• No results found

The effect of interparticle forces on the behaviour of gas-fluidized beds of fine particles

N/A
N/A
Protected

Academic year: 2021

Share "The effect of interparticle forces on the behaviour of gas-fluidized beds of fine particles"

Copied!
223
0
0

Bezig met laden.... (Bekijk nu de volledige tekst)

Hele tekst

(1)

The effect of interparticle forces on the behaviour of

gas-fluidized beds of fine particles

Citation for published version (APA):

Mutsers, S. M. P. (1977). The effect of interparticle forces on the behaviour of gas-fluidized beds of fine

particles. Technische Hogeschool Eindhoven. https://doi.org/10.6100/IR40603

DOI:

10.6100/IR40603

Document status and date:

Published: 01/01/1977

Document Version:

Publisher’s PDF, also known as Version of Record (includes final page, issue and volume numbers)

Please check the document version of this publication:

• A submitted manuscript is the version of the article upon submission and before peer-review. There can be

important differences between the submitted version and the official published version of record. People

interested in the research are advised to contact the author for the final version of the publication, or visit the

DOI to the publisher's website.

• The final author version and the galley proof are versions of the publication after peer review.

• The final published version features the final layout of the paper including the volume, issue and page

numbers.

Link to publication

General rights

Copyright and moral rights for the publications made accessible in the public portal are retained by the authors and/or other copyright owners and it is a condition of accessing publications that users recognise and abide by the legal requirements associated with these rights. • Users may download and print one copy of any publication from the public portal for the purpose of private study or research. • You may not further distribute the material or use it for any profit-making activity or commercial gain

• You may freely distribute the URL identifying the publication in the public portal.

If the publication is distributed under the terms of Article 25fa of the Dutch Copyright Act, indicated by the “Taverne” license above, please follow below link for the End User Agreement:

www.tue.nl/taverne

Take down policy

If you believe that this document breaches copyright please contact us at:

openaccess@tue.nl

providing details and we will investigate your claim.

(2)

THE EFFECT OF INTERPARTICLE

-FORCES ON THE BEHAVIOUR

OF GAS-FLUIDIZED BEDS OF FINE

-PARTICLES

(3)

THE EFFECT OF INTERPARTICLE FORCES

ON THE BEHAVIOUR

(4)

THE EFFECT OF INTERPARTICLE

FORCES ON THE BEHAVIOUR

OF GAS-FLUIDIZED BEDS OF FINE

PARTICLES

PROEFSCHRIFT

TER VERKRIJGING VAN DE GRAAD VAN DOCTOR IN DE TECHNISCHE WETENSCHAPPEN AAN DE TECHNISCHE HOGESCHOOL EINDHOVEN ,OP GEZAG VAN DE RECTOR MAGNIFICUS, PROF.DR.P.VAN DER LEEDEN, VOOR EEN COMMISSIE AANGEWEZEN DOOR HET COLLEGE VAN DEKANEN IN HET OPENBAAR TE VERDEDIGEN OP DINSDAG 1 NOVEMBER 1977 TE 16.00 OUR

DOOR

STANISLAUS MARTINUS PETRUS MUTSERS

(5)

DIT PROEFSCHRIFT IS GOEDGEKEURD DOOR

DE PROMOTOREN:

PROF. DR. K. RIETEMA

en

(6)

AAN MIJN VADER,

(7)

Dankwoord

He+. in dit proefschrift beschreven onderzoek werd verricht in de vakgroep Fysische Technologie, en de vele leden van deze vakgroep die, direct of indirect, een bijdrage aan de totstandkoming van

.

dit proefschrift geleverd hebben ben ik dank ver-schuldigd. Enkelen dienen echter met name genoemd te worden.

Frank Grootveld heeft met veel vernuft en grote precisie de fluid bed apparatuur geconstru-eerd, als ook de zeer gevoelige trilsysteempjes die voor de metingen noodzakelijk waren. Zijn bij-drage aan het onderzoek is zeer belangrijk geweest.

Eveneens van wezenlijk belang is het werk geweest van de studenten die op het onderzoekproject zijn afgestudeerd: Harrie van den Akker, Lambert van Golde, Bart van Oirsouw en Jos Goessens. Niet alleen hebben zij het grootste deel van de metingen verricht, maar ook hebben zij, als partners in soms uitputtende discussies, een essentiele bijdrage geleverd aan de totstandkoming van de in dit proef-schrift beschreven theorieen.

Ook ben ik dank verschuldigd aan de afstudeer-studenten Sef Heijnen, Ewoud van Nederveen en Leon Hermans. Hun werk aan andere onderzoekprojecten heeft, zij het indirect, zeer zeker belangrijk bijgedragen aan de inhoud van dit proefschrift.

Henk Eding ben ik zeer erkentelijk voor zijn behulpzaamheid bij het verzorgen van de lay-out van het proefschrift.

Tenslotte, last but not least, dient Hinke Lotens genoemd te worden, die met grote zorg dit

proefschrift op voortreffelijke wijze heeft getypt.

(8)

Samenvatting

In de tot heden ontwikkelde theorie~n op het gebied

van de gas/vast fluidisatie wordt vrijwel steeds veronder-steld dat de vaste deeltjes vrij zwevend zijn en worden eventueel optredende krachten tussen de deeltjes onderling verwaarloosd. Natuurlijk is de m.b.v. deze aanname bereikte vereenvoudiging van de berekeningen zeer aantrekkelijk; de toelaatbaarheid ervan is echter uiterst dubieus omdat allerlei waargenomen verschijnselen, zoals bijv. het optre-den van homogene expansie en het gedrag van gefluidiseerde systemen bij de in dit proefschrift beschreven "kantelbed experimenten11 er juist duidelijk op wijzen dat de krachten tussen de deeltjes onderling wel degelijk invloed hebben op het mechanisme van de fluidisatie. Het hoeft ons dan ook niet te verwonderen dat theorie~n waarin deze krachten verwaarloosd worden slechts zeer gebrekkig in staat blijken te zijn de waargenomen verschijnselen te verklaren.

Welnu, het onderwerp van dit proefschrift is bedoeld als een eerste stap in een geheel nieuwe aanpak van het fundamentele fluidisatieonderzoek, namelijk een waarbij de krachten tussen de deeltjes onderling ~ bij voorbaat verwaarloosd worden. In het kader van dit proefschrift wordt speciaal het effect van deze krachten op het gedrag van homogeen geexpandeerde

systemen bestudeerd. Allereerst wordt op grond van een groot aantal theoretische en experimentele gegeveris aangetoond dat, tussen elkaar rakende poederdeeltjes met een diameter van

100 ~ of kleiner, van der Waals cohesiekrachten optreden welke vele malen groter zijn dan het gewicht van de deeltjes. Vervolgens worden een aantal experimenten besproken welke aantonen dat deze krachten in homogeen geexpandeerde systemen permanente contacten tussen de deeltjes in stand houden en dat tengevolge hiervan de poederfase een structuur vormt met een zekere mechanische sterkte. Aangetoond wordt

(9)

dat het verschijnsel van homogene fluidisatie ten nauwste samen moet hangen met het optreden van deze krachten tussen de deeltjes: aileen door toekenning van elastische eigen-schappen aan de poederfase blijkt het optreden van stabiele homogene fluidisatie namelijk verklaarbaar. Aannemende dat de poeders~ructuur zich inderdaad zuiver elastisch gedraagt, wordt vervolgens een criterium voor het bellenpunt (= de

critische gassnelheid waarbij voor het eerst gasbellen beginnen te ontstaan) afgeleid. In de uit deze analyse

resulterende formule blijkt de porositeit bij het bellenpunt een £unctie te zijn van het dimensieloze 11£luidisatiegetal", waarin naast hydrodynamische parameters ook de elasticiteit van de poederstructuur voorkomt. Een sterke aanwijzing voor de relevantie van dit kengetal, niet aileen voor de bellen-puntsporositeit maar ook voor de dichte porositeit in sterk heterogeen gefluidiseerde bedden, werd gevonden in de resul-taten van fluidisatieexperimenten uitgevoerd in een centri-fugaalveld.

Teneinde de juistheid van het bellenpuntscriterium verder te onderzoeken werd ook een experimenteel onderzoek verricht naar de mechanische eigenschappen van de poederstructuur. Daartoe werd de interactie bestudeerd tussen het fluid bed

en een, in vertikale richting trillend, horizontaal gaasje dat in het bed werd gedompeld. De resultaten van deze experimenten wezen inderdaad op elastische eigenschappen van de

poeder-structuur, hoewel aanzienlijke discrepanties bleken op te treden tussen de theorie (welke de poederfase als een zuiver elastisch continuum beschouwt) en de experimenten. Een nadere analyse wees uit dat deze discrepanties waarschijnlijk niet veroorzaakt worden door de gevolgde continuumbeschouwing. Veeleer lijkt in de poederfase, naast elastische

verschijnselen, ook energiedissipatie een belangrijke rol te spelen. Ook na het in de beschouwingen betrekken van energiedissipatie bleek het echter tot nu toe slechts ten dele mogelijk de meetresultaten theoretisch te verklaren, hetgeen wijst op een zeer gecompliceerd karakter van de poederstructuur.

(10)

Summary

In most of the present theories on gas/solid fluidization the powder particles are assumed to. be free floating and the possibility of significant interparticle forces is neglected. Of course this assumption allows a drastic, and therefore very attractive simplification of the calculations. On the other hand, however, one must have, to put i t mildly, serious doubts about its admissibility because many observed phenomena, such as the mere occurrence of homogeneous fluidization and the behaviour of these

systems during the so-called "tilting bed experiments", clearly indicate that interparticle forces do influence the mechanics of fluidization. It is therefore not very surpri-sing that theories in which these forces are neglected fail in explaining many of the observed phenomena.

The subject of this thesis is to be considered as the first step in a study on the mechanics of fluidization, in which the interparticle forces are not neglected, at least not in advance. In the framework of this thesis especially the effect of these forces on the behaviour of homogeneously expanded beds has been studied.

At first i t is shown, on the ground of many theoretical and experimental data, that the van der Waals forces between powder particles with a diameter smaller than 100 p are many times larger than the weight of the particles.

Subsequently, a number of experiments are discussed which prove that these forces give rise, even in homogeneously expanded beds, to permanent interparticle contacts and, moreover, that these contacts cause the powder phase to form a structure with a certain mechanical strength. It is shown that, because the. stability of homogeneously expanded beds can only be explained by assigning elastic

(11)

properties to the powder phase, the phenomenon of homogeneous fluidization must be closely connected with the interparticle forces.

Assuming the powder structure to be perfectly elastic, a criterion

:o.

derived for the bubble-point (=the critical gas velocity at which, upon increasing this velocity, for the first time gas bubbles are observed). In the resulting expression the bubble-point porosity appears to be a function of the dimensionless "fluidization number" in which, in

addition to hydrodynamical parameters, also the elasticity of the powder structure is found. From fluidization experi-ments in a centrifugal field a strong indication was obtained that this dimensionless number is indeed the relevant para-meter to describe not only the bubble-point porosity, but also the dense-phase porosity in freely bubbling beds.

In order to investigate the correctness of the bubble.-point criterion further, i t was also tried to measure the mecha-nical properties o:f the powder structure directly. This was done by studying the interaction between the :fluid bed and a horizontal small-mesh wire-netting, vibrating in vertical direction, which was dipped into the bed. The experimental results indeed pointed to elastical properties o:f the powder structure, although a considerable discrepancy was :found between the experimental results and the .results of theoretical calculations (in which the powder phase was considered as a perfectly elastic continuum). A closer theo-retical analysis revealed that this discrepancy is probably not caused by errors resulting from the continuum approach. Instead, in addition to elastic phenomena also energy dissi-pation effects seem to play an important role in the powder phase. A theory has been set up which takes into account both these aspects.of powder behaviour. Even then, however, a complete explanation of the experimental results was not possible, which points to a very complicated character o:f the powder structure.

(12)

Contents

CHAPTER 1. 1 1. 2 1.

3

CHAPTER 2 2.1 2.2 2.j

2.4

2 • .5

2.6

CHAPTER

3

CHAJYI'ER

4

4.

1

4.2

INTRODUCTION Fluidization

Gas/solid £luidization

£ine particles

5

Statement o£ the subject o£ this thesis 10

INTERPARTICLE FORCES IN GAS/FLUIDIZED BEDS

OF FINE PARTICLES 13

Introduction 13

Electrostatic £orces 13

Capillary £orces 1.5

Van der Waals forces 20

Measurement o£ the cohesion £orces between

powder particles jO

The ef£ect of the interparticle cohesion forces on the behaviour of the powder phase

in homogeneously fluidized beds 31

THE EFFECT OF INTERPART·ICLE FORCES ON THE

EXPANSION OF A HOMOGENEOUS GAS-FLUIDIZED BED

37

Introduction

Bed elasticity,caused by interparticle forces

The equations of motion for a gas/solid fluidized system

Elaboration of (V.~)

Stability analysis h of the homogeneously fluidized bed

Calculation of Ebp Discussion

Appendix III.1 :Continuity waves

GAS/SOLID FLUIDIZATION IN A CENTRIFUGAL FIELD. THE EFFECT OF GRAVITY ON BED EXPANSION

Introduction

The experimental equipment

37

40

47

.51 .54

57

59

60

(13)

CHAPTER

5

5.1

5.2

5-3

5.Z.,

5.5

5.6

CHAPTER 6

Experimental results and correction proce-dure

Conclusions

DIRECT MEASUREMENT OF THE MECHANICAL RESPONSE

OF THE POWDER STRUCTURE TO VERTICAL

COMPRESS-ION OR EXPANSCOMPRESS-ION

77

Introduction

77

The construction of the vibrating system

78

The phase shift 83

The measurement of the phase shift

87

Some additional experimental details 92

The computation of the parameters charac-terizing the electro-mechanical oscillation

system

93

Preliminary experiments

96

Some additional tests of the measuring

system and the curve-fitting procedure

96

Some preliminary experiments with the

wire-netting dipped into a fluid bed 100

The experimental results 101

The influence of a harmonic interaction

force upon the phase shift curve 106

Appendix V.1 Appendix V.2 Appendix

V.3

The damping constant of the oscillation system

The mechanical vibration The measured phase shift curves

CALCULATIONS IN WHICH THE POWDER STRUCTURE IS

108 110 111

CONSIDERED AS A PERFECTLY ELASTIC CONTINUUM

117

6.

1 Introduction 117

6.2 The differential equation describing powder

velocity 120

6.3 The various modes of harmonic powder

vibration 121

6.4

Calculation of the powder motion around the

vibrating wire-netting 124

6.5

Calculation of the interaction force 131

6.6

Computation of the phase shift curves in powder ani comparison with the experimental

results 133

(14)

6.,7

CHAPTER 7

7-7

CHAPTER 8

Discussion

Appendix VI. 1 On the gas flow around the vibrating powder particles Appendix VI.2 On the extinction of the

upward moving wave

t

Appendix VI.

3

The fluctuation P (-0) in the gas pressure just below h=O

CALCULATION OF THE WAVE PHENOMENA BY MEANS OF A SINGLE PARTICLE APPROACH

Introduction

The momentum balance of one single average particle t Calculation of gdrag 1 Calculation of gVP I Calculation of gpowder Further elaboration of the and discussion of the wave Conclusions

momentum balance phenomena

CALCULATIONS IN WHICH

THE

POWDER STRUCTURE IS CONCEIVED AS AN ELASTIC CONTINUUM WITH INTERNAL ENERGY DISSIPATION

13.5 137 139

141

146

147

1.54

1.59

166

172 17.5 8.1 Introduction of internal energy dissipation

and calculation of the resulting phase shift

curves

17.5

8.2 Comparison of the model with the

experi-mental results 180 Appendix VIII • 1 Appendix VIII.2 Appendix VIII.3 CONCLUSIONS List Qf symbol§ References Levensbericht

The various modes of

harmo-nic powder vibration 185

The calculated values of

E and

D

187

Stability analysis of a homo-geneously expanded bed with internal energy dissipation

in the powder phase 189

197

198 201 205

(15)

CHAPTER 1

Introduction

1.1. FLUIDIZATION

"Fluidization is the phenomenon in which the gravitational forces acting on a dense swarm of particles are counteracted by the force exerted by the percolating fluid, cau&ing these particles to be kept in a more or less floating state".

The above is the definition of' the phenomenon of' fluidi7.ation which has been given at the International Symposium on

Fluidization in Eindhoven (1967). Emphasis has to be laid on the fact that always a dense swarm of' particles is involved. The term "dense swarm" means that the interparticle distances are so small that the motion of' each particle may not be described without taking into account its interaction ld th neighbouring particles. This interaction can occur in two ways:

1. Interactions resulting from the fact tha.t each particle has a marked influence upon the motion of' the fluid around the surrounding particles. From literature on "hindered settling" the volume fraction of' the particles at which these effects start to occur may be stated to be 1~ [1] • The distances between the particle centres are then of' the order of' J particle diameters. In actual fluidized systems the interparticle distances are

generally much smaller than this, viz. of' the order of' 1 particle diameter. The volume fraction of the fluid

(= "porosity") is then of' the order o:f 0 • .5. Very strong "hindered settling" e:ff'ects are to be expected in this case.

2. Interactions resulting :from direct momentum transfer between the particles. Depending upon the :fluidized

(16)

system, either permanent interparticle contacts (resulting ~rom interparticle cohesion ~orces, see

chapter 2) or interparticle collisions can be the origin 0~ these interactions. These e~~ects are only signi~icant

at interparticle distances o~ the order o~ 1 particle diameter.

As a result o~ the above-mentioned interactions the separate particles are not really ~loating at any time. In the de~inition o~ the phenomenon o~ ~luidization this

~act has been denoted by the term "more or less ~loating

state''.

Fluidization can be realized in a number o~ ways, the percolating ~luid being either a liquid or a gas, the dispersed phase being a solid or a ~luid (liquid or gas).

The ~ollowing combinations are possible:

- gas/solid ~luidization, in which solid particles are suspended in an upwards ~lowing gas.

- liquid/solid ~luidization, in which again the solid is the dispersed phase, while the liquid is the continuou$ phase.

- liquid/liquid ~luidization, in which a liquid continuous phase ~luidizes another immiscible dispersed liquid. - liquid/gas ~luidization, in which gas bubbles are

suspended in a downwards ~lowing liquid.

In nature the phenomenon o~ ~luidization sometimes occurs spontaneously. A very well-known example is quicksand, sand

~luidized by very small quantities o~ up~lowing water.

Sometimes ~luidization phenomena can also be observed in every day li~e. The many small gas bubbles ~or instance, which are caused in beer when it is being tapped, are a rather inconspicuous example o~ a liquid/gas ~luidized system.

(17)

in a container while the percolating ~luid ~lows through this container are called "~luidized beds" and have ~ound

many applications in industry since September 28, 1922. At that day the I.G. Farbenindustrie patented a coal

gasi~icatiun process (the "Winkler Process"), which has become known in the history o~ ~luidization as the first industrial application of ~luidization. Application of fluidized bed technique on a really large scale, however, stayed away until 1942, as the second world war urged to the development of new processes of crackj.ng heavy oils into high-octane gasolines, appropriate to be used by airplanes. Catalyst degrading by the deposit of carbon is very rapid in this process, so that a continuous.withdrawal of used catalyst and supply of regenerated catalyst are desirable. The excellent flow properties of fluidized

powders made the usc of a fluid bed very attractive in this case.

Research work, mainly carried out by the Standard Oil Development Company, resulted in 1942 into the start up o~

a first ~luid catalytic cracking installation in which the used catalyst was continuously replaced by regenerated cata-lyst so that a continuous operation o~ the cracking process was possible. In fig. 1. 1. the ~luid catalytic cracking process is shown schematically (see next page) •

Since 1942 hundreds of fluid catalytic cracking installations have been built. The success of this process also stimulated

e~forts to apply fluidization in other processes. Despite o~

sometimes very serious scaling-up problems, fluidization appeared to be very profitable in many industrial processes, especially for chemical reactions with a large heat effect and ~or processes in which heat or mass transfer is an important step. The advantage o~ ~luidization arises in these cases from the high rate of mixing which is.often found to exist in ~luidized beds. This mixing establishes a very uni~orm temperature in the bed and, moreover,

(18)

Stripper

Regenerator Reactor

To

f'ractionator

Fig. 1.1. :

The f'luid catalytic cracking process

provides the bed with excellent heat transf'er properties. Just to give some examples of' important industrial processes carried out in f'luidized beds: roasting of' sulf'ides, oxi-dation of' naphtalene and ethylene, drying processes. In the near f'uture coal gasif'ication seems to become increas-ingly important. For the sake of' brevity we shall restrict ourselves to this short summing up. A more extensive list of' the advantages and disadvantages of' f'luidized beds as compared with packed beds, and also of' the applications of' f'luidization in process engineering, is f'ound in various handbooks on f'luidization

[2,3,4] •

Most of' these

applications f'all under the heading of' gas/solid

f'luidization. Besides, the diameter of' the solid particles is of'ten of' the order of' 100 ~ or smaller. It is this f'orm of' f'luidization that will be the subject of' this thesis. In the f'ollowing section a more detailed des-cription of' the behaviour of' gas/solid f'luidized systems of' f'ine particles will be given.

(19)

1.2. GAS/SOLID FLUIDIZATION OF FINE PARTICLES

As mentioned before, a gas/solid fluidized bed is a container :in which solid particles are 11more or less floating" in an upward flowing gas stream. The gas enters the bed via a distributor plate providing a homogeneous gas distribution. For the small-scale fluidj.zed beds

normally used in fluidization research the distributor plate is generally made o£ some porous material such as cardboard or sintered metal. In industrial fluidized beds, on the other hand, the distr:lbutor plate is often similar to tray designs as used in destillation columns, incl.uding

similarly-shaped bubble caps. On top o£ the bed there is an empty space, the "disengaging zone", in which the entrained particl.es can settle. The height o£ this zone depends strongly upon the solid material being fluidized and upon the gas velocity. At very high gas velocities the particles carried along are usually separated from the gas by means o£ cyclones.

I£ a Newtonian fluid flows upwards through a powder, a vertical pressure gradient exists which is, according to Ergun [5] , given by:

dP - dh

( 1. 1)

The first term on the right-hand side o£ this equation represents the gas pressure gradient caused by gravity, the second term results from viscous effects in the

percolating gas, the third term is caused by inertia effects in the gas phase as a result o£ its interaction with the powder. The value o£ Ck is still a point o£ discussion.

Theoretical calculations by Carman

[6)

resulted into Ck= 180. Ergun

[5) ,

on the other hand, arrived at Ck= 150, based on a great number o£ experimental data.

(20)

It is this value o£ Ck that will be used throughout this thesis.

With gases, the gravity term is generally negligible. The remaining terms can be written as follows:

=

1.50 ( 1- € ) €

( 1.2) A Reynolds number Rep o£ the particles is introduced here:

€ pc(vc-vd)dp

Rep

= (

1-

€)

f'

Equation ( 1.2) can then be written as:

d:e dP

..l!i.Q

( 1. 3)

-(-;::E)

pc(v c-vd}2

dii

=

Rep

+ 1. 7.5

The second term on the right-hand side o£ equation

(1.3)

is negligible as compared with the first term as long as Rep is o£ the order o£ unity, or smaller. As £or the very fine powders under consideration this condition is always amply satisfied, equation

(1.1)

can be simplified to:

dP

-dh

2

.1.'i.2..t!.. (

1- f ) ( vc- vd) d 2 f2 p

In fluidized beds generally vd=

o.

Furthermore introducing a superficial gas velocity u

0

(= f vc)' equation

(1.4)

can also be written as:

dP _ ..1.i.Q1!_ ( 1-f ) 2

- dii -

2

€3

dp u c ( 1.

4)

( 1. 5)

We shall now discuss the effect o£ the percolating gas upon the state o£ the powder. Three different states can be

(21)

distinguished: 1. Packed state

---When the gas ve1ocity is increased ~rom zero, the vertica1 pressure f-":''l'ldient is, according to equation (

1.5),

proportiona1 to the super~icia1 gas ve1ocity. As a resu1t

o~ this, the powder experiences an upward directed ~orce

which per unit vo1ume o~ the dispersion equa1s -dP/dh. As 1ong as -dP/dh is smaller than ( 1- E )p dg , which is the

weight o~ the powder per unit vo1ume dispersed system, no powder movement is observed and the powder is said to be "packed''· Increasing the gas ~low further, a point is reached at which -dP/dh becomes equal to

(1-

E )pdg. The

super~icia1 gas velocity at this point is ca11ed the

"minimum ~luidization velocity11 or "incipient f1uidization velocity"umf· So the powder is in the packed state as long as 0 ~ uc ~ umf.

2 • ~~~~2~~~~~~!r_!!~~~~~~~-~!~!~

At u =umf the particles become ~or the ~i:t'st time "more or less floating". Increasing the superficia1 gas velocity above ~ a very interesting phenomenon is observed: the bed expands homogeneously, i.e. the porosity increases but no large inhomogeneities can be observed. This phenomenon therefore is ca11ed "homogeneous fluidization". Apart from interparticle ~orces, the effect o~ which will be discussed later on in this section, the powder in this state is

~loating so that -dP/dh equals ( 1-

E)

pdg. This means that the pressure drop ~P over the bed is equal to the weight

o~ the powder per unit area o~ the horizontal cross-section

o~ the bed.

With help o~ equation

(1.5)

the ~allowing relation between

the super~icial gas velocity uc and the bed porosity is

obtained:

u c =

1-€

( 1.

6)

(22)

In the mechanism which causes the phenomenon of homogeneous fluidization interparticle forces play an essential role. Here we will not deal further with this subject as it will be discussed in detail in chapters 2 and

3

of this thesis. 2. Heterogeneously fluidized state

---Increasing the superficial gas velocity, a considerable extent of homogeneous bed expansion can often be realized (sometimes up to 40% of the packed bed height}.

At a certain critical gas velocity, however, instability sets in and large voids are formed in the bed. These voids rise through the bed and are called bubbles on the analogy of gas bubbles in a liquid. This critical velocity is, therefore, called the bubble-point velocity ~p·

If u > ub , the powder is said to be heterogeneously

c p

fluidized. A theoretical expression predicting the point of transition from homogeneous to heterogeneous

fluidization will be derived in chapter 3 of this thesis. What happens with the bed height when the superficial gas velocity is increased above ubp depends upon the type of powder. With many powders the appearance of bubbles

reduces the total bed height due to the fact that the fast rising bubbles extract gas from the "dense phase"

(=

the fluidized bed outside the bubbles). However, this

phenomenon is not always found. At very high gas velocities the bed height generally increases as a result of an

increase of the bubble hold-up.

The above-described variations of pressure drop ~p and bed height H with the superficial gas velocity are re-presented in fig. 1.2 by the solid lines. If these para-meters are actually measured in a fluidized bed, however, some deviations from this rather idealized picture are

found. An example of actually measured values is represented in fig. 1.2 by the dotted lines.

(23)

.1P

t

H

f

u I m:f1 ub I .1P

-u u c Fig, 1. 2.

Pressure drop and bed height as :function of the superficial gas velocity

c

increased above umr the bed does not expand immediately at u = um:f and the pressure drop has to build up a little more before the expansion suddenly starts. The additional

t

pressure drop .1P which is needed in order to make the powder expand has been called the 11surpressure11 by

Rietema

[7] ,

This effect is due to the f'orces between the particles and the wall of the bed in combination with interpar-ticle forces inside the powder. Because these forces have to be overcome, an additional pressure drop is needed before the packed powder structure will yield. When :finally the expansion starts, the :forces necessitating the additional pressure drop are reduced so that a jump in the bed height and the pressure drop is found.

Another remarkable aspect o:f :fig. 1.2 is the hysteresis phenomenon which, as long as u < ubp' is :found in the

pressure drop and the bed height i:f measurements are carried out both at increasing and decreasing gas velocity. The magnitude o:f this phenomenon depends strongly upon the ratio of bed volume and area of the vertical walls: i:f this para-meter is decreased, the hysteresis phenomenon becomes more important. Forces between the powder particles and the walls o:f the bed, which are transferred inside the bed by

(24)

interparticle forces, must therefore be the origin of this effect. As a result of these forces, the weight of the powder is partly carried by the walls i f the gas velocity is reduced. This causes that the bed height at which the forces acting upon the powder are in equilibrium is

increased. In agreement with this explanation the pressure drop over the bed is reduced in this case. On the other hand, i f the gas velocity is increased the walls exert a downwards directed force upon the powder so that the bed height is decreased and the pressure drop is increased. An important aspect of this hysteresis phenomenon is, that its magnitude is not substantially affected after waiting a certain period of time (at least i f no vibrations of the bed occur ) • This indicates that the powder phase in homogeneously fluidized beds is able to resist stresses, in other words that there exists a powder structure with a certain mechanical strength. If the bed is expanded further, the powder structure becomes weaker so that the hysteresis phenomena decrease.

1.

3.

STATEMENT OF THE SUBJECT OF THIS THESIS

Since the early fifties literature on fluidization has assumed large proportions, both on experimental and theoretical aspects. In spite of this quantitative

abundance, however, when assessing the actual results one comes to the rather disappointing conclusion that the main questions largely remain unanswered. The phenomenon of homogeneous fluidization, for instance, has not yet been properly explained. Also with respect to the mechanics of bubbles many questions remain. As a result of this fact, the design of fluidized bed reactors (in which generally the powder is fluidized heterogeneously) still lacks a sound theoretical basis. Especially the impossibility to predict bubble behaviour when scaling up a fluidized bed often has caused troubles in designing fluidized bed

(25)

reactors. More fundamental research on the mechanics of fluidization is needed in order to arrive at a solution of these problems.

In most of the present theories on fluidization the powder

particle~ ' t e assumed to be free floating , which means

that interparticle forces are neglected. From the point of view of simplicity this picture is very attractive, and many beautiful calculations have been made starting from this assumption, for instance the famous bubble cloud model of Davidson and Harrison [3] • However, a study of the existing literature on van der Waals cohesion forces inevitably leads to the conclusion that, at least for powder particles smaller than 100P, these forces are

always considerably larger than the weight of the particles. This means that each collision between freely floating particles would lead to coherence, so that the simplifying assumption that all powder particles are free floating is certainly not correct. In fact the existence of strong interparticle forces, even in the expanded state of homo-geneous fluidization, has already been proved experimentally by the hysteresis phenomena discussed in section 1.2.

Besides, in chapter 2 of this thesis a great number of additional experimental evidence of this fact will be given. Because much is still unknown about the rheological

behaviour of cohesive powders, a very unattractive compli-cation is introduced by taking into account the effect of interparticle forces. On the other hand, in chapter 3 of this thesis i t will be proved that the phenomenon of homo-geneous fluidization cannot be understood i f these forces are left out of consideration, and we expect the same to be true for the mechanics of gas bubbles. In fact a better knowledge of these forces seems to be indispensable if one really wants to understand the mechanics of fluidization. For that reason a study of the effect of interparticle forces on the fluidization behaviour of fine powders was chosen to be the subject of this thesis.

(26)
(27)

CHAPTER 2

Interparticle forces

in

gas-fluidized

beds of fine particles

2.1. INTRODUCTION

In section 1.3 i t has been shown that some very fundamental aspects of the phenomenon of fluidization, such as the occurrence of homogeneous expansion, cannot be explained i f the powder particles are assumed to be free floating. For that reason an investigation of the tenability of this assumption is urgently needed. In this connection it is reminded that the existence of strong interparticle cohesion forces is incompatible with the assumption of freely

floating particles, because each collision between freely floating particles would give rise to permanent coherence between the colliding particles. For that reason this

chapter will be largely dedicated to a study of the cohesion forces between powder particles.

From literature, (see for instance Krupp [8] ), the following three types of cohesion forces appear to be significant in gas-fluidized beds o£ fine particles:

1. Electrostatic forces 2. Capillary forces

3.

Van der Waals forces

In the next sections o£ this chapter these £orces will be discussed separately.

2.2. ELECTROSTATIC FORCES

Electrostatic forces between particles are caused by electric charges on these particles.

(28)

Starting from electrically neutral particles, Charging is generally the result of a transfer of electrons or ions from one particle to the other. There are two mechanisms: - Charge transfer due to the contact potential between

different solids.

- Charge transfer caused by the formation of new boundaries between solid particles as a result of collisions or friction. The probability of charge transfer by this mechanism depends upon several factors, the main being the type of materials involved, the shape and structure of the contacting surfaces and the intensity of the momentum transfer. Also between two identical particles charge transfer is possible. In this case the probability of transfer in one or the other direction is equal.

Effects of this kind have been observed for the first time upon friction between two solids. For this reason the phenomenon is often referred to as tribo-electricity, i.e. frictional electricity. Several authors [

9,

10,11 J have studied tribo-electrical effects occurring in gas/solid fluidized beds. These effects necessarily are always measured at the boundary between the powder and a measuring device made of some conducting material. For that reason i t is impossible to establish whether the measured electrostatic phenomena are caused by redistribution of charge between the particles themselves, or between the particles and the measuring device. These experiments, therefore, do not give information about electrostatic effects inside the bed.

The nature of the phenomenon is still far from understood, but all authors agree that in fluidized beds of uniform material a continuous formation and breaking of inter-particle contacts is a necessary condition for the occurrence of electrostatic forces. This means that, i f a uniform material is fluidized homogeneously, electrostatic effects can be neglected because, as measured by Donsi

(29)

and Massimilla [30, 311 and con£irmed by our own

experiments, particle motion is practically absent and hence the interparticle contacts are permanent. According to Krupp [8] , electrostatic e££ects are in general also negligl.l.>. e as compared with the two other types o£ cohesion £orces mentioned in section 2.1 £or permanent interparticle contacts between di££erent materials.

In heterogeneously fluidized beds, on the other hand, interparticle contacts certainly are not permanent, so that additional charge trans£er as a result of friction is possible. However, because of the stochastic

distribution of charge over the surface of each single particle both attraction and repulsion can occur when two particle collide, so that not necessari~y a cohesive behaviour of the flowing powder mass is caused.

2.3. CAPILLARY FORCES

Sometimes condensation of liquid between two neighbouring particles occurs, even if the partial vapour pressure P of the liquid is considerably lower than the normal saturated vapour pressure P

0 o£ the liquid. In our case

of interest the condensating liquid is in general water. For condensation between spherical particles a situation arises as shown in fig. 2.1 (see next page).

The shape of the curved sur£ace o£ the water bridge is characterized by the convex radius R

1 and the concave radius R

2• According to Kelvin's law the vapour pressure P of this sur£ace is given by:

where: surface tension of water volume o£ one mole of water gas constant

= absolute temperature

(30)

/

I

.

/8,

:

R

/ p Fig. 2, 1. :

A liquid bridge between two spherical particles

From this equation i t is seen that P can be smaller than P

0, (viz. i f R2 is smaller than R1). Necessary conditions

are, however, that the vapour is strongly adsorbed on the solid surface (so that the contact angle 8

2 is small),

and that the distance between the particles is very small. Increasing the amount of condensed liquid, the left-hand side of the above-given equation decreases. This means that the size of the liquid bridge, which is in equilibrium with vapour pressure P, increases as P increases. On the other hand, below some critical value of P capillary

condensation does not occur at all (also because the contact angle

e

2 increases asP decreases). According to McFarlane

and Tabor [14], capillary condensation of water does in general not occur with the type of powders studied in this thesis i f the relative humidity is lower than 80

%.

If capillary condensation of water between powder particles does occur, very strong interparticle cohesion forces

develop. There are two contributions to these forces: - a contribution resulting from the pressure difference

A P between the water bridge and the surrounding air ( AP = Pair - Pwater) •

(31)

This pressure difference is caused by the surface tension of the water in combination with the curved shape of the surface of the water bridge. The va1ue of .:!lP can be calculated with help of the equation of Gauss-Laplace:

LlP

a water

The attractive force F .:!lP which results from this pressure difference is given by:

F.1P nR2 p sin2

o

1 .1P = nR2 sin2

o

1 awater ( 1 p R2 R1 With help of R

1 _ Rp sin81 i t can also be written:

n a water

The values of R

2 and

o

1 depend upon a great number of system parameters such as the dist~nce between the particles, the relative humidity of the air, the hydro-philic character of the solid material etc ••

- a contribution resulting directly from the surface tension of the water at the transition from the water bridge to the surface of the particles. The attractive force Fa,

which is caused by this, is given by:

As mentioned before, the contact angle 02 decreases strongly at increasing water adsorption on the surface of the particles. If this surface is completely wetted,

(J

2 equals zero.

(32)

Adding up the expressions :for F.1P' and Fu gives :for the total capillary attraction :force Fcapillary:

Fcapillary

=

n a water

A complete mathematical elaboration o:f the problem has been given by Pietsch and Rump:f

[12]

and by Schubert

[13].

In order to get at least a rough idea o:f the order o:f magnitude o:f F .

11 , we shall discuss a relatively cap1. ary

simple case which is :frequently :found in practice, viz. that o:f two completely wetted spheres in contact. In this case 8

2 equals zero, so that :for R2 i t can be written (see :fig.

2.2):

R p

(

1 cos 81 - 1 ) Fig. 2.2. :

A liquid bridge between two completely wetted spheres in contact

For F i t is then obtained: capillary

F

(33)

From this expression i t is seen that, i f

a

1 v~ries between

0 and 4.5 degrees, F .

11 varies between 2 n R u t

cap1 ary p wa er

and 1.

5

n R u t • So, as a reasonable approximation i t

P wa er may be written:

Fcapillary 1.7.5nR u p wa er t

Realizing uwater to be of the order of 0.07 N/m i t can easily be shown that; for powder particles

R ~ 50~ , capillary condensation leads to

w~ich

are of the order of 103 to 10

4

times the particles.

of which

attractive forces the weight of

In the above the influence of

a

1 (i.e. the amount of condensed water) on the attraction force appeared to be very small, the variations of F ~P and Fa with

a

1

almost exactly counterbalancing.

In practice, however, the surface of the powder particles is never perfectly smooth and always irregularities in the form of surface asperities and subparticles occur, even with apparently perfect spheres such as glass beads. With help of an electroscanning microscope these irregularities can be made visible, Some examples of electroscanning photographs will be given later on in this thesis in fig. 5.10. In general these irregularities are the sites at which the particles get into contact. For very small values of

a,

these asperities become increasingly important and the capillary attraction force is more and more

!

determined by the radius R of the asperities instead of p

the overall radius R of the particles. As a result of this p

effect the capillary attraction force is reduced by orders of magnitude. The fact that the total number of contact points generally increases is hardly relevant as compared with this strong decrease. However, even if a diameter of the irregularities of 1 ~ is substituted, the capillary attraction force is still 10-100 times the weight of the

(34)

particles (for particles of which R p

z

50~). This means that, as soon as capillary condensation occurs, immediately strong interparticle cohesion forces are caused.

As stated before, with the type of powders used in our

fluidization experiments (i.e. with particle diameters lower than 100~) capillary condensation does in general not occur at values of the relative humidity smaller than

80

%.

In our fluidization experiments the relative humidity was always kept lower than

60

%.

For that reason capillary forces will be left out of consideration in explaining the observed fluidization phenomena.

2.4.

VAN DER WAALS FORCES

In homogeneously fluidized beds the two above-mentioned types of cohesion forces are in general small or even absent, except under some special circumstances. Van der Waals

forces, on the other hand, are always present and, what's more, they appear to be much larger than generally is assumed so that they must play an essential role in the phenomenon of interparticle cohesion forces in gas/solid fluidized systems. For that reason they will be amply discussed in this section.

Van der Waals forces are caused by the fact that the electrons of an electrically neutral solid do not occupy fixed states of sharply defined energy, but are rather subject to random excitations into states of higher energy. This results into spontaneous electric and magnetic

polarizations of the atoms or molecules. These polarizations vary quickly with time, the average in time being zero. The polarizations of adjoining atoms or molecules interact

in such a way that they are more or less in phase. This phase correlation decreases the energy of the system and leads to attractive forces between the atoms or molecules. The same phenomenon occurs also between the atoms and

(35)

molecules of two different particles.

The van der Waals attraction force F d W

1 between van er aa s

two molecules is, according to London

[15]

given by:

Fvan der Waals

6 }'

r7

where;

Y

=

"London-van der Waals constant" of the molecules.

r distance between the molecules.

(2. 1)

A great number of' expressions have been derived f'or y ,

a.o. by London

{ 1.5]

and by Eisenschitz and London

[ 16

J

.

A survey of the results of these calculations has been given by Visser [ 17

J

.

As a result of' the intermolecular van der Waals forces, an attraction force arises also between macroscopic bodies. This force will be called here the "Hamaker force"

FHamaker· It is in general calculated by summation of the van der Waals forces over all the molecules of the two bodies. For two neighbouring particles of the same material, the volumes of which are Ip

1 and rp2, i t is then obtained:

FHamaker

f

f

6y

r7

where: n number of' molecules per unit volume.

(2.2)

For spherical particles this integral has been calculated by Bradley

[18]

and Hamaker [

19] •

Let dp

1 and dp2 be the diameters of the spheres, and let the distance in between be denoted by z (see Fig. 2.3 on next page). Then the following expression is obtained

(36)

Fig. 2. 3

£or FHamaker' assuming z to be much smaller than dpl and dp2

A

=

12 z2

In this equation A is equal to n2n2y and is called the "Hamaker constant". Dahneke [20] gives a survey of' values o£ the Hamaker constant f'or various materials. In general A appears to be o£ the order of' 10- 1

9

to 10- 18 J.

For cohering particles a typical value of' the distance z

is

4

~. which is roughly speaking the lattice constant of'

weakly van der Waals bonded molecular crystals. From now on the distance between the surf'aces of' the cohering particles will be denoted by z

0• It is practically

impossible to decrease z below z

0 because immediately

very strong repulsive f'orces are generated by the inter-action of' the electron orbits. For that reason z may be

0

(37)

For cohering powder particles of which d p

<

100 ~ the Hamaker attraction force as calculated from equation (2.J)

is always much larger than the weight of the particles. To give an example: glass beads, 100

~

= 10-4 m - 19 10 J, see Dahneke [20] Pglass = 2600 kg/m3

4

i

=

4

10-10 m

From equation (2.3) i t is obtained: FH ama er k = 26 10-7 N. The weight F of the particLes equals 13.6 10-9-N

so that:

grav •

Fvan der Waals Fgrav

200

In the foregoing calculations, the cohering particles were assumed to be perfect and rigid spheres. In practice, how-ever, cohering particles are always more or less deformed. The origin of this lies in fact that, i f no external forces are exerted upon the cohering particles, an equilibrium must develop between the Hamaker attraction force and the repulsive forces caused by the interaction of the electron orbits. As stated before, these repulsive forces prevent that the distance between the surfaces of the cohering particles becomes significantly smaller than z

0 • As a

result of all this, the tips of the cohering spheres are flattened, and a contact plane is formed in which the dis-tance between the surfaces is z0 • This situation is shown schematically in fig. 2.4.

(38)

Fig. 2.4. :

Flattening o£ cohering spheres and .formation o£ a contact plane

The deformation o£ the particles can be elastic or plasti·c. The influence o.f elastic deformation on the cohesion o.f particles has been studied by Dahneke (20J • The .following symbols characterizing the state o.f deformation o£ the particles are introduced here:

zoverlap the overlap distance o.f the particles i.f they were not deformed (see .fig. 2.4)

= z overlap + zo

= twice the elastic compression o.f the cohering particles.

o.f the tips

On the analogy o.f the derivation o.f equation (2.3), · Dahneke [20) derived .for the Hamaker attraction .force in this case, assuming z

0 and ~ to be much smaller than

dp 1 and dp2 : A d p1 dp2 2~ FHamaker = - - 2 - ( 1 + - ) 12 z dp1 + dp2 zo 0 (2.4)

From equation (2.4) i t is seen that extremely small deformations o.f the contacting particles (values o£

~

o£ the order o.f z

0) have already a strong influence on the

Hamaker attraction .force. This is caused by the .fact that, according to equation (2.1), the van der Waals attraction

(39)

force between two molecules falls off very rapidly with increasing r , so that the shape of the particles in a very small area around their point (or plane) of contact determines almost completely the total Hamaker attraction force bei;,")en the particles.

The deformation of the particles corresponds with a repulsive force F rep which, according to Hertz [21] , is given by:

j

d }21 d}22 3/2 F rep

=

2 hE 3k d p1 + dp2

(2 •

.5)

1 2

where: k =

-

v v

=

Poisson's ratio

y

y Young's modulus

In table 2.1 some values of v,

Y

and k are given.

material v Yx10- 12 N/m2 k X 1011 m2/N plexiglass 0.35 0.3 27 polystyrene 0.33 0.3 28 typical glass 0.20 7 1. 4 fused quartz 0. 16 7 1. 3 steel 0.29 2 1 0.4 3 copper 0.34 13 0.68 Table 2. 1. :

Some values of v, Y and k

From equations (2.4) and

(2 •

.5)

the following expression is obtained for the net attractive force Fnet (=FHamaker- Frep):

Fnet

j

2 d}21 d}22 dp1+dp2

~3/2

(2.6)

25

(40)

Expression (2.6) is only valid i£ ~ ~ 0. I£ no

deformation occurs, equation

(2.J)

may be used for Fnet (i£

z

is much smaller than dpl and dp2).

In fig. 2.5 an example is shown o£ Fnet as a function o£ h •

E

B

Fig. 2.5.

Fnet as a function o£ ~

Point A in fig. 2.5 represents the deformation o£ the

cohering particles i£ no external forces are exerted on them. The value o£ hE at this point (= ~,A) can be calculated from equation (2.6) by putting Fnet

=

o.

It appears that compression o£ the particles by an external force ( i.e. increasing ~ from ~.A) generates a net repulsive force resisting this compression. I£, on the other hand, hE is decreased from ~,A , a net attractive force is caused. In fact the above means that the contact between the two particles has elastic properties. Later on in this thesis this fact will prove to be essential in order to understand the properties o£ the powder phase in homogeneously

fluidized beds. An elasticity coefficient K

1 o£ the contact can be defined as:

=

(41)

d d I A 6z3 0 + - - pt p2

~,A

t

(2.7)

2k dp1+dp2

As stated above, an attraction £orce is caused when the distance between the centres of the particles is slightly enlarged by an extern~l force. Increasing this distance further, a maximum in the attraction force is found. This maximum attraction £orce, which is in fact the force needed to separate the particles, is called the 11cohesion force F h"

co In fig. 2.5 this force is represented by point B. The value of ~ at point B (= ~,B) can be calculated from:

·( 3 Fnet) :lh ~ =

0

,B

With help of equation (2.6) it is obtained for ~,B:

dp1 dp2 dp1+dp2

Substitution of this expression into (2.6) yields for the cohesion force: F coh = F net (~ =

B)

= A dp1 dp2 A2k2 d p1 dp2 12z2 1 + 108z

7

(2.8) d p1+dp2 dp1+dp2 0 0

The second term between the braces represents the increase o£ the cohesion force as a result of elastic deformation. In table 2.2 the ratio of the cohesion £orce with elastic flattening and without elastic flattening is shown for various materials and particle diameters (see page 28).

(42)

In calcu1ating table 2.2 it was assumed: A= 10- 1

9

J

z = 0

4

X

=

4

10-10 m

F coh

A dpl dp2 12z! d p1+dp2 particle very hard material hard material size

{p)

k=2 1o-12 m2/N k=2 1o-11 m2/N

o. 1 1.000 1.002

1.0 1.000 1.02'

10 1.002 1.226

100 1.023 3.261

Table 2.2: The influence of' elastic :f'lattening on the cohesion :f'orce.

so:f't material k=2 1o-10 m2/N 1.226 ,.261 2,.61 227. 1

Calculation of' the cohesion :f'orce with help of' equation (2.8) results into values which are, :f'or powders of' which dp 5 100 p , at least two orders of' magnitude larger than the weight of' the particles. Some examples of' this ratio are given in table 2., {see next page).

The calcu1ated values of' F co h/F grav (table 2.3) are exceedingly high, especially if' it is realized that any in:f'luence of' plastic de:f'ormation, which wou1d enlarge the cohesion :f'orce even more, is le:f't out of' consideration. Experimental measurements of' this ratio {see section 2.5) always result into much lower values, The reason of' this discrepancy between theory and experiment is f'ound in the existence of' sur:f'ace asperities • In section 2., these have already been discussed. Asperities which are smaller

(43)

type o:f material particle diameter ~!~!~

50

10-20 J

A ::::

9 100 k ::= 1.4 10-11 m2/N p :::: 2500 kg/m3 150 d 4

i.

z ::= 0 E~!rE!~Er!!~= .50

A

= k = p = d z = 0 10-20 J 7 100 27.5 10-11 m2

/N

900 kg/m3 1.50

4

i.

Table 2.3. :

Some examples o:f the ratio o:f cohesion :force and

par-ticle weight

(!-')

F /F coh grav 2000 680 370 33 104 16.5 10

4

11 10

4

than, roughly speaking, 0, 1 p. are in general completely compressed by the Hamaker attraction :force and therefore hardly a:f:fect the overall cohesion :force.

With irregularities o:f about micron size or larger, however, this does not happen so that in this case the cohesion :force

'

is determined by the diameter d o:f the irregularities p

instead o:f the overall diameter o:f the particles. On the analogy o:f the capillary attraction :force (see section

2.3),

also the van der Waals cohesion :force is reduced by the irregularities by orders o:f magnitude. I:f a diameter o:f the

irregularities o:f 1 p. is substituted into equation (2.8}, then the ratio F co h/F .!!:rav appears to be o:f the order o:f

10-102 :for the powders investigated in our experiments. This ratio is about the same as was calculated in section 2.3 in case capillary condensation o:f water would occur.

In the next section i t is briefly explained how the cohesion between powder particles is actually measured.

(44)

2.

5

MEASUREMENT OF THE COHESION FORCES BETWEEN POWDER PARTICLES

In the past four decades a great number of methods have been developed in order to measure the cohesion of powders. For the sake of brevity a survey of these methods will not be given in this thesis.

The interested reader is referred to Morgan [24] and

Krupp

[8].

Here we restrict ourselves to a brief discussion of the method which is nowadays most widely used and which is very suitable for measuring the cohesion of fine powders, viz. the centrifugal method. The procedure consists of centriguging a plane covered with powder particles at increasing angular velocity w (see fig.

2.6).

Fig.

2.6. :

The centrifugal method

F centrifugal

=

mw2r

+

-The centrifugal force acting on a powder particle with mass m is given by:

Fcentrifugal = mw 2 r

The powders used must satisfy the condition that F h/F »1, so that the release of the particles

co grav

(45)

After centrifuging at a small angular velocity the centrifuge is stopped and the number and size of the

released particles are recorded. This procedure is repeated at increasing angular velocities until all the cohering

particle~ have been released. From the experimental results

the frequency distribution of the number of cohering particles as a function of their cohesion force can be calculated.

The experimental results obtained with the centrifugal

method and with other methods irrefutably prove the existence of cohesion forces which are, for the powders under

consideration, many (10-102) times larger than the weight of the particles. Even with monosized powder particles a wide spread in the cohesion force is found. This probably is caused by the wide spread in size of the asperities which happen to be the sites of contact. A detailed discussion of the experimental results obtained by the various authors has been given by Krupp [8] • Here we only mention the conclusion drawn by this last author from a great number of experimental data, viz. that in general a reasonable agreement exists between the theory based on van der Waals forces and the experimentally measured values of Fcoh•

2.6 THE EFFECT OF THE INTERPARTICLE COHESION FORCES ON

THE BEHAVIOUR OF THE POWDER PHASE IN HOMOGENEOUSLY

FLUIDIZED BEDS

In the preceeding sections i t has been shown that the cohesion forces between powder particles of which dp ~ 100 p. are much larger than the weight of the particles. From this fact i t follows that in fluidized beds of these powders the particles cannot be free floating, because each occa-sional collision in such a system would lead to coherence between the colliding particles. In fact the interparticle cohesion forces give rise to the formation of a powder

(46)

structure with a certain mechanical strength, even in the expanded state o£ homogeneous £1uidization. The existence o£ such a powder structure has been proved by the £o11owing experiments:

- The electrica1 conductivity o£ £1uidized beds o£ coke particles appears to be so high, that i t cannot be explained by incidental collisions between £reely

£1oating coke particles [7,28,29] • Instead, i t must be due to permanent interparticle contacts.

- When measuring the bed height and pressure drop o£ a homogeneously £1uidized bed as £unction o£ the super-£icia1 gas velocity, hysteresis phenomena occur, see section 1.2. Friction and cohesion £orces between the powder and the walls o£ the bed, and also between the powder particles themselves, are the origin o£ this

phenomenon. When vibrations o£ the bed are avoided, these e££ects remain unchanged £or longer periods o£ time. This £act proves that the powder phase is able to resist stresses, i.e. that i t has a mechanical strength.

- Massimilla and Donsi

(30,31]

made care£ul observations o£ powders in the expanded state o£ homogeneous

£luidization. Cavities o£ a size o£ a £ew to about ten particle diameters were £ound to exist, see £ig. 2.7. The walls o£ these stagnant cavities apparently are stabilized by interparticle cohesion and £riction £orces. Besides, an almost complete lack o£ particle motion was £ound. Also these £acts point to the existence o£ a

powder network with permanent interparticle contacts, not only near the walls o£ the cavities but also continuing throughout the bed.

- At Eindhoven University o£ Technology the £ollowing experiment has been carried out:

In a specially designed bed (horizontal dimensions

10

by

4

em) a powder was homogeneously £luidized. Vibrations o£ the bed, which might disrupt the powder

Referenties

GERELATEERDE DOCUMENTEN

Ja zeker, maar we hebben ons tot doel gesteld dat 80% van alle docenten zich moeten kunnen vinden in onze opzet van de Tweede Fase.. Om dat voor elkaar te krijgen werden er

entration gradients.. The inlet of the chromatographic column is placed in the center of the mixing tube. Therefore, the concentratien of a sample component must

Effecten van verschillende maten van zichtbaarheid van de voortgang van het werk op enige produktie-karakteristieken van kleine werkgroepen.. De Ingenieur,

• The final author version and the galley proof are versions of the publication after peer review.. • The final published version features the final layout of the paper including

When these texts are used as starting point, modernist claims about the inherent dignity and quality of human life based on biblical texts have to be carefully considered in both

Uitwerkingen Meetkunde MULO-B 1918 Algemeen Opgave 1.. Van  ABZ is zowel de basis als de

• Het vrouwtje zet 300-500 eieren in een gelatinepakket af buiten haar lichaam • Larven komen zonder lokstoffen vrij bij bodemtemperatuur boven 5-10 °C • Larven hebben waardplant

Bij dosering 4 werd voor bronwater geen significant verschil gevonden in het aantal levende planten tussen geen waterconditioner toevoegen of gebruik van Easi-mix.. Wel was