wet grinding and dispersing fundamental considerations

1

Wet grinding and dispersing

Fundamental Considerations

Carsten Schilde and Arno Kwade

Institute for Particle Technology

Technische Universität Braunschweig

03.05.2019 | Arno Kwade Fundamental Considerations | Seite 2

Content

3.1 Description of grinding and dispersing results

•Product quality

•Productions capacity

•Results related to grinding time and specific energy

3.2 Stress mechanism and stress models

•Mill related stress models

•Product related stress models

•Relation between model parameters

3.3 General application of the stress models

•Particles between two grinding media

•Estimation of stress events and frequency

•Estimation of stress energy and intensity

•Comparison of stress intensity and particle strength

•Specific energy and efficiency factor

2


Introduction

Question

Which parameters can be changed if we want to design or optimize a stirred

media milling process?


Important operating parameters of stirred media

mills

1. Operating parameters of the mill• Grinding or dispersing time

• throughput

• Stirrer tip speed

• Grinding media size

• Grinding media material (density, elasticity and hardness)

• Filling ratio of the grinding media

2. Operation mode of the mill (One or multiple passage mode, pendulum or circuit operation)

3. Formulation (composition of the suspension)• Solids concentration of the pigments

• Fluid (water, solvents, resins and so on)

• Additives or dispersing agents (Reduction of the viscosity and/or avoidance of reagglomeration or flocculation)

4. Mill geometry• Type of the mill

• Size and dimensions of the mill

3


Main objectives

a) Product quality, which is defined among others by

Particle size distribution, gloss, intensity of colour, transparency

Product purity (no contamination by wear of mill and grinding media)

No product degradation (for example by too high temperatures)

Stability (against reagglomeration, flocculation, sedimentation and so on)

b) Economy, which is determined above all by

Investment costs

Operating costs (energy, cooling water, maintenance and so on)

Production capacity

Cleaning expenditure


Content


•Product quality













4


Description of product quality

Depending on the industry and on the product the quality is determined for

example by:

• Optical (visual) characteristics of the particles or pigments respectively

(intensity of color, glace, transparency)

• Mechanical characteristics of fillers

• Storage stability of dispersions and suspensions

• Reactivity of disperse solids because of larger surfaces

• Sintering activity of ceramic materials

Product properties are mainly determined by the physical properties, namely

the particle size distribution (property function)


Property function:

Transmission as function of median particle size

Fig. 3.1: Relation between transmission (quality parameter) and median

particle size

15 20 25 30 35 40 45 50

0

20

40

60

80

100

Tran

smis

sion

TM

[%]

Median particle size x50.3

[nm]

Pin-Mill

-Al2O

3/ H

2O

pH 5 (HNO3)

cm = 0.1

GM-Material: (Y3O

2) ZrO

2

dGM

= 200 µm

vt= 4 m/s

5


Description of product quality

Depending on the industry and on the product the quality is determined for

example by:

• Optical (visual) characteristics of the particles or pigments respectively

(intensity of color, glace, transparency)

• Mechanical characteristics of fillers

• Storage stability of dispersions and suspensions

• Reactivity of disperse solids because of larger surfaces

• Sintering activity of ceramic materials

Product properties are mainly determined by the physical properties, namely

the particle size distribution (property function)

Particle size distribution is taken as main quality parameter

Product quality is described by characteristic numbers (e.g. median size x50

and characteristic size x90)


Specific energy

Energy transferred into the grinding chamber related to the stressed product

mass

Batch operation:

CP

0

P

t

0

0

P

CCm t

m

PP

m

dPP

m

tEtE

C

Continuous operation:

P

0stationarym

m

PPE

where P := mean power draw of the motor

P0 := no-load power

(3.2)

(3.4)

6


Question

Why is it important to minimize the specific energy consumption?


Basic equation of production rate

where := Solids mass throughput (solids mass flow rate)

mP,Batch := Mass of a batch

tBatch := Production time for a batch

P := Power draw of mill motor (gross power)

P0 := No-load power draw of mill motor (mill without content)

PGC := Power transferred into grinding chamber (net power)

Em := Specific energy for demanded product quality

Pm

m

GC

m

0

batch

batchP,P

E

P

E

PP

t

mm

0

mBatchP,Batch

PP

Emt

7


Example 1

Determination of production capacity

The installed motor power of the mill is 25 kW with a no-load power of 5 kW

for the stirrer tip speed under consideration.

The specific energy requirement of your product (related on solids mass) for

the given operating parameters is 100 kWh/t

Which product mass of solids can you produce per hour with your mill?

1. net power: 25 kW – 5 kW = 20 kW

2. Production rate:

You can produce 200 kg/h of mass of solids product per hour

t/h0.2kWh/t100

kW20

E

PPm

m

0P


Example 1

Determination of production capacity

The installed motor power of the mill is 25 kW with a no-load power of 5 kW

for the stirrer tip speed under consideration.



Which product mass of solids can you produce per hour with your mill?

1. net power: 25 kW – 5 kW = 20 kW

2. Production rate:

You can produce 200 kg/h of mass of solids product per hour

t/h0.2kWh/t100

kW20

E

PPm

m

0P

8


Example 2

The demanded production rate is 1 t/h of solid product



Which net power input must the mill or mills have under the assumptions,

that the specific energy requirement is independent on mill size?

1. net power:

The net power required is 100 kW whereas the operating parameters of the

production scale mill must be chosen in a way, that this net power is really

transferred into the grinding chamber

kW100t/h1

kWh/t 100

m

EPP

P

m0


Question

m

GC

m

0

batch

batchP,P

E

P

E

PP

t

mm

0

mBatchP,Batch

PP

Emt

When do we get the maximum possible production rate?

9


Basic equation of production rate

Maximum production rate is achieved, if

• power input into grinding chamber, P – P0, is as high as possible

• specific energy for production of certain product quality, Em, is as

low as possible.

Minimum specific energy decreases relative mill and grinding media wear to

a minimum

Power input and specific energy requirement depend on several operating

parameters like vt, dGM, rGM, cm etc.

Problem: Finding set of operating parameters, which cause the

highest power input P – P0 and the lowest specific energy Em

Equation is also basis for transfer of results from laboratory mill to a

production mill (Scale-up)


Determination of power draw and

specific energy

Power draw

Highest possible power draw of a stirred media mill is restricted by

• installed motor power

• installed cooling capacity (in case of temperature sensitive product)

• wear of mill and grinding media.

Determination of operating parameters, at which the highest possible power

draw is really transferred into the grinding chamber using relation between

power number and Reynolds number

Specific energy

Determination of operating parameters, at which the specific energy

consumption for a certain product quality has a minimum value, using the so-

called stress model

10


Determination of product quality as function of

milling time and specific energy

Experiments give information how the product quality at different operating

parameters depend on

• Grinding and dispersing time

• Specific energy.

Experiments show how

• Power draw

• Throughput behavior

• Cooling behavior

• Wear behavior

depend on the operating parameters.

Different possibilities to run a grinding or dispersing test


Different possibilities to run a test

1. Batch operation

2. One Passage mode (continuous operation)

3. Multiple passage

4. Circuit operation (with stirred vessel)

Sample

2,4,...passage pendulum

1,3,... passage

1,3,... passage


Fig. 3.2

11



1. Batch operation


3. Multiple passage


Sample


1,3,... passage

1,3,... passage


Fig. 3.2



1. Batch operation


3. Multiple passage


Sample


1,3,... passage

1,3,... passage


Fig. 3.2

12


Mean milling time for different operation modes

Discontinuous operation (i.e. no flow through grinding chamber)

Continuous operation (e.g. one passage mode)

Batch operation (circuit or pendulum operation)

tottt

Susp

GMGC

V

VVt

tottotSusp

GMGC tV

VVt

,

1. Batch operation


3. Multiple passage


Sample


1,3,... passage

1,3,... passage


1. Batch operation


3. Multiple passage


Sample


1,3,... passage

1,3,... passage


1. Batch operation


3. Multiple passage


Sample


1,3,... passage

1,3,... passage


(3.3)

(3.6)


Discontinuous Operation (i.e. no flow through grinding chamber)

Continuous operation (e.g. one passage mode)


Specific energy for different operation modes

CP

0

P

t

0

0

P

CCm t

m

PP

m

dPP

m

tEtE

C

ττ

P

0stationarym

m

PPE

CP

0

P

t

0

0

P

CCm t

m

PP

m

dPP

m

tEtE

C

ττ

1. Batch operation


3. Multiple passage


Sample


1,3,... passage

1,3,... passage


1. Batch operation


3. Multiple passage


Sample


1,3,... passage

1,3,... passage


1. Batch operation


3. Multiple passage


Sample


1,3,... passage

1,3,... passage


(3.4)

(3.2)

13


Example 3

Discontinuous operation

Grinding time 20 min, Mass 1 kg, net power 2 kW

Mean residence time:

Specific energy:

min20tt tot

kWh/t 666h 0.33tm

PP

m

dPP

m

tEtE C

P

0

P

t

0

0

P

CCm

C

kg

kWττ

1

2

1. Batch operation


3. Multiple passage


Sample


1,3,... passage

1,3,... passage



Example 3

Continuous operation

Volume flow rate of suspension 5 l/h,

solids concentration by volume 20%, solids density 2 kg/l,

mill volume 1 l,

grinding media filling ratio 0.8, porosity of bulk grinding media 0.4

net power at stationary operation 2 kW


Specific energy:

min6h0.1l/h5

1l0.4)(10.8l1

V

VVt

Susp

GMGC

kWh/t1000kg/l20.2l/h5

kW2

m

PPE

P

0stationarym

14


Example 3


Grinding time 10 h,

solids concentration by volume 20%, solids density 2 kg/l,

mill volume 1 l, suspension volume 50 l

grinding media filling ratio 0.8, porosity of bulk grinding media 0.4

net power 2 kW, Grinding time 10 h


Specific energy:

kWh/t 1000h 102kg/l0.250l

kW2t

m

PP

m

dτPτP

tE CP

0

P

t

0

0

Cm

C

min60.1h10h50l

1l0.4)(10.81lt

V

VVt tot

totSusp,

GMGC


Question

What diagrams would you plot after running the grinding or

dispersing tests?

15


Product fineness as function of specific energy

(linear scale)

Fig. 3.3

20 2000 4000

0

10

20

30

40

50

60

median particle size x50

particle size x90

Feed-Material: -Al2O

3

GM

= 0.8

cm = 0.2

dGM

= 1.1-1.5 mm ((Y2O

3) ZrO

2)

vt = 6 m/s

Part

icle

siz

e x

[µ

m]

Specific energy Em [kJ/kg]


Product fineness as function of specific energy

(log-log scale)

Fig. 3.4

20 100 1000 4000

0,6

1

10

60


particle size x90


3

GM

= 0.8

cm = 0.2

dGM

= 1.1-1.5 mm ((Y2O

3) ZrO

2)

vt = 6 m/s

Part

icle

siz

e x

[µ

m]

Specific energy Em [kJ/kg]

16


Product fineness as function of grinding time

(log-log scale)

Fig. 3.5

0,08 0,1 1 3

0,6

1

10

60


particle size x90


3

GM

= 0.8

cm = 0.2

dGM

= 1.1-1.5 mm ((Y2O

3) ZrO

2)

vt = 6 m/s

Part

icle

siz

e x

[µ

m]

Grinding time tG [h]


Content


•Product quality













17


Resistance against fragmentation

(dispersing and grinding)

Strength of particles (primary particles and particles collectives as for

example aggregates) depends on

• Particle structure

• Binding and adhesion forces between nanoparticles

• Size of the particle collectives and primary particles


K.Borho et al.: Produkteigenschaften und Verfahrenstechnik,

Chem.-Ing.-Tech. 63 (1991), 8, pp. 792-808


Particle structures

Primary particle Aggregate Agglomerate Flocculate

The stress intensity required for

fragmentation (grinding or dispersing) decreases

18




Strength of particles (primary particles and particles collectives as for

example aggregates) depends on


• Binding and adhesion forces between nanoparticles



K.Borho et al.: Produkteigenschaften und Verfahrenstechnik,

Chem.-Ing.-Tech. 63 (1991), 8, pp. 792-808




100

101

102

103

104

105

103

105

107

109

1011

1013

1015

[-]

va

n d

er

Wa

als

- a

dh

esio

n fo

rce

g

ravity fo

rce

(w

eig

ht)

Particle size x [nm]

101

102

103

104

105

force ratio of

adhesion to gravity

strength of

primary particles

part

icle

str

ength

[N

/m2]

Fig. 3.6

19


Different stress mechanism

b) by shearing on one surface

v

v1

v2

b) by shearing on one surface

v

v1

v2

c) between two surfaces

v1

v2


v1

v2

b) by impact on one surface

v

v1 v2

b) by impact on one surface

v

v1 v2

c) between two surfacesc) between two surfaces

Shear stress

a) by means of a fluid

laminar stream turbulent stream

Shear stress


laminar stream turbulent stream

Compressive stress


pre

ssu

re

time

Compressive stress


pre

ssu

re

time

pre

ssu

re

time

laminar flow turbulent flow


v1

v2


v1

v2

Fig. 3.6


Stress mechanisms in different dispersing machines

1) shear stress

2) compression stress

laminar flow

turbulent flow

v1 v2

at one surface

between two surfaces

dissolver

Antrieb

ω

Antrieb

ω

ω2ω1 ω3ω2ω1 ω3ω2ω1 ω3

3 roller mill

kneader

ω2ω1 ω2ω1

between two surfaces


Antrieb

ω

Antrieb

ω

ω2ω1 ω2ω1

dissolver

stirred media mill 3-roll-mill

kneader

ω

high-pressure-homogeniser

Ultrasonic-

homogeniser


Antrieb

ω

Antrieb

ω

ω2ω1 ω2ω1

dissolver

stirred media mill 3-roll-mill

kneader

ωω

high-pressure-homogeniser

Ultrasonic-

homogeniser

stirred media

mill

Fig. 3.16

20


Basic idea of stress models

Practical example

Smashing a stone with a hammer into pieces

Different possibilities to hit the stone

Small or large hammer

Low or high speed

One or more hits


Two different points of view

What is the hammer doing?

I. How often does the hammer

strike (independent on

number of stones)?

Frequency of strokes

II. How strong are the strokes?

Energy of the hammer

Mill related model

What happens with the stone?

I. How often are the stone and

the resulting fragments hit?

Number of hits

II. What are the intensities

of the hits?

Specific energy supply

Product related model

21


Mill related stress model

The grinding behaviour of a mill is determined by

• the type of stress (e.g. impact or compression and shear)

• frequency of strokes or stress events

stress frequency, SFM

• the energy made available at each stress event

stress energy, SE

Total number of stress events: SNM = SFM · tc

where tc is comminution time for a certain product quality

Stress energy is not constant for all stress events

Frequency distribution of the stress energy

(3.13)


Density function of stress energy

SEmax0

sf(

SE

j)

SEj

SFM,j

= sf(SEj) • SE

verwzeit-vwzc6-2

Fre

quency dis

trib

ution s

f [ s

-1 J

-1 ]

Stress energy SE [J] Fig. 3.7

22


Product related stress model

The product quality and fineness achieved in a grinding or dispersion

process is determined by

• how the feed particles and the resulting fragments are stressed

type of stress (e.g. impact or compression and shear)

• how often each feed particle and the resulting fragments are stressed

stress number per feed particle, SNF

• how high the specific energy or specific force at each stress event is

stress intensity, SI

Number of stress events and stress intensities are not constant for all

particles and can only be characterized by distributions

The stress intensity determines, how effective the specific energy

transferred to the product is transposed into product quality and product

fineness.


0,1 1 10 100

Limit o

f real g

rinding

a = 1

Real grinding and dispersing 0

< a < 1

ideal Deagglomeration a = 0

PM5_glas-dmkopt5n-9

Pro

duct qualit

y

e.g

. specific

surf

ace

Sm [m

2/g

]

relative stress intensity SI / SIopt

[-]

Effect of stress intensity on product quality

for one stress event

a

optSI

SIqualityoduct

Pr

Fig. 3.8

23


0,1 1 10 100

0,01

0,1

1

4

upper limit of grinding

grinding / non-ideal dispersing

ideal deagglomeration

Relative energy utilization as a function of the relative stress intensity

Re

lative

en

erg

y u

tiliz

atio

n E

U / E

Um

ax [-]

Relative stress energy SE / SEopt

[-]

Effect of stress energy on energy utilization

Energy utilization EU = S / E = S / SE

1

max

optSE

SE

EU

EU

Fig. 3.9


Macroprocess - Relation of stress energy and

stress number with specific energy

E = m

SE SN =

m

SE

= E Mm,EtotP,

t

totP,

i

SN

1=iPm,

t

SE1

SE2

SE4

SE3

Em,M

Em,P E

where Em,M := Specific energy input into grinding chamber

Em,P := Specific energy transferred to product particles

E := Energy transfer factor

(3.16)

24


Relation between model parameters and

specific energy consumption

Grinding and dispersing result is constant, if

• Specific energy Em,P = E Em,M SNM SE

and

• Stress energy SE

are constant.

V

SE SF =

V

P =

V

P

GCE

M

GCE

P

GC

M

Power density

where PP [J/s] := power available for the product

E [-] := energy transfer factor

PM [J/s] := power consumption of the mill

(3.18)


Content


•Product quality













25


Number of stress events

Number of stress events of each feed particle and the resulting fragments, SN:

P

SC

N

PNSN

where Nc := Number of grinding media contacts

PS := Probability, that a particle is caught and sufficiently stressed

NP := Number of feed particles in the process

Probability, that a particle is caught and sufficiently stressed:

2

GMS dP

GMS dP

Desagglomeration/ Desintegration:

Real grinding:

(3.23)

(3.25)

(3.26)


Stress number

Deagglomeration/Disintegration:

Real grinding:

GMvGM

GM

d

tn

c))1(1(

)1(SN

2

GMvGM

GM

d

tn

c))1(1(

)1(SN

where n [s-1] := rotational stirrer speed

t [s] := grinding or dispersing time

GM [-] := filling ratio of the grinding media

[-] := porosity of the bulk grinding media

cV [-] := solids concentration by volume

(3.28)

(3.29)

26


Energy and intensity of stress events

Kinetic energy is consumed for

• Displacement of the suspension between two grinding media

• Deformation of the grinding media during stressing

• Deformation and stressing of the product particles

2

2

1vmE GMkin

232

62

1

2

1vdvmE GMGMGMkin r


Stress energy of the grinding media

Conditions

• Only one particle is stressed intensively

• The tangential velocity of the grinding media is proportional to

the stirrer tip speed

• The mill geometry and size is constant

• The displacement of the suspension does not result in a

decrease of grinding media velocity

• The elasticity of the product particles is much higher than the

elasticity of the grinding media

Definition of the stress energy of the grinding media

SE SEGM = dGM3 · rGM · vt

2

SEGM is a measure for the real maximum stress energy in the

grinding chamber

(3.30)

27


Example 4

Calculation of stress energy of grinding media

a) Grinding media size 1 mm, grinding media density 6000 kg/m3, Stirrer tip

speed 10 m/s

SEGM = dGM3 · rGM · vt

2 = (110-3 m)3 6000 kg/m3 (10 m/s)2

= 10-9 6000 100 kg m2 / s2 = 6 10-4 J = 0.6 mJ

b) Grinding media size 2 mm, grinding media density 6000 kg/m3, Stirrer tip

speed 10 m/s

SEGM = dGM3 · rGM · vt

2 = (210-3 m)3 6000 kg/m3 (10 m/s)2

= 8 10-9 6000 100 kg m2 / s2 = 48 10-4 J = 4.8 mJ


Stress energy of products with low elasticity

mGM

v0 v0

Grinding Media Grinding MediaProduct Particle

s = sGM + sPsP

GM P

mGM

mGM mGM

Fig. 3.13

28


Stress energy of products with low elasticity

1

GM

P2

tGM

3

GMPmax,P,VEl

El1vdSEE

r

1

GM

P

GMP

GM

max,GM,Vmax,P,V

max,P,V

rel,PEl

El1

ElEl

El

EE

EE

Part of the energy, which is transferred to the product particles:

Measure for the stress energy transferred to the product:

(3.32)

(3.34)


Effect of the Young modulus of grinding media on

the part of energy transferred to the product

0 1 2 3 4 5 6 7 8 9

0.0

0.2

0.4

0.6

0.8

1.0

Relative volume-related energy of the feed material EP,rel

as a function of the ratio of moduli of elasticity EIGM

/EIP

ElP = 410 GPa

ElGM

= 100 GPa

ElP = 410 GPa

ElGM

= 265 GPa

ElP = 410 GPa

ElGM

= 625 GPa

ElP = 30 GPa

ElGM

= 63 GPa

ElP = 30 GPa

ElGM

= 240 GPa

corundum (ElP = 410 GPa)

for moduli of elasticity between

100 GPa and 625 GPa

limestone (ElP = 30 GPa)

for moduli of elasticity between

63 GPa and 240 GPa

EP

,rel

[ -

]

ElGM

/ ElP [ - ]

Fig. 3.14

29


Stress intensity at two important stress

mechanisms

Shear stress in a fluid (laminar flow)

Compression stress between two surfaces (grinding media)

GM2t

3GM

2kin ρvdvm

2

1E

stress intensity c f(x)

3

kinkin E

m

E

xstress intensity


1 10 100 1000 10000

particle strength

shear stress transferred by fluid

stress transferred by grinding media

str

ess in

ten

sity o

f th

e m

achin

e

particle size x [nm]

pa

rticle

stre

ngth

Comparison of particle strength with stress

intensity as function of particle size

Limited particle

sizes and particle

strengths till a

fragmentation is

possible

Fig. 3.15

wet grinding and dispersing fundamental considerations

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