect of the various independent variables on the segregation_

DISCUSSION Here are considered two matters not touched on previously. This is followed by an assessment of prior work_ The distribution of floaters Consider a surface element (Fig_ 2) of unit width, unit depth of packing deposited, of side d_r_ The volume of bulk material passing a given point x will decrease linearly with distance down the slope and is given by (I - x)_ There will be deposition of tracer in the element as a result of both the systematic escaping flux of tracer from the depositing material due to segregation and the natural deposition of bulk. Hence, by mass balance on the tracer on the element, the change in flus of tracer c(Z --x) is given by

where c is the concentration of tracers per unit volume of packing and K is a constantThe first term on the right-hand side is the contribution due to escaping flus and the second due to bulk deposition_ It is assumed that the escaping flus is directly proportional to the tracer concentration, ie_ particles are lost from the moving surface layers in a random manner_ Equation (3) reduces to

(Z-x)~=Kc

t-11

which on integration In

5 =-

yields

Z---X h_ In

co

-

1

where co is the concentration Now since

of tracer

fed.

s=l-_x

]n

_5= -Kin+ co

(5)

An esample of the relationship between t-he logarithm of the proportion of the total number of tracers and the logarithm of the fractional distance from the far end is shown in Fig_ la_ It is evident that the relationship is linear for t.hose points away from the conveyor end. Howeser, these four points at the far end contain 85% of the t.racers. The slope cf the linear position, det.ermined by a leastsquares regresssion fit, gives K. The variation of K with d,/db for two bulk materials, 400 mm glass and 4-98 mm acrylic resin, is shown in Fig. 15 and an approsimately linear relationship is present_ Figure 16 shows the relationship between K and pp/pb for the same two bulk materials at two values of d,/d+ For 4.00 mm glass bulk and d,/d,, = 1.0, R decreases approsimately linearly with increasing pp/pb, but for 4-95 mm acrylic resin bulk no trend is apparent. for d,]db = 1_2_ It is thus probable that for floaters in small quantities the model is a suitable mathematical description of the spatial distribution of floaters as a result of free surface segregation_ The analysis is not relevant under the pouring point; some tracers are perhaps too well covered by bulk material before being subject to an avalanche_

48

Fig_ 14_ Logarithmic plot of proportion of total number of tracers C/COagainst fractional of slope. Bulk: 4.00 mm glass beads_ Tracer glass: d,Id, = l-45. &-,ID~= l-00_

distance s/l from far end

10 K

08 06 Oi :

Fig_ 15. Relationship resin beads.

between K and d,/d,,

(pB/p,, = 1.0);

9

bulk: 4.00

mm glass beads; g, bulk: 4.98

mm acrylic

Fig. 18. Relationship between K and pPlpb_ 0, bulk 4.00 mm glass beads, tracers with dJdb = 1.00; o, bulk 4.98 mm acrylic resin beads, tracers with dPldb = 1.00; X, bulk 4-00 mm glass beads, tracers with d,fd,, = 120.

Bekaviour of sinkers The mean position S/Z of the distribution of sinkers has been found to vary little with par-

title properties, although sinkers by virtue of size are located closer to the conveyor end than those by virtue of density.

49

A possible explanation for this behaviour is: (i) Sinkers, once on the free surface, are on average in the same position_ (ii) When avalanching (or shimmering) takes place, tracers are convected down the slope but also percolate down through gaps formed between bulk particles_ (iii) After passing through a certain number of layers, the sinkers reach a depth at which avalanches (or shimmering) have no further effect. On this hypothesis, the observation that the distribution scales with slope length may be explained by inferring that the displacements in avalanches are proportional to the slope length. (iv) The observation that S/Z is very similar for different sinkers could be explained by either (a) percolation rates are very similar, or (b) percolation rates are different but all fast so that sinkers percolate to the bottom of the avalanche but are not immediately halted by the stationary layers below. The reasons for the small difference in g/I for size and density effects are not clearStudies on strain-induced percolation [33 indicate that size is a more significant factor than density_ However, in layers near the free surface where stressses are lower, the forces acting depend on the weight of the particle as well as the size and it is probable that the percolation rate will then by affected by PJPbPrevious work -An assessment (a) Physical mechanisms Brown (63 gave an early qualitative explanation of segregation and identified two types of segregation; the first was that occurring in a bed of material due to vibration, and the second that occurring at a free surface during flow down an inclined slope_ For free surface segregation, Brown considered that the primary factor was the collisions between particles flowing onto the heap and those forming the free surface_ He suggested that four types of collision were possible_ The types of collision and the consequences predicted were: (i) A small particle striking a large particle of identical density would be bought to rest and push the large one a small distance down the slope_ (ii) A large particle striking another large one would cause both to move away from the

initial line of fall onto the surface(iii) A small particle striking another small one would push the iatter a short distance down the slope. (iv) A large particle striking a small one would cause the latter to be dislodged and either to be moved towards the periphery or to be buried in the heapBrown hypothesized that, as a consequence of these collisions, small particles would be given either large or small velocities, whereas the large ones would be given a more uniform velocity_ The next stage of the process was the rolling of particles down the slope. The slope is an irregular plane, the average height of protuberances being less than the diameter of a large particle. Consequently, Brown considered that large particles would roll or slide down the slope more easily than small ones and thus would move further away from the initial point of feed_ Any small particles of high velocity on the free surface would tend to hit large particles and be brought. to rest, whereas those with small velocit.ies would concentrate close to the feed point. He also argued that the impact of the stream on the heap would cause small particles to fall through spaces between the large onesBrown’s hypothesis is, however, somewhat at variance with the present experimental evidence_ If the feed were directly onto the slope, such as was usual in the inclined plane work, the collisions Brown considered would be too weak to cause the displacements implicit in his reasoning. His analysis could be applicable to pouring with a free-fall height, although he ignored the possibility of small particles being carried down the slope by bouncing_ A high free-fall height has been found to cause reversal of the distribution of sinkers. Thus, Brown’s hypothesis was somewhat simplified and has described only part of the picture_ He recognised the part played by rolling and percolation, but his views on the importance of collisions now seem less significant_ Brown also considered the segregation of identically sized particles due to density difference_ He believed that the greater momentum of the denser particles would cause these either t-o sink beneath the line of fall or to roll down the slope; consequently, they would be concentrated partly beneath the point of feed and partly at the periphery_ Experimental

50

evidence, however, shows that the latter case is not found_ Williams 17, S] gave an explanation for free surface segregation during heap pouring. He stated that material rolls down a sloping surface which contains holes of the same order of size as the diameter of the bigger particles; small particles will tend to sink through these holes preferentially. On the other hand, the larger particles that are unable to locate adequately sized holes will tend to roll to the bottom of the heap. If a steady flow of material is discharged onto the heap, Wlliams believed the particles near the surface to be in a state of agitation and act as a screen through which only the small particles are able to pass. This mechanism differed from Brown’s in that collisions were not considered and interparticle percolation was regarded as the prime segregating factor; large particles rolled to the periphery by default. Although Williams described a percolating and a rolling mechanism, the latter was regarded as a consequence of the former_ To illustrate this point, an esample from the inclined plane experiments can be considered_ If a large particle in very low concentration is used as tracer, the large particles will remove to the periphery. However, there would be too few of the large particles to act as a screen and segregation in such ceses cannot be attributed to percolation. 0th.2r authors who have proposed mechanisms . is free surface segregation have usually considtred one to the exclusion of others. Lawrence and Beddow [9] said that segregation occtirs by the filtration of small particles down through the moving mass. In this, they are describing inter-particle percolation in the top layers of the heap. The view that this might be the sole mechanism in operation is invalidated by the example just quoted. The example also casts suspicion on the reason put forward by Lawrence and Beddow to explain their ‘inverse segregation’, i.e. the excess of fines at the periphery when the mean proportion of fines exceed 60%. They considered that since there were relatively few large particles, these were unable to flow readily through the matrix of fines. On this basis, the small amounts of large tracer often used on the inclined plane would make such tracers behave like sinkers_ Further doubt is cast by the series of inclined plane experiments in which the proportions of two components

were varied. In an experiment where the ratio of the volume of small to large was approximately 3 to 1, no such inverse segregation was present_ The reasons for Lawrence and Beddow’s findings are not clear- However, their results can be reconciled with the present work if they had employed a free-fall height; they did not report whether or not such a height was used_ Syskov and Tszi Lyan [lo] took t.he opposite view to Lawrence and Beddow and considered that particles rolled down the inclined slope and that small ones were readily hindered by the protuberance on the surface and were caught by cavities present. Thus, they considered segregation to be caused mainly by the roughness of the free surface. Although they stated that heavy particles might be abie to break through and sink, they ruled out percolation by small particles_ A similar view was held by MatthGe [ll]_ The present work on the inclined plane suggests that convection of particles occurs in avalanches with inter-particle percolation and particle migration determining the extent of free surface segregation. There is no mention in the literature of the occurrence and significance of avalanches during the pouring of the heap. It is likely that avalanches or shimmering may have been overlooked because gravity flow onto the heap has usually been used, which is much faster than that on the inclined plane_ Consequently, the build-up and breakaway of avalanches would be correspondingly more rapid and such a swift succession of avalanches could well be misinterpreted as continuous rolling. (b) Influence of independent variables Williams [12] stated that difference in particle size, density, shape and particle resilience could each, under certain circumstances, cause segregation but considered that ‘all the available evidence’ showed particle size difference to be far the most important_ However, Williams has not recorded the detailed experimental evidence on which he based his findings. Such conclusions may well be true for vibration- or strain-induced segregation, but the results on the inclined plane show that density is a significant factor in free surface segregation. Moreover, there is other published evidence of the importance of density, for example that of Syskov and Tszi

51 Lyan [lo]_ Holmes 1131 also described a number of experiments which were of an illustrative nature rather than quantitative reseanA. He poured a misture of anthracite and

fluorspar, screened between the same two sieves, out of a small conical bunker and divided the resulting heap into a number of samples. Zero and 6 ft free-fall heights were used. The specific gravities were 1.43 for anthracite and 3-l for fluorspar. In both experiments, Holmes found that the denser fluorspar was concentrated at the centre of the heap whereas the anthracite was predominantly at the peripheryHarris and Hildon [14] considered size to be the most important factor controlling free surface segregation. They suggested that segregation would be largely eliminated if the particle size of the bleaching agent were limited to a narrow size range. This is probably because the size of the bleaching agent fraction is then closest to the mean size of the detergent base. They believed that density has a small effect on segregation_ On the other hand, Lawrence and Beddow [ 9 J considered size to be of major importance and density to have no effect. The literature indeed suggests that both size and density are significant factors in causing free surface segregation but frequently the effect of density has been neglected; often studies on density are a sketchy afterthought_ The importance of both size and density is clearly demonstrated in the present studiesOther particle properties that might cause free surface segregation have received little attention_ Lawrence and Beddow [9] investigated the segregation of spherical, flake and irregular particles and concluded that part.icle shape has little effect. Harris and Hildon’s experiments [143 using two different granular bleaching agents, one approximately spherical, the other less so, suggested that shape plays a minor role in segregation_ The inclined plane studies on non-spherical tracer particles confirm that particle shape, except in estreme cases such as flat discs, has little effect. The influence of surface roughness on free surface segregation has not been studied elsewhere; the present studies indicate that surface roughness has no effect. Lawrence and Beddow 191 found that increasing the free-fall height decreased the extent of segregation unless the particles were

below about 250 grn in diameter_ Syskov and Tszi Lyan [lOI found that, for particles of differing density, the extent of segregation was decreased by increasing the free-fall height. In both cases, the increase in energy, which caused greater scattering as a result of bouncing, was cited as the reason for the decrease in segregation_ Lawrence and Beddow explained that absence of an effect below 250 pm as a manifestation of the low coefficient of restitution of the material usedThe esperiments on free-fall height on the inclined plane were in agreement for tracers differing from the bulk in size. since the distributions tended to be spread more along the length of the slope, but there was little change in the distribution of particles of differing densities_ The free-fall heights used by Syskov and Tszi Lyan were up to 50 cm, whereas that on the inclined plane was 3 cm_ It is possible that the density effect may be more apparent if larger free-fall heights were used_ It was found that if the height was great enough, the distribution of sinkers by virtue of size could be reversed_ This has not. been reported elsewhere, presumably because suitably large free-fall heights have not been employed_ Lawrence and Beddow 191 and Syskov and Tszi Lyan ]lO] found that the extent of segregation decreased if the pouring time was decreased. This was attributed to particle motion on the free surface being hindered by the rapid discharge of material onto the surface_ In neither case was the discharge rate reported. Variation of the rat.e of discharge onto the inclined plane was found not to affect the distribution for the low rates of flow used. Although the existence of free surface segregat.ion has long been recognised, there have been few attempts to produce theories that would predict quantitatively the amount of segregation. Most investigators were primarily interested in the prevention of segregation rather than the factors, per se, that caused it and, consequently, the conclusions put forward were to solve a particular problem %ithout understanding the controlling phenomena. A number of workers (e.g. Harris and Hildon [14]. Syskov and Tszi Lyan [lo]) have presented their results in terms of arbitrary degrees of segregation, but these are not universally applicable_ However, the

52

physical conclusions drawn with the present results.

are compatible

(c)Predictive models Matthee [ll] tried to quantify segregation on a slcpe in terms of the sliding or rolling motion of a single particle down a smooth inclined plane. An energy balance following the motion of the particle indicated that if sliding friction only were present, the distance the particle travelled would be independent of its size and mass; if rolling friction were present, the distance travelled would depend on the particle diameter, the larger particles rolling further than the small ones. However, this approach is idealised since, firstly the free surface cannot be considered to be smooth, and secondly the possibility of percolation is ignored. The inclined plane experiments suggest that rolling and sliding do not contribute greatly to segregation- Matthee proceeded to consider a rough surface but t.he only conclusion he proposed was that a large particle was less likely to be halted by the roughness elements of the surface than a small one. The experiments Matthee presented did not appear to bear any relation to his theory. Two materials separated in a bunker by a partition were poured together via a long feed tube into a bin from which samples were taken. Unfortunately, the description of the equipment and presentation of results was incomplete. Tanaka [ 151 proposed a model predicting the extent of segregation arising from density difference. The model considered twodimensional arrangements of three touching spheres, one on top of the other two_ Tanaka asserted that the relative distances moved by heavy and light spheres as a result of the upper sphere forcing apart the lower pair, were based on the magnitude of the limiting coefficient of friction, the value at which motion commences, between the lower spheres and the surface beneath it. However, a serious drawback of the concept is that the surface on which the spheres rest was considered to be both horizontal and smooth_ The model predicted that the proportion of heavy spheres would vary with distance from the feed point in a series of discontinuous steps- The relative lengths of the steps were based on the ratios of values of the limiting coefficient of friction for different arrangements of heavy and light spheres in the original static system.

Experiments were performed using mixtures of 1.4 mm diameter lead shot and glass beads. The density ratio was 4.5. The mixture was blended by hand and poured from a storage bunker into a narrow rectangular bin. Sample taps were located near the top of the bin along two lines at 25” to the horizontal which presumably represented the shape of the free surface of the material in the bin. The size of samples, depth of sampling beneath the free surface and distance of sampling from the centre of the box were not reported_ Tanaka claimed good agreement between his theory and esperiment but used an arbitrary length scale to accommodate the experimental results to the theory. The results bear some similarity to the behaviour of sinkers on the inclined plane. The proportion of heavy particles rose with increasing distance from the feed point, passed through a maximum and then decreased to zero. Tanaka, however, overlooked the existence of the maximum in his results. The generality of the model was not tested by altering the slope length. Thus, although the experimental results may be satisfactory, the theoretical model was oversimplified. In particular, the present work shows surface friction to be unimportant. In general, analytical attempts have found it hard to model the key features of free surface segregation.

CONCLUSIONS

Experiments have been performed on the free surface segregation which occurs when particles form a two-dimensional heap in a controlled manner, the results being presented in a dimensionless form. Such control of studies on free surface segregation has not been achieved previously. It has been found that: (i) Free surface segregation occurs by avalanching, inter-particle percolation and particle migration. (ii) An increase in particle velocity onto the surface, for the range of variables studied, influences the material distribution controlled by diameter but not that controlled by density. In particular, increase in free-fall height causes small particles to bounce down the free surface to the far end.

53

(iii) A small change in the location of a tracer particle in the feed material can markedly influence its final position in the bed formed. Thus, slight segregation in a feed device or feed hopper can influence free surface segregation _ (iv) Tracer concentration is a significant variable_ (v) The particle diameter ratio influences segregation_ Small particles sink by percolation and are found close to the pouring point, whereas large particles rise to the surface by particle migration and are found at the far end of the surface. (vi) The particle density ratio influences segregation, dense particles being found near the pouring point and less dense particles at the far end. (vii) It is possible to diminish free surface segregation by an appropriate balance of size ratio and density ratio. (viii) Tracer particle shape, unless extreme such as platelets, does not have much effect(ix) Tracer particle surface roughness is not important. For the future, there is a need to extend the range of variables studied to date, to analyse the behaviour of systems with a continuous distribution of sizes and to estend the technique to segregation in conical heaps.

LIST OF SYMBOLS b C

co 4

d,

(thickness of layer on conveyor belt)/& tracer concentration at position x iniet tracer concentration equivalent spherical volume diameter for glass and non-spherical materials, otherwise mean diameter from micrometer measurements equivalent spherical volume diameter for glass and non-spherical materials, otherwise mean diameter from micrometer measurements

K L I 4

S

s _x Y

Pb PP

rate constant in eqn- (3) actual length of slope length of free surface projected onto a horizontal plane spatial probability distribution of particles horizontal distance of tracer from far end mean horizontal distance of tracer from end horizontal distance from conveyor end free-fall height onto top of free surface true density of I,alk particles true density of tracer particles

REFERENCES V. Stanek and J. Szekcl-. Can. J. Chem. Engng_, 22. J_ A. Drahun and J. Bridgwaier. I. Chem. E. Symposium Series. 65 (1951) SllQiI. J. Bridgwater, AI. H. Cooke and -4. XI_ Scott. 51 (1953)

Trans.

Irrstn. Chem.

Engrs..

56 (197s)

137. Tech-

D_ J. Stephens and J. Bridgwater. Powder noz_, 21 (1978)

29.

J_ A. Drahun. D. Phil. Thesis. Oxford University (1978). 15_ 6 R. L. Brown, J. Inst. Fuel, 13 (1939) i J. C. Williams. Fuel Sot. J_, Unir- of SheffieZd. I4 (1963) 29. (_4priZ 1963). 8 J. C. Williams. CZzemicaZ Processing S6. 9

10 11 12 13 11 15

L. R. Lawrence and J. K. Bcddow. Powder Technot_. 2 (1969) 253. Ii. I. Syskov and Tszi Lyan. C&e and Chemisfr_v. U.S.S.R., 2 (1960) 5_ H. Matthee, Powder Technol.. I (1968) 265. J. C_ Williams. powder TechnoL. 15 (1976) 245. C. W. H. Holmes. CollieEng.. Z Z (1939) 10. J. F. G. Harris and A. AI. Hildon, Ind. Eng_ Chem. Proc. Des. (19’70) 363. T. Tanaka. Ind. Eng. Chem. Proc. Des. Develop.. 10 (1971) 332.