The role of particle interactions in powder mechanics :
international symposium, Eindhoven, August 29-31, 1983 :
preprints
Citation for published version (APA):
Senden, M. M. G., & Verkooijen, A. H. M. (Eds.) (1983). The role of particle interactions in powder mechanics : international symposium, Eindhoven, August 29-31, 1983 : preprints. (EFCE event; Vol. 289), (EFCE publication series; Vol. 28). Wibro.
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EUROPEAN FEDERATION OF CHEMICAL ENGINEERING EUROPÄISCHE FÖDERATION FÜR CHEMIE-INGENIEUR-WESEN FÉDÉRATION EUROPÉENNE DU GÉNIE CHIMIOUE
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THE ROLE OF PARTICLE INTERACTIONS
IN
POWDER MECHANICS
PREPRINTS OF THE INTERNATIONAL SYMPOSIUM EINDHOVEN, AUGUST 29-31, 1983
EDITED BY
THIJS M.G. SENDEN ADRIAN H.M. VERKOOIJEN
EINDHOVEN UNIVERSITY OF TECHNOLOGY
PREPRINTS
INTERNATIONAL SYMPOSIUM
THE ROLE OF PARTICLE INTERACTIONS
IN
POWDER MECHANICS
EINDHOVEN AUGUST 29-31, 1983 EDITED BYBIBLIOTHEEK
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T.H.EINDHOVEN
THIJS M.G. SENDEN ADRIAN H.M. VERKOOIJENEINDHOVEN UNIVERSITY OF TECHNOLOGY
THE SYMPOSIUM IS ORGANIZED BY
KONINKWKE NEDERLANDSE CHEMISCHE VERENIGING
SECTIE ANORGANISCHE EN FYSISCHE CHEMIE SECTIE CHEMISCHE TECHNOLOGIE
KONINKWK INSTITUUT VAN INGENIEURS
AFDELING CHEMISCHE TECHNIEK
NEDERLANDSE INGENIEURSVERENIGING NIRIA V~KSECTIE CHEMISCHE EN FYSISCHE TECHNIEK
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RESPONSIBLE FOR THE CONTENTSi THE AUTHORS OF THE CONTRIBUTIONS.
ALL RIGHTS RESERVED. NO PART OF THIS PUBLICATION MAY BE REPRODUCED, STORED IN A RETRIEVAL SYSTEM, OR TRANSMITTED IN ANY FORM OR BY ANY MEANS, ELECTRONIC, MECHANICAL, PHOTOCOPYING, RECORDING, OR OTBERWISE, WITHOUT THE PRIOR WRITTEN PERMISSION OF THE EDITORS. EINDHOVEN UNIVERSITY OF TECHNOLOGY, P.O.BOX 513, 5600 MB EINDHOVEN, THE NETHERLANDS.
PRINTED IN THE NETHERLANDS, WIBRO DRUK, HELMOND ISBN 90-9000485-8
SCIENTIFIC COMMITTEE
Chairman: Akers R.J. (Loughborough) Briscoe B.J. (London)
Frens G. (Eindhoven) Geldart 0. (Bradford) de Jong J.A.H. (Arnhem) Lyklema J. (Wageningen) Molerus 0. (Erlangen) Mollet H. (Basle) Nielsen H.C.A. (Valby) Overbeek J.Th.G. (Utrecht) Rietema K. (Eindhoven) Müller B.W. (Kiel)
Verkooijen A.H.M. (Eindhoven) Volpicelli G. (Naples)
Visser J. (Vlaardingen)
ORGANIZING COMMITTEE
STICHTING CHEMISCHE CONGRESSEN XII Frens G. (Eindhoven}. Chairman Senden M.M.G. (Eindhoven). Secretary Stein H.N. (Eindhoven), Treasurer Verkooijen A.H.M. (Eindhoven} de Jong J.A.H. (Arnhem)
TO THE MEMORY OF
CONTENTS
Akers R.J.
lntroduction to the symposium. Rietema K.
Powders, what are they?
Geldart D., Harnby N., Wong A.C. Fluidization of cohesive powders
1
5
24
Donsi G., Formisani B., Valentino R., Volpicelli G. 37 The measurement of characteristic angles of powders in the
prediction of their behaviour in the gas fluidized state
Lindstad T., Hoggen B. 46
The role of gas atmosphere in the sieving process
Piepers H.W., Cottaar E.J.E., Verkooijen A.H.M., Rietema K. 51 Effêcts of pressure and type of gas on particle-particle
interaction and the consequences for gas-solid fluidization behaviour
Bailey A.G.
Electrostatic phenomena during powder handling
67
Derjaguin B.V., Muller V.M., Toporov Yu.P., Aleinikova I.N. 82 The role of the pressing-on in.the adhesion of elastic
particles
Höfer H.H., Wolter A.
Dust resistance and dust separation behaviour of electrostatic precipitators
Schubert H.
Capillary forces - modelling and application in particulate technology
89
Seville J.P.K •• Clift R.
The effect of thin liquid layers on fluidisation characteri sti es
Jenike A.W.
Analysis of solids densification during the pressurization of loek hoppers
Molerus 0., Nywlt M.
The influence of the fine particle content on the flow behaviour of bulk materials
Mathia T., Louis F.
Powder mechanics in tribology Briscoe B.J., Pope L., Adams M.J.
Interfacial friction of powders on concave counterfaces Knight P.C.
The role of particle collisions in determining high strain rate flow behaviour
Overbeek J. Th .G.
Interparticle forces in colloid science Leuenberger H., Jetzer W.
The compactibility of powder systems - a novel approach Tsubaki J., Jimbo G.
Theoretical analysis of the tensile strength of a powder bed
Neumann A.W., Visser J .• , Smith R.P., Omenyi S.N., Francis O.W., Spelt J.K., Vargha-Butler E.B., Zingg W., van Oss C.J.,
Absolom D.R.
The concept of negative Hamaker coefficients. III. Determination of the surface tension of small particles Bridgwater J.
Fluid effects in powder mechanics Cheng D.C.-H.
Further observations on the rheological behaviour of dense suspensions 110 123 136 146 159 172 183 197 207 216 232 242
van Diemen A.J.G., Stein H.N.
Energy dissipation during flow of coagulating concentrated suspensions
Steenberg B.
Wet milling: A model based on hydrodynamics and particulate media mechanics
261
THE ROLE OF PARTICLE INTERACTIONS IN POWDER MECHANICS
Introduction
This symposium has been organised on behalf of the Working Party on the Mechanics of Particulate Solids of the European Federation of Chemical Engineering and as is clear from its title the aim of the meeting is to consider the microscopie phenomena that to a large extent determine the bulk properties of powders and granular materials. To do this it has brought together those whose concern is the appli-cation of engineering science to the design of plant for the storage, conveying and mechanical processing of particulate solids and those who are concerned with the microscopie phenomena of
particle-particle interáctions.
In the context of storage .and discharge from silos particle mechanics as we now know it was put on a firm engineering basis by the work of Andrew Jenike [ l]. In this work Jenike showed how the abil ity of a silo to discharge under conditions of gravity flow depended on the material within the silo experiencing failure at the orifice and being able to continue flowing towards the orifice in a "mass flow" mode once failure had occurred. In order to establish the stresses present leading to the failure condition and the response of the materials present to those stresses use was made of the methods of soil mechanics and it is appropriate to consider the development of soil mechanics in discussing the background to the present meeting.
The science of modern soil mechanics was established in 1773 by Coulomb [2] who identified friction and cohesion as the properties determining the flow of a soil, as is made clear in the opening sentence of his essay "Ce Mémoire est destiné à determiner, autant que le mêlange du Calcul
&
de la Physique peuvent le permettre, l'influence du frottement&
de la cohésion, dans quelques-problèmes de Statique". The problems of staties that concerned Coulomb were the stability of structures and their foundations and the stability of military earth-works. The prediction of the stability of foundations and retaining walls is sttll the main objective of soil mechanics and the methods used have their origins in the original continuum equation of Coulomb. Although he was dealing with a continuum model Coulomb speculated ·- that the difference in fracture properties between wood and stone weredue to the presence of stiff, inextensible fibres within a sample of perfectly elastic wood. Almost a century before Coulomb, Bullet [31
suggested that the stable angle of rounded sand grains "in a natural disposition" would be 60° and in 1726 Couplet [4] calculated the natural slope of a hexagonally packed array of spheres. At the time of Coulomb's work the only significant information available about the mechanics of contacting bodies was the friction law of Amontons.
published in 1702 [5]. CGuplet did not make use of Amontons' law but merely considered the spheres to be resting on one another.
The next major conceptual advance in soil mechanics was the idea of "effective stress". introduced by Terzaghi [6], which emphasised the importance of the pressure within the pore space on the stresses ex-perienced by the material. This is very important because many soils are in a saturated state and may be under considerable hydrostatic pressure. A modern development of these ideas is the "critical state" model of SchofieldandWroth [7]. In this model the soil is seen as a "frictional fluid" in which a "stochastic process of random movements of irregular solid particles which tear, rub, scratch, chip and even bounce against one another during the process of continuous deforma-tion" is envtsaged. However to. make their model practical the authors "stand back" from this detail and describe the whole process of power dissipation as friction. A more "microscopie" model of soil behaviour was considered in the Stress Dilatancy Theory of Rowe [8]. With the small rates of deformation occurring in soil~ the flow of pore fluid through the structure is considered to obey Darcy's Law, the pressure drop in a given direction being inversely proportional to the permea-bility in that direction and proportional to the volume rate of flow and liquid viscosity.
Whilst working from the same general continuum principles the final objectives of powder mechanics differ from soi1 mechanics. In powder mechanics there is concern beyond predicting the point of failure to understanding the behaviour of materials in continuous flow. These materi a 1 s may extend from the complete ly "dry" to the saturated state and in a fluidised condition have a porosity which is mucrr greater than that corresponding to the critical state. The pressures in flowing and stored powders are much less than are corrmon in soils hut the materials may be very friable and undergo attrition under the influence of very small forces. The properties of the mátetials may vary wtdely, they may be insulators, conductors, have high or low energy surfaces, they may be smooth or rough, spherical, laminar.or a,eicular, have differing coefficients of friction and they may be hard elastic or soft plastic substances. Additiona11y the pore fluid may vary greatly in viscosity, it may profoundly affect the coefficient of friction at the particle-particle contacts, it may permit the leakage of elec-trical charge and due to the presence of surface and interfacial tensions may give rise to capillaric phenomena.
Additionally the worker in powder mechanics may be concerned with using the wide range of variables that may be available to formulate a powder to a specific profile, for example it may need to be reason-ably free flowing, dustless and insensitive to a wide range of ambient humidities.
During this century·our understanding of the forces present at inter- . faces has expanded greatly, a significant part of that work originating in the Netherlands. One eventual aim of powder technology is to arrive at a state where the bulk properties of powders and granular materials may be established on the basis of the properties of the individual powder grains. Such a powder technology would be analogous to the position of statistical. mechanics in physics and chemistry. Much difficult work inmany disciplines must be carried out before such a
"bottom up" approach becomes a practical reality. but i t is appropriate at this time to review the present state of knowledge in some of those areas that go to make up this composita picture.
When considering the .present meeting the organisers had little diffi-culty in identifying areas that were of possible interest to the worker in powder mechanics, the difficulty being in restricting the range of subjects covered in order to keep within the allotted time span and for the presentations to be relevant to as many present as possible. The areas identified for attention were colloidal forces (electrical double layer phenomena, dispersion forces, etc.), frictional and elastic effects, capillaric phenomena, electrostatic effects and the interaction of particles with their surrounding fluid medium. Whilst it is recognised that the properties of bulk particulate systems are very strongly determined by the size, size distribution and shape of their constituent particles it was agreed that this was already the subject of regular conferences and that the present meeting should concentrate on the interactions that particles experience when in close proximity rather than treat them as inert geometrical entities. Nevertheless a way of describing the geometry of irregular particles and predicting how they pack is an absolute prerequisite of any quantitive microscopie understanding of powder behaviour. From the contributions following this introduction you will note that many of the authors have covered more than one of the identified areas. Whilst this sometimes posed problems for the organising cOD111ittee in deciding where to :place a given contribution in the prograrmie it did emphasise the closely interlocked nature of the chosen subject areas within the context of powder mechanics.
The organisers do not expect this meeting to resolve many questions but they will be more than .satisfied i f the participants leave with an enhanced awareness of both the problems involved in understanding the mechanical properties of powders and granular materials and an awareness of those areas of science which may yield clues to the solution of these problems.
In preparing this brief introduction 1 would like to acknowledge Heyman's monograph on Coulomb [9) for its fascinating account of early developments in soil mechanics.
Richard Akers
Loughborough University References
1. Jenike A.W.: Bulletin 108, Vol.52, No.29, University of Utah (1961) 2. Coulomb C.A.: Essai sur une application des règles de maximis
&
minimis à quelques problèmes de statique, Mémoire de Mathématique et de Physique, l'Académie Royale des Sciences, Paris, Vol.7, 1773, 343, Paris (1176).
3. Bullet P.: L'architecture pratique, Paris {1691).
4. Couplet P.: De la poussée des terres contre leurs revestemens, et de la force des revestemens qu'on leur doit opposer. Histoire de l'Académie Royale des Sciences, 1726, 106, Paris {1726).
5. Amontons G.: De la résistance causêe dans les machines, tant par les frottements des parties qui les composent, que par la roideur des Cordes qu'on y employe, et la manière de calculer l'un et l'autre. Histoire de l'Académie Royale des Sciences, 1699, 206, Paris (1702).
6. Terzaghi K. and Peck O.K.: Soil Mechanics in Engineering Practice, Wiley (1951).
7. Schofield A. and Wroth P.: Critical StateSoil Mechanics, McGraw-Hi 11, London ( 1968).
8. Rowe P.N.: in Stress Strain Behaviour in Soils, ed. Parry, R.H.G. Foulis, Henley-on-Thames (1972).
9. Heyman J.: Coulomb's Memoir on Staties, Cambridge University Press
POWDERS, WHAT ARE THEY? K.Rietema
Department of Chemical Engineering
Eindhoven University of Technology, The Netherlands
1. Introduction
Powders are not a solid, although they can withstand some deformation when not pressed too hard.
Powders are not a liquid, although they can flow under certain circum-stances.
Neither are powders a gas, although they can be compressed to a certain degree.
Can powders be treated as a single continuum? Sometimes they can. Mostly they cannot.
Powders comprise discrete, sol id particles which do not fill the whole space taken up by the powder as such. the remaining space being filled with gas. Nevertheless this definition is inadequate as most people would not call a heap of pebbles a powder.
Most powders have the ability to expand when gas is blown through them in upward direction. They are then said to be fluidized.
There are powders in very great variety according to the nature of the solid particles characterized by their chemical and physical composi-tion and their particle-size distribucomposi-tion. It is seldom realized, however that, in order to understand the behaviour of powders, the (continuous) gas phase should be considered as well.
This paper deals with the importance of the interstitial and circum-ambiant gas in the handling of powders owing to interaction between gas and solids. This interaction is two-fold, one hydrodynamic and the other physicochemical caused by adsorption of gas to the surface of the solids (see also [1]).
2. Geldart•s classification
When fluidized, a powder starts to expand at a critical gas rate called the minimum or incipient fluidization rate (Umf). At and above this critical gas rate the pressure drop over the powder bed equals the total weight W of the bed over its cross-section A (AP = W/A).
On the basis of the various modes of expansion of powders when flwidized, Geldart [2] proposed a classification of powders as A, B. C and D-powders, based mainly on empirical ob~ervation.
An A-powder is characterized by the fact that, when fluidized at a gas rate not too far above ~.mf• the expansion is homogeneously distri-buted over the powder bed. wnén the gas rate is further increased above another critical gas rate homogeneous expansion is no longer possib le and part of the gas moves through the powder bed as voids, generally called "bubbles", which rise rapidly through the bed. This critical gas rate is called the bubble-point velocity (Ub0). Further increase in the gas rate only increases the size and nUlllf)er of bubbles rising upwards,the total expansion being due in part to expansion of the real powder mass, generally called "the dense phase", partly to the hold-up of bubbles.
B-powders are generally coarser than A-powders and in constrast to Ä-powders, cannot be fluidized homogeneously. This means that as soon as the minimum fluidization rate is exceeded bubbles appear and start to flow upwards. Hence Umf = Ubp· The expansion is due solely to the occurrence of bubbles.
When fluidized, both A and B-powders can easily flow round the rising bubbles and objects placed in the bed, as well as through discharge tubes or openings in the wall of the fluidization vessel.
C-powders are finer than A-powders and are characterized by relatively strong cohesion which causes that, as soon as the minimum fluidization rate is exceeded, more or less horizontal fractures occur in the bed, connected by irregular vertical channels through which the excess gas seeks its way upwards. There is hardly any movernent in the bed and the pressure drop over the bed is found to be considerably below the
value W/A. ·
D-powders are the coarsest powders. Reynolds nuni>ers at incipient flu1d1zation are » 10 while the Euler-nuni>er is about :\; 6 (Molerus [31). At higher gas rates the excess gas escapes along bubble trains which coalesce easily into vertical .channels through which particles are swept upwards (spouting). returning to the bed in the disengaging zone . above the bed. Here, too, the pressure drop is considerably lower than W/A.
In a diagram of the solids density pd versus the average particle size d (see figure 1) Geldart has indicated the boundaries between these p8wder classes [2]. This classification has .been very successful and is often referred to.
When the solids are rather hard, inorganic materials fluidized by air at normal pressures and nonnal temperatures in the gravitational field of the earth (nonnal laboratory conditions) Geldart's diagram is pro-bably correct and it certainly has the merit of defining the different classes by their properties.
Nevertheless, for amore generally valid seheme this diagram should be transferred into a diagram of dimensionless groups which also ilCcount for cohesion, gas viscosity and gravitational accelleration. A proposal for such a diagram is given in the appendix.
It is believed, however, that Geldart's classification is applicable also to most other powder-handling operations. such as transportation, mixing, grinding, agglomeration and separation. This is because, in all these operations, powders are continuously in an expanded state either by applying gas deliberately or, simply in consequence of the
Pd t
A-powders
C-powders
Figu:l'e 1 Geldarrt'e claeeification
D-powders
continuously turning over and reshuffling of the powder. causing gas to be entrapped. The final result is that the powder is fluidized and its flow properties greatly improved.
3. Hydroclynamic interaction
When gas is entrapped in the powder for some reason or other so that it is in an expanded state then, owing to gravity a pressure gradient arises in the powder to give
(1)
In this equatfon g is the stress tensor acting on the solids. When the porosity € is-dhigher than €
0 (the porosity in the packed state) gd is very small. For e = €
0, however, the z-component of V.gd will
6e close to a value
-As we are mainly interested in the expanded state we may neglect _ v.gd. This leaves
*
= -(1-e)pd g (2)OWing to this pressure gradient the entrapped gas.tries to escape at the slip velocity Us so that the powder will settle. For low Reynolds numbers. Us can be calculated from the Carman-Kozény relation
_ Ê.R = 150µ US.
(l-2
)2az
i
pe;
(3)
At the same time a continuity shock wave moves up in the powder mass at a velocity Vcs [4] given by
Below this shock wave the porosity has become e:0 while above this shock wave the powder is still fluidized.
(4)
In most cases the powder handling is done at such a rate that the shock wave cannot reach the upper surface in time. When V is a cri-tical velocity of the powder-handling apparatus (e.g. in ~he case of a ball mill tlie circumferential velocity) then the powder can be expected to be in a fluidized state when Va >> Vcs· This condition can be converted into
p d2 g
N
=
dP
<< 1001 µVa {5)
The main theme of this symposium is the effect of cohesion on powder mechanics. Cohesion may be expected to have influence when the cohe-sion number defined as
N - C
coh - pd dp g {6}
is greater than 2.
Now N1 = N2~Nçoh with N2 = Cdp/µVa· " . . . · . A character1stü:: v9lue of C 15 4 N/m2 wh1le d < 100 µm, µ
%
2M10-ó Ns/m2 and generally Va > 0.1 m/s. Hencg N2 < 200. With Ncoh > 2 it follows that Nf << 100. In other words, for the majorityot cohesive powders V wil alWilJS be >> Vc , which means that, in handling cohesive powaers, these powders w1~l always be in an aerated and expanded state, which greatly facilitates the handling operations. Furthermore, the higher the gas viscosity the greater the remaining expansion of the powders and the better the flow properties. 4. Gas adsorption and cohesion
It is well-known that gases are adsorbed to solid surfaces. This adsorp-tion can be of a purely physical nature, as in the case of inert gases
(helium, neon, argon) or with a more or less strong chemical bonding. At atmospheri c pressure and room temperature adsorpti on can geilera lly be neglected, but it increases considerably with pressure and, in the case of physical adsorption, also does so with decreasing temperature. In figure 2 the adsorption of some gases to cracking catalyst is given in moles/m2 at room temperature as a function of pressure.
There is a general consensus of opinion that cohesion of dry powders is mainly due to Van der Waals farces. Physical adsorption of gases is attributed to Van der Waals farces· as well, and its bonding is much
mol/m2 8 5 2 1 8 y.10 1 8 10 15 20 bar
-P
Figu:l'e 2 Gas adso!"ption to cracking catalyet in moles/m2 versus pressu:ve
weaker than that of chemically adsorbed gases. Hence, physically ad-sorbed molecules can be expected to have a higher mobility on the sur-face and may be active at the contact area between two sol id particles more or less in a way similar to that in which thin liquid films are active, and thus increase the cohesion force between these particles. lt is therefore not at all remarkable that physically adsorbed gases increase the cohesion of powders and that this cohesion increases further when the gas pressure is raised.
At the Eindhoven University of Technology the cohesion of fine powders (A-powders according to Geldart) was measured in a tilting bed at bed heights of only 0.02 m while gas was passed through the bed at diffe-rent gas rates U < Urnf· The cohesion constant C was determined by measuti1ng·:the ti~ting·angle a at which the bed starts to shear off. and plotting sina versus (cosa - U
0/U f} (see figure 3). This experi-ment was done with fresh cracking catW1yst at a constant porosity of 0.40. The gas passed through the bed was·argon at pressures between
1 and 10 bar. The results are given in figure 4 and are self-evident. 5, Flow properties of expanded powders
At Eindhoven the flow of expanded powders was studied in a vertical rig consisting of two closed fluidized beds -each of
2ooi -
one above the other and connected by a vertical standpipe 2.5 m in length and 0.06 min diameter (see figure 5). The downward flow velocity of the powder was controlled by means of two butterfly valves and by adjusting the pressure difference between the two vessels by means of a gas by-pass line. In this way it was possible to maintain the flowing powder in the homogeneous fluidized state at a constàntJ porosity between 0.40 and 0.52 and at average velocities between 0 and 0.25 m/s. The bu]k velocity. the porosity and the pressure gradient could be measured accurately[5.6). From these data the rheology of fluidized solids could be · determined using a modified Rabinowitz equation which also accounts for
0.15 sin a.
t
0.10
0.05
0 0.1 0.2 0.3 0.4 0.5
Figu:roe 3 Measu:roement of powder aohesion C
=
(1-E)pd g h sina.0
0 10 20
Figu:roe 4 Yield aurves of araaking aatalyst at various gas pressu:roes (argon)
30 N/m2
Figure 5
Saheme of VePtiaal Pig to determiru; Pheology of fluidized
pOü)é/er>s
slip at the wall. It was found that fluidized solids behave as a Bingham-plastic. complicated by slip along the wall. The slip velocity vw depends on the wall roughness but also on porosity and wall shear stress. The yield value < • before shear of the flowing powder sets in, depends on porosity a~ does the viscosity µd. The following rela-tions were found to bold'for cracking catalyst flowing through a smooth glass pipe (see figure 6}.
-llw.vw = •w - •wo with llw = 78.5 - 28.9E Ns/rn3 2 'wo
=
6.84 - 12.7E N/m . dvdand -µ.
ar-
= < - •o with µ = 1.59 - 2.54E Ns/m2 -< 0 = 8.10 - 15.0E N/rn2 (7} (8} (9) ( 10) (11} (12).45 -G .10
î
.04 .02 .9. l.l 1. 3 l. 7Fi(JUl'e 6 Qua:ntity G vePsua waz:l ehBar stress G
=
(v -
v )/R Corrrpar>ieon of measu:remente with equatione (~) ~ (10).NumbePs indiaate valwe of po!'Osity.
i umf ubp H-H 0 nm
t
m.a•
•
t
50 40 3 30 2 u -0 20 1 10 0 1 2 cm/sFigupe 7 Eleatl'iaal aurrent i through aharaoal bed and bed 11.Bight Ve!'8ua gas veloaity
6. Structure of expanded powders
From the Bingham-plastic character of powder flow it follows that, even in the expanded (fluidized)state. powders maintain a mechanical structure of a given strength.
Earlier it was found that when charcoal particles are fluidized the bed retains an appreciable electric condûctivity (figure
7).
This contradicts the concept of free-floating particles and proves that, also in the fluidized state, the particles stay in contact with each other and create a loose network [7].The best proof of such a mechanical structure. however, is found in the fact that a homogeneous fl ui di zed bed can be tilted over a certai n angle without the bed surface shearing off. The maximum angle over which the bed can be tilted without shearing off, decreases with in-creasing expansion and becomes zero at the maximum bed expansion before bubbling sets in, as shown in figure 8 [8.91. This means that the strength of the mechanical structure -indicated by the
cohesion-decreases when the expansion increases which. of course, is reasonable.
a(O)
t .---
H (cm) FifJU!€ 8 50 40 30 20 10 0 APbed(cm,water) 5t
2,
,
,
/t
I 1 : I,
'
0.1 0.2 0.3 0.4 U 0 (cm/s) -130Maximum titting angte,
120 pressu:I'e expansion of ftuidized drop and bed
110 bed versus gas ve toci ty
90 80 70 60 50 40
The mechanical structure of an expanded powder probably consists of a whole network of particle chains with many cross-links. Generally each particle will have at least two, but probably three, four or even more contacts with other particles.
When the powder is further expanded by being blown up, some particle contacts must be broken, so that a rearrangement of the particles results in a looser network with a lower effective cohesion.
Another consequence of the network structure is that, like all mecha-nical structures, a powder will have some elasticity.
This means that when the powder is deformed a little by external forces without breaking particle contacts, the powder structure generates a compensating force which tries to undo the deformation. When the defor-mation is mainly in the z-direction, it is accompanied by a change in the local porosity, while the z-component of the compensating force Fe per unit volume can be expressed as
(13)
in which Eis the elasticity modulus in N/m2.
In a stability analysis [8,9] it was shown that this elasticity -if strong enough- can stabilize the powder structure against perturbations when the powder is fluidized. Slight perturbations in the powder always move upwards and are called continuity waves. The continuity wave velo-city Vc [4] is given by
ct2
_ pd p g 2 (. 3-2E)
VC - l50µ E ~ (14)
When moving upwards, these continuity waves exert a force Fez on the powder structure. Per unit volume
2 (ClE)
Fez= Pd Vc az (15)
where (C!E/Clz) is the porosity variation caused by the perturbation. When IFczl < IF
l
the perturbation is damped out and the powder structure is st~~1lized. When this criterion is exceeded the pertur-bations grow to bubbles which drain off the excess gas, so that the dense phase remains at a lower porosity. Elaborating this criterion results in a dimensionless fluidization number NFl given byWhen
N < {150(1-E)}2
Fl e:2(3-2e:)
the powder structure will be in the homogeneous fluidized state.
(16)
(17)
As the origin of the powder elasticity is to be sought in the strength of the powder structure and hence in the interparticle forces, it must
be clear that a relation to the powder-cohesion is to be expected. Since the number of particle contacts per unit volume decreases with increasing porosity, both E and C should decrease with increasing porosity.
Earlier in this paper it was shown and explained that the cohesion constant C wi 11 increase due to adsorption of some gases at higher pressures. It is therefore to be expected that the elasticity modulus E will be equally affected by gas adsorption at higher pressures, which explains why the maximum expansion increases at higher pressures, as is found by many authors [e.g. 10,11]. For more details on this aspect of fluidization reference is made to the paper by Piepers et al. also presented at this symposium [12].
A method for measuring E directly is not yet available. It can, however, be calculated from the equation
150( 1-e ) 2
Nn= 2· m
e:m(3- 2e:m)
(18)
which holds when the maximum possible porosity e ts reached at the bubbling point velocity Uba· Assuming that the e'fects of gas adsorp-tion can still be neglect~a at atmospheric pressure, the relation between E and e can be found by applying different gases with different viscosities. The viscosity range covered by the gases H2, N2 and neon is about a factor of 4 {see table 1). The results obtained with this method are shown in figure 9. See also [8,9].
Tab'le 1 Data on gases used
gas viscosity ~t 2ooc density at 1 bar (Ns/m ) (kg/m3) Hydrogen 0.88 ~ 10-5 0.089 Nitrogen 1. 78 f( 10-5 1.25 Air 1.83 ~ 10-5 1.29 Argon 2.22 ~ 10-5 1.78 Neon 3.10 ~ 10-5 0.89
Another method is to use centrifugal methods to increase the effective gravitational accelleration. These experiments were done in a so-called human centrifuge, normally used to test aeroplane pilots [13]. The effective gravitational accelleration was increased by a factor of 3.
By using the gases H2 and N2 the gas viscósity was changed by a factor of 2 so that g/µ was changed by a factor of 6. The results exactly confirmèd the dependence of maximum expansion on µ and g as predicted by equation (18).
N/m2..--~~~~~~~~~~~~-.
fresh cracking catalyst Figu:M 9
10 fluidization with •air
Elastiaity möduius of araaking aata'lyst bed
"hydrogen vePsus po.Posity. Numbers indiaate size
• propane fraation in µm •neon 10-1
so-10.
0.40-t
0.10 \cr/dp Ebp20~\
e:bp- 20-40* 20-40 -10 0.40 0.50 0.60 0.707. Grinding powders in a ball mill
As explained, the behaviour of powders when fluidized is of importance in nearly all powder-handling operations, since the handling generally involves tumbling the powders over to facilitate the desired operation. To prove this effect the influence of the ambient gas on the powder behaviour was studied during the grinding of powders in a ball mill
(see also Cl41).
Two powders (crack.ing catalyst and quartz powder) were irwestigated in a closed ball mill which could be operated at different pressures up to 10 bar. Three gases were used: air, neon and hydrogel'I. At one side the ball mill was provided with a glass flange through which the powder behaviour could be observed.
During th:e milling the powder layer at the bottom is lifted up until a critical slope aç is reached which depends on the retating speed and on the powder and gas characteristics. Near the top of this layer the entrained powder partly flows down again along the slope and is partly entrained further upwards to rain down from the top of the milling vessel (figure 10). _
With quartz powder (d0 ~ 50 µm) the dependence of ac on the gas atmos-phere was studied at a constant rotation speed. In figure 11 ac is plotted versus the gas pressure for the three different gases. From this figure it is clear that the flow properties of the powder improve
20
P-.05 .2 .5
Figure 10
Sah&matia view of powder flow
in rotating d::eum
1.0 bar
Figure 11
Stope a of powder
sm-faae ina rotating d::eum
versus pressure with different gases. Rotation speed 80 :rpm
as the viscosity of the gas increases. At these low pressures gas adsorption can probably be neglected. The influence of pressure can be understood, however, when it is realized that at pressures<0.1 bar the free path length À of the gas molecules becomes comparable to the size of the pores between the particles. This is accompanied by a decrease in effective viscosity within the pores.
It was also observed that, during rnilling. the bulk volume of the powder increases when the gas viscosity increases, which is in confor-mity with the presented theory.
To describe the grinding process, the particle-size distribution of the powder was divided into 8 intervals with a constant upper to lower size ratio, the contents of each interval being given by
w
1• During the process, the contents of an i nterva 11 wil l a) decrease because i ts particles are ground into smaller particles (~ {dW;/dt)_) and b) will increase because of the grinding products of particles of larger size(= (dW;/dt)+)· If it is assumed that the breaking is a first order process, a specific breakage,rate S; can be defined for each interval
in accordance with
c~i
)_
=
-siwi
(19)With regular sampling during th:e process. all the breakage parameters can be determined by means of an iterative procedure carried out on a digital computer (for further details see {14]).
•
p
-1 10 bar
Figure 12
Specnfie breakage rate S..2 Ve%'8U8 preeeure With
diffe'!'ent gaeee
In figure 12 the breakage rate
s
2 of the second interval (68-106 µm) is plotted versus the gas pressure for the three gases used. Once more the favourable effect of high gas viscosity is clear when the results for the three gases are compared and the effect of low pressures( < 0.2 bar) is considered as well. In the range above 0.2 bar but
below 3 bar hardly any effect of pressure was found. Increase above 3 bar appears to be favourable again. This must be due to gas adsorpticm which increases the interparticle forces and hence the elasticity modulus. so that a further increase of the maximum powder expansion becomes possible. Similar effects are found for Sp
s,, s
3 ands
4•s
1 for i > 4 coul d not be determi ned with suffici ent äccuracy. 8. Powders, what are théy?Returning to the original question it can now be stated that a powder is a dispersed two-phase system consisting of a dispersed phase of solid particles of various diameters and gas as a continuous phase. The sol id particles forma mechanical network in consequence of inter-particle forces. This network can be expanded under certain circum-stances but always will try to return to the packed state under the influence of gravity. It has a certain mechanical strength and a cer-tain elasticity.
solid phase. The stronger this interaction, due to higher gas visco-s ity and/or gavisco-s advisco-sorptjon, the higher the powder can expand. The higher expansion is accompanied with improved flowability of the powder which can be characterized by lower apparent powder viscosity and lower yield values. Hence the remarkable effect is found that, the higher the gas viscosity the lower the powder viscosity.
These properties of powders play a role in all more or less cohesive powders and should be taken into consideration in all powder-handling operations which are carried out by shuffling, tumbling over or fluidization of the powder.
D-powders are not really considered in this paper. These are too coarse to be really cal led powders; their behaviour is determined solely by hydrodynamics. Interparticle forces do not play any role. Hence they certainly fall outside the scope of this symposium.
It is incorrect to classify the non.,.D•powders as A, B or C-powders unless an the powder conditions (gas viscosity, gravity, gas adsorption, temperature, etc.) are specified.
A certain powder which shows A-powder behaviour might show B-powder behaviour when the effective gravitation is increased or a gas of lower viscosity is used. Similarly, a powder which shows C-powder behaviour might evince A-powder behaviour when a,gas of higher visco-sity is used.
Hence it seems better to speak only in terms of A, B or C-powder behaviour.
Acknowledgement
The author would like to thank his present and former fellow-workers in alphabetical order J.Boonstra, E.J.E. Cottaar, J.H.B.J. Hoebink, J. Koolen, G. van den Langenberg-Schenk, S.M.P. Mutsers, R.D. Oltrogge, H.W. Piepers, A.H.M. Verkooijen. They all contributed to the deve=lop-ment of the theory presented in this paper.
Appendix .
A dimensionless presentation of Gel dart 's classification in A, ,B
and C-powder behaviour.
a) The boundary between
A
and B-powder behaviourFrom the theory presented in [8,9] and sulllllarized in this paper it follows that homogeneous expansion of a powder is possible when
N < {150(1-E0 )} 2 Fl 82(3_28 )
0 0
in which the Eo is the porosity of the packed bed. Hence the boundary between
A
and B-powder behaviour is given by2
NFl
=
{1~0(1-Eo)}
Eo(3-2e:o)
b) The boundary between A and C-powder behaviour
lt will be clear that a specific powder will evinee C-pawder behaviour when the cohesion is too strong. Hence in the first·instance this would be the case when the cohesion number Ncoh exceeds a certain critical value.
There is experimental evidence that, in the packed state (or at low
porosity~ the elasticity modulus of a powder has about the same value as the cohesion constant,so that for packed powders the fluidization nUIN>er could be modified to
*
NFl can also be written as the quotient of the Archimedes number Ar = pd2dp3g/µ2 and the cohesion number:
*
-1NFl = Ar. (Ncoh) (20)
Hence, in a single graph of Ar versus N60h,both the boundary between
A and B-powder behaviour and that between A and C-powder behaviour can be indicated where the first boundary varies with the porosity
e:o
of the packed bed (see figure 13).However, there is further evi dence [ 15] that the boundary between A ·
and C-powder behaviour also depends on gas viscosity. In as ye! un-published work it was found that when fine cracking catalyst (d
13% 30 µm)
was fluidized with nitrogen or neon it showed homogeneous expansion (A-powder behaviour),but when fluidized with hydrogen h@mogeneous expansion was not possible. It showed horizontal fractures and vertical channels (C-powder behaviour). Similar effects were found with fluidi-zation of fine iron oxide pawder ( d i\l 30 um).
As yet no theory is available whichpexplains this effect of gas visco-sity on C-powder behaviour. It is believed, however. that the
expla-A-behaviour
c
Pdgdp
-1 10 100
Fig'la'e 13 Dimensionless presentation of Geldart 's alassification in
A, B and C-:-p01JJde:t> behavioU:t>.
nation must be sought in the apparent brittleness of very cohesive pow-ders, which points to rather small elasticity regions,i.e. the maximum deformations which are possible without breaking the powder structure are much smaller than with less cohesive powders. Hence, the more smooth expansion caused by high-viscosity gas {lower velocity of the continuity waves), seems to be better endured by the, powder.
The foregoing suggests that the boundary in figure 13 between A and C-powder behaviour should not be given by a vertica.1 line but by one with a negative slope. The exact position and the exact slope should be determined by further experimental evidence.
c) The boundary between D· and non~D-powder behaviour •.
The criteria for this boundary are given by Melerus [3], viz. that the Euler number :t: 6 and that the Reynolds number>::>lO, say >100. By eli-minating the gas velocity from these two criteria it is found that
p p d 3 g p
d g
2P =Ar
.(.'.J!.)
> 60,000µ pd
It should be realized that it is as yet difficult,if not impossible to translate figure 13 back to a graph of Pd versus dp even at constant gas viscosity, gravity and pressure. This is because so· far insufficient information is available on thè dependence of the elasticity modulus E on particle size dp· This remains the case even when it is justified to
assume a relation between E and the coh~sion constant C, since reported theories on the relation ~etween C and d0 are often contradictory too. Other complications arise owing to the effect of particle hardness (the harder the material the lower the cohesion) and, as shown in this paper, to gas adsorption under the influence of pressure.
References
1. Rietema K., Boonstra J" Schenk G .• Verkooijen A.H.M.: "The inter-action between gas and dispersed solids and its effect on handling operations of solids", Proceedings European symposium Particle Technology, Amsterdam (1980} 981.
2. Geldart D.: "Types of gas fluidization", Powder Technology 7 {1973) 285. See also:
Baeijens J., Geldart D.: "Predictive calculations of flow para-meters in gas fluidized beds and fluidizatfon behaviour of various powders", Proceedings Int.Symp. Fluidization and its Applications, Toulouse (1973) 263.
3. Molerus 0.: "Interpretation of Geldart's type A, B, C and D pow-ders by taking into account interparticle cohesion forces", Powder Technology 33 (1982) 81.
4. Wallis G.B.: "One-Oimensional two-phase flow", Mc.Graw-Hil 1 Book Comp. ( 1969).
5. van den Langenoerg-Schenk G.: "The rheology of gas-fluidized pow-ders as determined in a vertical standpipe", Ph.D.Thesis Eindhoven University of Technology (1982).
6. van den Langenberg-Schenk G., Rietema K.: "The rheology of homo-geneously gas-fluidized solids, studied in a vertical standpipe", to be published in Powder Technology.
7. Rietema K.: "Application of mechanical stress theory to fluidiza-tion", Proceedings Int. Symp. on Fluidization, Eindhoven {1967), 154.
8. Rietema K" Mutsers S.M.P.: "The effect of interparticle forces on the expans f on of a homogeneous gas-fl ui di zed bed", Proceedi ngs
Int. Symp. Fl ui dization and its Appl i cations, Toul ouse. ( 1973) 28. 9. Mutsers S.M.P., Rietema K.: "The effect of interparticle forces
on the expansion of a homogeneous gas-fluidized bed", Powder Technology 18 (1977) 239.
10. Guedes de Carvalho J.R.F., Harrison D.: "Fluidization under pres-sure", Fluidization Technology, D.L. Keairns, ed. (1975) 59. ll. Sobreiro L.E.L.. Monteiro J.L.F.: "The effect of pressure on
fluidized-bed behaviour". Powder Technology 33 (1982) 95. 12. Piepers H.W •• Cottaar E.J.E •• Verkooijen A.lf:"R., Rietema K.:
Effects of pressure and type of gas on particle-particle inter-action and the consequences for gas-solid fluidization behaviour", This symposium.
13. Mutsers S.M.P •• Rietema K.: 11
Gas-solid fluidization in a centri-fugal field. The effect of gravity on bed expansion", Powder Technology 18 (1977) 249.
14. Cottaar E.J-:t'., Rietema K.: "The effect of interstitial gas on mi 11 i ng". to be pub lished in Powder Techno 1 ogy.
15. Piepers H.W., Rietema K.: "Investigation into C-powder behaviour", to be published.
Notations w Wi z ctm ctc €. €.0 em Pct Pg lld J.lct j..tw T TO •w Two Ar Eu Ncoh ~ NFl
cross section of fluidized bed cohesion constant of powder particle diameter
elasticity modulus of powder bed
force per unit volume exerted by continuity wave elastic force per unit volume of powder bed quantity in Rabinowitz equation = (\id-vw)/R gravitational acceleration
gas pressure
radius of standpipe
specific rate of breakage of interval time
gas velocity
minimum fluidization velocity gas velocity at bubble point
slip velocity of gas relative to solids
characteristic velocity of powder-handling apparatus velocity of continuity wave
velocity of continuity shock wave velocity of solid particles average velocity of powder
slip velocity of solid particles near standpipe wall
total weight of powder in powder bed total weight of parttcles in interval i verti ca 1 coordinate
maximum tilting angle of fluidized bed slope of powder surface in rotating drum porosity of powder
porosity of packed bed
maximum porosity of homogeneous fluidized bed density of solid particles
dens i ty of gas
stress tensor in powder
apparent viscosity of fluidized powder rate parameter in equation (7)
shear stress yield stress wall shear stress wall yield stress
Archimedes number
=
pd2ctp3g/µ2 Euler number=
(pddpg/p 9U2) - e2 Cohesion number=
C/pddpg Fluidization number = pd3dp4g2/µ2Erm
2J [N/m2J [µm] [N/m2] [N/m3] [N/m3J [s-1] [m/s 2 21 [N/m ] [m] cs-1] [S] [m/s] [m/s] [m/s] [m/s] [m/s] [m/s] [m/s] [m/s] (m/s] [m/s] [N] [N] [m] [-] [-] [-] [-] [-] [ka/m3] Ekg/m3] [N/m2] [Ns/m2J [Ns/m3] [N/m~] [N/lll?] [N/nr-] [N/m2] [-] [-] (-] [-]FLUIDIZATION OF COHESIVE POWDERS D.Geldart, N.Harnby and A.C.Wong
University of Bradford, School of Powder Technology, United Kingdom
Abstract
Relatively small changes in particle size and other parameters which affect interparticle forces can transf@rm a fine free-flowing powder into one which is cohesive. The influence of these parameters on the fluidization behaviour of fine powders has been investigated and can be readily assessed by measuring the ratio of tap to aerated bulk density.
Introduction
It has been known for more thaó 30 years that very fine particles are difficult to fluidize due to their cohesive properties. Interparticle forces have been a separate subject of study for many more years, but the first systematic study of interparticle forces in fluidized beds only appeared in 1966 Cl]. It included fine particles which are natur-ally cohesive because of their small size as well as larger particles made artificially cohesive with additives.
The term "fine particles" is somewhat vague, and in his classification of powders into groups according to their fluidization behaviour, Geldart [2] distinguishes between free-flowing easy-to-fluidize groupA pc:Mders and cohesive difficult-to-fluidize group C. A considerable amount of research has been devoted to group A powders largely because most commercial fluidized bed catalytic reactors use them; our basic scientific understanding of these powders has been advanced signifi-cantly by the research of Rietema and co-workers [3] and of Donsi, Massimilla and their co-workers [4], but the fluidization behaviour of group C powders has attracted much less attention [1,5]. Interest has increased recently [6,7,8] under the stimulation of commercial proces-ses which wish to make use of them.
The interparticle forces in group A powders are small compared with the hydrodynamic forces acting within the fluidized bed and their influence is beneficial since they are responsible for the expanded dense phase which limits the growth of bubbles; for this reason group A powders should perhaps be called "slightly cohesive". In greup C the inter-particle forces are substantially larger than the hydrodynamic forces,
the gas cannot readily separate particles and channelling occurs, giving poor fluidization. A better knowledge of the factors which influence the transition between groups A and C is of practical as well as scientific interest.
5000 Bubble si:;:es < 0 • lm
B
D
1000A
(Aeratablel 500c
(Cahesive) 50 100 500 1000 5000 dp mx1ö6Figure 1 POûJder alassifiaation diagram.
The work reported here fonns part of a study financed by ICI PLC aimed at locating the group A/C borderline, and at understanding the extent to which the gas and particle characteristics influence the fluidizat-ion properties. In this paper we concentrate on some aspects of the fluidization behaviour of cohesive solids which appear to have gone unnoticed, or unreported, hitherto, and we compare and contrast them with the well-known behaviour of group A powders.
Choice of fluidization criteria and of powders and gases
The major differences between group A and B powders are sunimarised in table 1 and the most useful quantifiable criteria are the ratio uM8/UMF' the bed expansion ratio H/HMF' and the bed deaeration rate. Since it is largely the interplay of hydrodynamic and interpartic.le forces which gives rise to these differences, we thought that measuring the same parameters in cohesive solids would be infonnative. We also decided to measure the rate of entráinment and the discharge rate through an orifice since both are of practical and scientific interest. Entrainment depends, inter alia, on bubbling behaviour as well as on particle interaction in the bed and freeboard.
In principle all the particle and gas properties shown in table 2 should be independent variables, but in practice one is limited to what is connnercially available and can be modified cheaply so as to
Tabte 1 Summary of fluidiza:tion p:ropenie8 for pewdsr<s in groups
A and B
GROUP
A B
e.g. C_racking catalyst e.g. 75µm< san<t< 500 µm dp % 60 µm
UMB/UMF > 1 % 1
Bed Considerable, goes Moderate, increases expansion through a minimum monotonically with U
at l<U<S cm/s
Deaeration rate Slow Very fast
Other Maximum bubble size, No maximum bubble size, properties "fast" fluidization "fast" fluidization
possible unlikely
TabZe 2 Parameters infl,uencing fl,uidization behaviour.
INDEPENDENT VARIABLES Particle properties
Density, Si ze Size distribution Shape, Hardness Surf ace roughness Porosity Gas properties Density Viscosity Relative Humidity (%RH) Total pressure Temperature DEPENDENT VARIABLES Van der Waals farces, capillary farces electrostatics, gas adsorption
be hard, low density solids soft; as-received powders tend to have a normal distribution, separated fractions are usually skewed. It is therefore virtually impossible to vary only one particle characteristic at a time. Although we used more than 30 powders and size fractions, much of our work centred on the behaviour of two types of alumina, each available in several mean sizes, and some alumina size-blends: their properties are given in table 3.
Air having a range of controlled relative humidities was used for most experiments but dry argon, nitrogen and arcton-12 ( di ch 1 orofl uoromethane) were also used.
Table 3 Properties of powd.ers used in e:x:perimental programme
PWD. Powder
aP
pp PBA PBT ~T ShapeNO. ,(µm) (kgm- 3) (kgm-3) (kgm-3) PBA 1 a320-N 30.0 3970 1542 2032 1.318 Angular 2 a320-0 28.0 3970 1579 2006 1.270 Il 3 a360 23.9 3970 1420 1961 1.381 Il 4 A4 23.4 3970 1535 2048 1.334 Il 5 t,r,a500 Vl 15.3 3970 1217 1830 1.504 Il c:C 6 FRF5 z:
-
70.0 2430 1141 1364 1.195 Rounded 7 FRF20 :::.: ::::> 12.0 2430 778 1276 1.640 ·~ 8 FRF40 ...J 10.0 2430 665 1195 1. 797 Il c:C 9 FRF85 5.0 2430 465 1005 2.161 Il 10 FRF20/16 25.0 2430 990 1290 1.303 Il 11 FRF20/70 55.0 2430 1075 1307 1.216 Il 12 9G4 34.5 1810 1039 1201 1.156 Il 13 Il 120.0 1542 912 1061 1.163 Spherical 14 Cl 51.0 1117 590 715 1.212 Il 1-15 E-CAT c:C 33.0 1500 778 1006 1.293 Il 16 E-CAT <...> 12.0 2370 715 1032 1.443 Il (!) FINES z: -::..:: <...> c:C c::: <...> 17 F2/5 77.4 418 352 352 1.000 Spherical 18 F0.3 Vl 78.7 364 202 204 1.001 Il 19 F3/7 LLJ 67 .5 369 186 190 1.002 Il 1-20 SG-
...J ~25.0 638 440 443 1.007 Il 21 F2/5/50 ...J 40.0 418 197 240 1.218 Il -22 F2/5/50-63 l.J... 55.0 418 217 242 1.115 Il 23 IO LLJ 28.0 5000 2053 3168 1.543 Angular c 24 10(+45)-
60.0 5000 2547 2959 1.162 Il x 25 I0(-45) 0 20.0 5000 1819 2814 1.547 Il z: 0 c::: -26 FRF5/45 90.0 2430 1165 1361 1.168 Rounded 27 5%FRF85 ~ 42.0 2430 1160 1382 1.191 Il 28 10%FRF85 ~ 30.0 2430 1147 1427 1.244 Il 29 30%FRF85 ~ 14.0 2430 997 1565 1.570 Il 30 50%FRF85 9.0 2430 793 1400 1.765 Il 31 CORVIC/M 29.7 1637 252 444 1. 762 Angular 32 CORVIC/U 26.2 1637 274 587 2.142 Il 33 B20 25.7 1 2782 1597 1820 1.140 SphericalEquipment and experimental techniques
The measurements of UMF' UMB' ~p and bed expansion were carried out in a 0.152 m diameter x 1 m tall perspex column with a 0.2 m tall steel bottom section. The distributor was made up of two layers of thick IBECO papers glued at the edges with "Copydex" adhesive, and supported by a perforated zine plate to give a total pressule drop of about 650 mm H2
o
at a superficial gas velocity of 0.01 ms- • Bed pressure drop was measured using a 1 m long stainless steel probe of 3 mm diameter and 1. 6 mm nomina l bore. Th is had a 1 om diameter hole (covered with filter paper to prevent ingress of powder) 6 mm above the sealed lower end. The probe was inserted so that it touched the surface of the distributor and the other end was connected directly to a water or mercury manometer. In addition, a pressure tap in the wall of the bed 0.063 m above the distributor provided an alternative for bed pressure drop measurements.A
transparent scale was stuck on the bed wall to provide direct bed expansion measurements. The same bed was used for the bed co 11 apse experiment but with the addi ti ona 1 arrangement of a solenoid valve which was positioned in the air line immediately before the bed inlet. This arrangement allowed the fluid-izing gas supply to be interrupted virtually instantaneously.The relative humidity of the fluidizing air was controlled by a simple humidification rig, which consisted of two columns, one filled with water and packed with raschig rings, and the other filled with silica
gel.
A 0.08 m diameter glass column with a total height of about 2.6 m was erected for the elutriation test. For simplicity, vacuum cleaner bags were used to collect the carryover instead of using a cyclone. The presence and extent of electrostatic forces were measured by suspend-ing an earthed copper rod above the bed. The greater the electrostatics, the greater the mass of solids adhering to the rod.
Results and discussion
Incipient fluidization and bubbling
One of the difficulties associated with fluidization of the very fine powders of group C characteristics is that the incipient fluidization velocities are so low (0.01 cm/s) that sintered porous plates cannot give the high pressure drop required for even fluidization, and dis-tributors have to be made up from several layers of paper. Even so, it qui ckly became apparent that any meani ngful measurement of UMF became virtually impossible for cohesive powders because the bed pressure drop was non-reproducible; it varied with time due, probably, to the creation, destructio.n and re-format ion of channels. As we fluidized the more cohesive powders we experienced increasing difficulty in deciding what was U ; even at velocities of several centimeters per second no clear bubn,es could be identified. We therefore decided to ignore both and UMF' and to concentrate rather on other reproduc-ible measu ts. Dry et al. [7) have also recently reported similar expe ri en ces.
Bed pressure drop deficiency
In a free-flowing group A powder, providing the distributor has an adequate pressure drop, the pressure drop across the fluidized bed is
within one or two per cent of the theoretical value; that is 6P A/W = I. It is wel 1-known that the actual/theoretical pressure drgb ratio decreases as powders become more cohesive and this effect can be seen in figure 2 where cohesiveness is increased by (a) de-creasing particle size. and (b) inde-creasing the relative humidity (%RH) of the fluidizing air.
1.2 1.0 0.8 0.2 . - - - FRF 5 170,..ml {AIR,30%RHl IGROUP A) FRF 5 (70vml (AIR,90%RHJ {-GROUP() FRF 20 !12vml (AIR,30%RH) IGROUP Cl QL----,,----,~--.~--.~--.~--.~~ o m m s ~ ~ • m U (m/s)
FigUI'e 2 Bed pressu:r>e <b>op - gas veZoaity au:l'Ves shOUJing effeats of parrtiaZe size a:nd gas humidity.
Bed expans ion
There is a significant difference in the slope of the expansion curves of the two aluminas shown in figure 3. The reduction in the bed ex-pansion observed just above UMB with the group A powder occurs because the volume of the dense phase ln the bubbling bed is reduced more rapidly than the bubble hold-up increases. This rèductioh in dense phase voidage is caused because the interparticle contacts are contin-ually disrupted by the passage of bubbles and the·consequent increase in overall powder circulation. In the more cohesive powder, the strong-er intstrong-erparticle forces allow the microvoids described by Massimilla and Oons'i [9] to increase in number and/or size. Numerous horizontal and sloping cracks or channels form, and the bed expands without true bubble formation. Some small bubbles do form and although at the wall they can be seen to "wi pe out" the cracks, the cracks reform with a different inclination and· length. The addition to the bed of moisture in the form of air of high RH decreases bed expansion at low velocities but increases it at higher velocities. This too can be explained by
