Compressibility and Flow Properties of a Cohesive Limestone Powder in a Medium

Pressure Range

Lilla Grossmann (1), Jürgen Tomas (2) and Barnabás Csőke (3)

(1, 2) Otto-von-Guericke-University Department of Mechanical Process Engineering Universitätsplatz 2, D-39106 Magdeburg, Germany Fax.: +49 391 67 11160 Phone: +49 391 67 12711 e-mail: lilla.grossmann@student.uni-magdeburg.de (3) University of Miskolc Department of Mechanical Process Engineering Egyetem út 17. H-3515 Miskolc, Hungary Fax: +36 46 563 465 Phone: +36 46 565 054 e-mail: ejtcsoba@gold.uni-miskolc.hu

Abstract

The most important design parameters for roller presses can be referred to flow characteristic

of bulk materials. Usually the flow properties are measured in the low stress range 1-50 kPa at

the shear rate about 1 mm/min. But this does not fit the stressing conditions in the roller press.

Press shear cell was used for shear tests with cohesive limestone powder from Gummern in the

so-called medium pressure range 50-1000 kPa.

Keywords: Agglomeration, Bulk properties

1

Introduction

An important agglomeration process is the press agglomeration by roller press.

The result of the process is fundamentally influenced by the flow properties of the

powder feed [1, 2]. Roller presses can be designed using Johanson’s [3] theory.

The most essential design parameters of roller presses can be referred to

characteristic powder properties, like stationary angle of internal friction,

compressibility index and angle of wall friction. The flow behaviour of a powder

is usually tested using Jenike shear cell in the low stress range 1-50 kPa at shear

rate of about 1 mm/min and shear displacement only up to 6 mm. However the

most roller presses operate with circumferential roller speeds from 0.01 m/s to

1 m/s at high pressure range of p > 1 MPa. Therefore, the compression and flow

behaviour of a powder have to be investigated for higher pressures, shear rates

and shear displacements. Such studies are presented in this work. Equivalent to

the stressing in a press agglomeration test, the powder is pre-consolidated and

presheared in a shear cell. Then the resulting shear strength is measured as a

function of normal stress or pressure. Consequently this happens also during

compression and the agglomeration strength test for the proof of stability of

granulated materials. In the chair of Mechanical Process Engineering in

Magdeburg a press shear cell was built in order to test the flow behaviour of

cohesive powders under similar conditions like those of the roller presses. With

this press shear cell the shear rate up to 0.042 m/s can be reached. This machine

operates in the medium pressure range which is suitable to avoid too high power

consumption by dissipation.

Agglomeration by roll press

2

The feed material is drawn into the roller gap during the agglomeration by the roll

press and compacted under the influence of the gravity force and friction of the

rotating rollers. Depending on the contact mechanism between the particles the

bulk material leaves the rolls as more or less firm and porous strip. Johanson [3]

developed a theory for the description of the correlation between bulk material

properties and the machine operational data. His model applies to describe the

compaction of isotropic, compressible bulk materials, and the flow properties of

which can be characterized using Jenike theory. The powder is drawn into the slip

range and accelerated by the rotating walls. The powder is precompressed and

sheared by contraction of the gap. The elastic-plastic deformations of the particles

occur in the nip zone. The two zones can be differentiated using nip angle, see

Fig.1.

Fig. 1: Slip and nip area in the roll gap

The calculation of the pressure gradient in the slip zone is based on the bulk

material mechanics. In the slip zone the pressure gradient will transfer from the

roller surface into the bulk material. Relative motions take place in this zone both

between the bulk material and the roll surface and in the bulk material. The border

of slip zone and nip zone can be determined from the intersection of the functions

for the pressure gradients. The effective compression of the bulk material takes

place in the nip zone. Detailed discussion about the theory of Johanson was

carried out by Molerus [2], Mähler [4], Herrmann [5] and Klasen [6]. The

compression result depends on the product properties of the feedings, on the

elastic-plastic compression behaviour, on the machine- and process data.

Important influencing variables are:

- particle characteristics (particle size distribution, powder density )

- mechanical characteristics of the powder bed (angle of friction between

material and roll, cohesion]

- process parameters (feed pressure)

- apparatus variables (roll diameter, roll width, roll gap, roll revolution number)

- and mechanical properties of the strip (compressive and tensile strength,

porosity, agglomerate size and distribution, abrasion strength)

For design of roll presses the flow characteristics can be measured by shear tests. 3

Compressibility of cohesive powders

Compressibility and compactability of a powder are influenced by the flow

properties, and in the microscale, by the adhesion forces between the particles.

Compressibility is the ability to reduce the volume under pressure and

compactability is the ability to build a solid “agglomerate” under pressure with

sufficient strength and stability. These properties of bulk materials can be

analysed using a shear cell. And the strength of the agglomerate – here the

compressed powder – can be determined by shear test. The compression can be

described by compression rate, compression function or specific compression

work [7]. Only three material parameters from powder mechanics are used for the

correlation between bulk density or agglomerate density ρb and the characteristic

stress during steady-state flow or average pressure σM,st, the bulk density ρb,0 for a

loose packing without any compaction, the isostatic tensile strength σ0 for the

loose packing and the compressibility index n. The so-called compression rate

describes a compression increment [8, 9], which includes the compressibility

index n as the characteristic for volume reduction of a cohesive powder:

stM

b

stM

b nd

d

,0, σσρ

σρ

+⋅= (1)

The physical basis of this comfortable expression was shown in previous paper

[7]. The compression function describes the relationship between the applied

pressure and the produced agglomerate density. The compression function can be

obtained by integrating the compression rate Eq. (1) n

stM

b

b

+=

0

,

0,

1σ

σρρ

(2)

and the mass related or specific compression work is obtained by an additional

integration of the reciprocal compression function Eq. (2).

−

+⋅

−=

−

111

1

0

,,

nstM

bm nnW

σσ

(3)

4

The compressibility index n lies between n = 0, i.e. incompressible stiff bulk

material and n = 1, i.e. ideal gas [4], see Fig. 2.

n = 1 ideal gas compressibility index

n = 0 incompressibleρb,0

0 < n < 1compressible

σM,st

ρ b

σ0 Centre stress

Bul

k de

n sity

0

Fig. 2: Compression function of a cohesive powder [4]

The compressibility indices of powders are summarised in the Table 2 which are

referred to the semi-empirical estimation [7] for low pressure. The extension of

this classification for the medium pressure range is recommendable.

Table 2: Compressibilty indices [7]

Index n Evaluation Examples Flowability

0 – 0.01 incompressible gravel free flowing

0.01 – 0.05 low compressibility fine sand free flowing

0.05 – 0.1 compressible dry powder cohesive

0.1 - 1 very compressible moist powder very cohesive Press shear cell

The tests of the flow behaviour were carried out by means of the press shear

cell [10], see Fig. 3. The test instrument consists of the ring piston and the ring

cell. the gap is filled with powder during the test. The ring piston is installed

under the hydraulic cylinder, which allows the load or stress levels to be set. The

pressure up to 5 MPa can be created in the shear cell. During running shear tests

the ring cell rotates, while the ring piston is kept from rotating using the

transverse bar and the force sensors fixed on the frameworks. The drive consists

5

of the electric motor and the transmission to reach low revolutions number per

minute, which is necessary for the measurements.

Ring piston

Ring cell with bulk material

Axial bearing

Pressure

Revolution

Shear strength

Piston head

σ

Preshear

ShearEnd point

Preshear, steady-state flow

σ2 σc σ1

τc

Normal stress

Shea

r str e

ss

Shear displacement s

Shea

r for

ce F

sFig. 3: Press shear cell and shear testing method

The sample in the ring cell is sheared with the preset normal force FN and with

the shear force FS to be measured. The normal force is set using the ring piston

and the shear force can be measured by means of the force sensor. A defined

density must be reached before each measurement of one yield locus (steady-state

flow). The sample is sheared with the predetermined vertical load FN,d until the

horizontal force FS,d reaches steady-state flow and therefore constant bulk material

density is achieved. This procedure is called preshear. Then the normal force is

reduced to FN (FN < FN,d), and the shear stress is measured under this new load,

which is necessary for the incipient flow. This process is called shear. The

procedure should be repeated with the same powder sample several times under

the same preshear conditions but different normal load at shearing values and in

this way all other values σ = FN / A and τ = FS / A can be obtained, see Fig. 3. The

value of normal stress during steady-state flow σst = FN,d / A and the shear stress

during steady-state flow τst = FS,d / A results the initial shear point, see Fig. 3.

Test results

Tests with cohesive limestone powder from Gummern were carried out. The

particle size distribution versus particle size was shown on the Fig. 4. The

determination of the granulometrical characteristics was carried out with

Mastersizer 2000 equipment.

6

0,1 10

25

50

75

100

CaCO3 ; d50,3= 1,3 µm

Parti

cle

size

dis

tibut

ion

Q3 i

n %

Particle size d in µm

Fig. 4: Particle size distribution of limestone powder from Gummern

Tests were carried out with shear rates from 25 to 2500 mm/min and preshear

displacement from 0.1 to 2 m. Five yield loci were measured. The preshear force

versus time or preshear displacement is shown on Fig. 5. The fluctuations of the

measured curves with longer preshear displacement can be referred to local

compression and expansion (dilution) of the shear zone. It is worth to be noted

here, that the average value of the preshear force changes slightly with the time

at longer preshear displacement.

0 100 200 300 400 5000

500

1000

1500

2000

2500

3000

3500

Pres

hear

forc

e F s in

N

Time in s

spre = 0,1 m spre = 1 m spre = 2 m

v = 252 mm/minYL 1

Fig. 5: Preshear force versus time

The preshear stress τpre as a function of the shear rate is shown in Fig. 6.

Increasing normal stresses of yield loci (YL 1 to YL 5) were used as curve 7

parameter. One should notice here, that the averaged preshear stresses are hardly

influenced by the shear rate in the given range of shear rates.

0 500 1000 1500 2000 25000

100

200

300

400

500

600

700

800YL 5

YL 4

YL 3

YL 2

Pres

hear

stre

ss τ pr

e in k

Pa

Shear rate v in mm/min

YL 1

s = 1 m

Fig. 6: Preshear stress versus shear rate

As an example, selected yield loci are shown on the figure 7 at the shear rate

25,2 mm/min and at the preshear displacement 100 mm. The flowability of the

limestone powder for all shear rates lies between 2 and 4, and can be classified as

cohesive by the flow function ffc according to Jenike [1].

Normal stress σ in kPa

Shea

r stre

s s τ

in k

Pa

200 400 600 800

200

400

600

YL 2

YL 3

YL 1

Fig.7: Selected yield loci at shear rate v = 25,2 mm/min and at preshear

displacement s = 100 mm

8

The typical compression function of bulk density is shown on Fig. 8. The

compressibility index lies between 0.057 and 0.15. According to the Table 1, the

limestone powder can be classified as a compressible powder. The bulk densities

of the yield loci increase with the shear rate.

-200 0 200 400 600 800 10000

200

400

600

800

Den

sity

ρb in

kg/

m3

Centre stress during steady-state flow σM,st in kPa

v = 25,2 mm/min v = 252 mm/min v = 2520 mm/min

Fig. 8: Compression function as the bulk density versus centre stress during

steady-state flow

The compression rate as the function of the centre stress σM,st during steady-state

flow is demonstrated on Fig. 9 for three different values of shear rate. All three

degressive curves fit completely the model approach predicted from Eq. (2). The

compression rate is infinite when σM,st approaches the isostatic tensile stress in the

negative stress range. The isostatic tensile stress σ0 characterises the average

adhesion level between the particles. Here one may consider the largest slope of

increasing bulk density to create the random packing of particles.

9

-200 0 200 400 600 800 10000,0

0,5

1,0

1,5

2,0

Com

pres

sion

rate

dρ b/d

σ in

g/J

Centre stress during steady-state flow σM,st in kPa

v = 25,2 m m /m in v = 252 m m /m in v = 2520 m m /m in

Fig. 9: Compression rate versus centre stress during steady-state flow

The specific compression work as the function of the centre stress σM,st for steady-

state flow is illustrated on Fig. 10. The shear rate was used as curve the parameter.

All three nearly linear curves (exponent 1 – n ≈ 1) of specific compression work

fit accurately the model predicted from Eq. (3), see Fig 9. Obviously, the

consequence for the largest shear rate used here is a higher bulk density and a

larger compression work.

0 100 200 300 400 500 6000

10

20

30

40

50

Spec

ific

com

pres

sion

wor

k W

m,b in

J/k

g

Centre stress during steady-state flow σM,st in kPa

v = 25,2 mm/min v = 252 mm/min v = 2520 mm/min

Fig. 10: Specific compression work versus centre stress during steady-state flow

10

In order to be able to characterize the more rapid, friction-dominant flow of

cohesive powders, a so-called bulk Reynolds number was introduced. This bulk

Reynolds number can be determined using shear rate v, height of shear zone hsz,

apparent viscosity of the flowing powder in the shear zone ηb. Using the material

parameters from powder mechanics like the bulk density ρb,0 for a loose packing

without any compaction, the isostatic tensile strength σ0 for the loose packing,

stationary angle of internal friction ϕst and the characteristic stress during steady-

state flow (average pressure) σM,st, this dimensionless number can be written as: 1

0

,

0

0,2

12sin

2Re

−

+⋅

⋅

⋅⋅≈

⋅⋅=

nstM

st

b

b

bszb

vhvσ

σσϕ

ρη

ρ (4)

The Reynolds number of the bulk material (see Fig. 11) is substantially smaller

than 1. The flow of the cohesive limestone powder can be classified as apparently

“laminar” flowing [7].

0 200 400 600 800 10001E-9

1E-8

1E-7

1E-6

1E-5

1E-4

1E-3

Bulk

-Rey

nold

s nu

mbe

r Re b

Centre stress during steady-state flow σM,st in kPa

vs = 25,2 mm/min v

s = 252 mm/min

vs = 2520 mm/min

Fig. 11 : Bulk Reynolds number versus centre stress during steady-state flow

Additionally, the specific power consumption as the function centre stress during

steady-state flow is expressed as: n

stM

bsz

stprebm h

vP−

+⋅

⋅⋅⋅⋅

=1

0

,

0,

0,, 1

22sin

σσ

ρσϕ

(5)

11

and is shown on Fig. 12. The shear rate was used again as curve parameter. It is

worth to be noted here, that the consequence for the larger shear rate is a higher

energy dissipation during the preshear process.

0 200 400 600 800 10000,1

1

10

100

Spec

ific

pow

er c

onsu

mpt

ion

at p

resh

ear

Pm

,b,p

re in

W/k

g

Centre stress during steady-state flow σM,st in kPa

v = 25,2 mm/min v = 252 mm/min v = 2520 mm/min

Fig. 12: Specific power consumption versus centre stress during steady-state flow

Conclusions

Compression and flow properties of the cohesive limestone powder were

tested by means of press shear cell in similar process conditions like at the roller

presses. The compression of limestone was described using compression rate,

compression function and specific compression work. These functions are based

on the physical approach and can be described only by three material parameters,

the bulk density ρb,0 for a loose packing without any compaction, the isostatic

tensile strength σ0 for the loose packing and the compressibility index n which

were obtained from powder mechanics. Additionally a bulk Reynolds number and

the specific power consumption are introduced to characterize the steady-state

powder flow related to a fluid mechanics approach and energy dissipation during

preshear.

12

Symbols FN [N] Normal force

FS [N] Shear force

hsz [mm] Height of the shear zone

n - Compressibility index

Reb - Bulk Reynolds number

v [mm/min] Shear rate

Wm,b [J/kg] Specific compression work

ηb [Pas] Viscosity

ϕi [Grad] Internal angle of friction

ϕst [Grad] Stationary angle of friction

ρb [kg/m3] Powder density

ρb,0 [kg/m3] Bulk density for a loose

packing

σ [kPa] Normal stress

σ0 [kPa] Isostatic tensile strength

σpre [kPa] Normal stress at preshear

σM,st [kPa] Centre stress during

steady-state flow

τ [kPa] Shear stress

τpre [kPa] Preshear stress

References

[1] A. W. Jenike, Storage and flow of solids, Bull. 123 University of Utah,

(1964)

[2] O. Molerus, Schüttguttechnik – Grundlagen und Anwendungen in der

Verfahrenstechnik, Berlin: Springer – Verlag (1985)

[3] J.R. Johanson, A rolling theory for granular solids, Transactions of the

ASME, 842-848 (1965)

[4] S. Mähler, Kompaktieren feindisperser Schüttgüter in Walzenpressen,

Diss., Universität Paderborn (1999)

[5] W. Herrmann, R. Rieger, Auslegung von Walzenpressen, Aufbereitungs-

Technik 12, 648-655 (1977)

13

[6] C.-J. Klasen, Die Agglomeration partikelförmiger Feststoffe in

Matrizenpressen, Diss., Universität Hannover (1990)

[7] J. Tomas, Zur Mechanik trockener kohäsiver Schüttgüter, Schüttgut 8,

522-537 (2002)

[8] K. Kawakita, K-H. Lüdde, Some considerations on powder compression

equations, Powder Technology 4, 61-68 (1970)

[9] P. R. Mort, R. Sabia, D. E. Niesz, R. E. Riman, Automated generation an

analysis of powder compaction diagrams, Powder Technology 72, 111-119 (1994)

[10] B. Reichmann, Modellierung der Filtrations- und Konsolidierungsdynamik

beim Anpressen feindisperser Partikelsysteme, Diss. Universität Magdeburg (1999)

14