particle shape of micronized powders

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© 2013 HORIBA, Ltd. All rights reserved. Measuring the Particle Shape of Micronized Powders Jeffrey Bodycomb, Ph.D. [email protected] www.horiba.com/us/particle

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Page 1: Particle Shape of Micronized Powders

© 2013 HORIBA, Ltd. All rights reserved.

Measuring the Particle Shape of

Micronized Powders

Jeffrey Bodycomb, [email protected]/us/particle

Page 2: Particle Shape of Micronized Powders

© 2013 HORIBA, Ltd. All rights reserved.

What we’ll talk about

Importance of particle shape

Dynamic image analysis principles

Case studies

Q&A

Page 3: Particle Shape of Micronized Powders

© 2013 HORIBA, Ltd. All rights reserved.

Starting point

Somewhat familiar with particle technology

Particle sizes over 1-5 microns and up to many millimeters

Stay current with free webinarsParticle size essentials

Page 4: Particle Shape of Micronized Powders

© 2013 HORIBA, Ltd. All rights reserved.

Featured technologies

LA-950Laser Diffraction

SZ-100Dynamic Light Scattering & Zeta Potential

CAMSIZER & CAMSIZER XTDynamic Image Analysis

PSA300Static Image Analysis

SA-9600Flowing Gas BET Surface Area

Page 5: Particle Shape of Micronized Powders

© 2013 HORIBA, Ltd. All rights reserved.

CAMSIZER XT: Fine Image Analysis

High resolution size & shapeExtends lower detection rangeCohesive & free-flowing powders,

suspensions1 micron – 3 millimeter

Page 6: Particle Shape of Micronized Powders

© 2013 HORIBA, Ltd. All rights reserved.

What we’ll talk about

Importance of particle shape

Dynamic image analysis principles

Examples

Q&A

Page 7: Particle Shape of Micronized Powders

© 2013 HORIBA, Ltd. All rights reserved.

Why is Shape Important?

Most (all?) particles are not perfectly behaving spheres

Shape can influence almost everything Particle processes, making products Product performance Making measurements

So in other words, shape can affect almost everything

Page 8: Particle Shape of Micronized Powders

© 2013 HORIBA, Ltd. All rights reserved.

Particle Processes

Powder flow; spheres flow easily, needles do not

Liquid flow; increased aspect ratio will increase viscosity

Powder mixing; blend time may change with shape

Also VERY associated with size, hard sometimes to separate size and shape

Page 9: Particle Shape of Micronized Powders

© 2013 HORIBA, Ltd. All rights reserved.

Powder Flow

Understand that spheres flow more easily than needles

How to quantify? Need to first know something about powder flow testing

Won’t go into great detail in today’s talkJust show results including particle

shape

Page 10: Particle Shape of Micronized Powders

© 2013 HORIBA, Ltd. All rights reserved.

Powder Flow*

Qc =hopper angle

BC = outlet diameter

Angle of internal friction

*

Page 11: Particle Shape of Micronized Powders

© 2013 HORIBA, Ltd. All rights reserved.

Powder Flow

Unconfined Yield Strength

Major principle stress that causes an unconfined bulk material to fail in shear

Directly proportional to arching & formation of rat holes

Influences by # contact points From: Johansen, Effect of Particle Shape on

Unconfined Yield Strength, Material Flow Solutions,Inc.

Page 12: Particle Shape of Micronized Powders

© 2013 HORIBA, Ltd. All rights reserved.

Powder Flow*

Glass spheres CaCo3 Talc

Similar size ~ 5 µm But different shape

*Bumiller, et. al., A Preliminary Investigation Concerning the Effect of Particle Shape on a Powder’s Flow Properties, Proceeding from WCPT4, July 2002

Page 13: Particle Shape of Micronized Powders

© 2013 HORIBA, Ltd. All rights reserved.

Powder Flow

BC: minimum outlet diameter to prevent archingQc: hopper wall angle (from verticle) to achieve mass flowCritical flow rate: predicted flow from outlet d : effective angle of internal friction

Page 14: Particle Shape of Micronized Powders

© 2013 HORIBA, Ltd. All rights reserved.

Powder Flow*

*Podczeck & Miah, The influence of particle size and shape on the angle of internal friction and the flow factor of unlubricated and lubricated powders, International Journal of Pharmaceutics 144 (1996) 187 194

d

AR

Page 15: Particle Shape of Micronized Powders

© 2013 HORIBA, Ltd. All rights reserved.

Rheology/Viscosity

0.01 0.025 0.050

Volume Fraction

Vis

cosi

ty

100 200 300 nm

Complex relationship between size/shape and rheology

More spherical shape = lower viscosity

Small particle size = higher viscosity

Wider particle size distribution = lower viscosity

spheres

cubes

fibers

Page 16: Particle Shape of Micronized Powders

© 2013 HORIBA, Ltd. All rights reserved.

Mixing

Shape affects mobility and therefore causes segregation

Smaller effect than size Shape differences could still be substantial

*Koller et. al.,Continuous quantitative monitoring of powder mixing dynamics by near-infrared spectroscopy

Powder Technology, Volume 205, Issues 1–3, 10 January 2011, Pages 87–96

*

Page 17: Particle Shape of Micronized Powders

© 2013 HORIBA, Ltd. All rights reserved.

Shape Effects Size Measurements

Inherent effect since light scattering instruments report equivalent spherical diameter

Sieve vs. laser diffraction vs. image analysis

Consider cylinder vs. sphere

=V = pr2h

V = 4pr3

3

Sieve = 50 mmLaser = 72 mm IA = full description

Page 18: Particle Shape of Micronized Powders

© 2013 HORIBA, Ltd. All rights reserved.

Modeling/Predicting Differences

In particle size; choose a technique, influence the answer

Well explained in this paper

Presented at the Spring Meeting of the Parenteral Drug Association in Philadelphia, June 1977

Page 19: Particle Shape of Micronized Powders

© 2013 HORIBA, Ltd. All rights reserved.

Defining Size

Measurement Results

xc min

xc min

“width”

A

A‘ = A

xare

a

“diameter overprojection surface”

xarea

“length”

xFe max

xFe max

CAMSIZER results are

compatible with

sieve analysis

Page 20: Particle Shape of Micronized Powders

© 2013 HORIBA, Ltd. All rights reserved.

x [mm]0.1 10

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

Q3

Tinovetin-B-CA584A_BZ_xc_min_002.rdfSyngenta-1mm-2min-Sieb.ref

Meßwertdiagramm:D:\...-Demo-Muenchwillen\CAMSIZER-Messungen\Tinovetin-B-CA584A_BZ_xc_min_002.rdfMeßaufgabe: Syngenta-BZ.afg

Width Sieving

--- width measurement

-*- Sieving

comparison

CAMSIZER-measurement xc min (red)and sieving * (black)

xc min

xc min

“width”

Page 21: Particle Shape of Micronized Powders

© 2013 HORIBA, Ltd. All rights reserved.

Want to Measure Shape?

Use image analysis ! Direct measurement of size + shape Get not only size but also shape distribution

CAMSIZER PSA300

Page 22: Particle Shape of Micronized Powders

© 2013 HORIBA, Ltd. All rights reserved.

Summary

Particle shape a critical physical parameter

Affects the product, the process and lab measurements

Understand how shape affects your business

Understand how shape influences your measurements

Page 23: Particle Shape of Micronized Powders

© 2013 HORIBA, Ltd. All rights reserved.

What we’ll talk about

Importance of particle shape

Dynamic image analysis principles

Examples

Q&A

Page 24: Particle Shape of Micronized Powders

© 2013 HORIBA, Ltd. All rights reserved.

Dynamic:particles flow past camera

1 – 3000 um

Static:particles fixed on slide,stage moves slide

0.5 – 1000 um2000 um w/1.25 objective

Image Analysis: Two Approaches

Page 25: Particle Shape of Micronized Powders

© 2013 HORIBA, Ltd. All rights reserved.

Static or Dynamic Image Analysis? Dynamic

Broad size distributions (since it is easier to obtain data from a lot of particles)

Samples that flow easily (since they must be dropped in front of camera)

Powders, pellets, granules

StaticSamples that are more difficult to disperse (there

are more methods for dispersing the samples)Samples that are more delicatePastes, sticky particles, suspensions Precious samples

Page 26: Particle Shape of Micronized Powders

© 2013 HORIBA, Ltd. All rights reserved.

Data Evaluation

BinarizeFind Edges

Analyze Each Particle

Output Distribution

Raw Image

Page 27: Particle Shape of Micronized Powders

© 2013 HORIBA, Ltd. All rights reserved.

Features

Use gravity, or, better, vacuum (from a compressed air supply and venturi) in order to draw particles through instrument. Vacuum helps keep the windows clean.

27© Retsch Technology GmbH

Dynamic Image Analysis:

Moving Particles

Page 28: Particle Shape of Micronized Powders

© 2013 HORIBA, Ltd. All rights reserved.

Why Dynamic Image Analysis? Robust measurement….the interaction between the instrument and the particle is optical, so there is no wear and change in calibration.

High resolution size distribution resultsFast

Also, these are all reasons to use Dynamic Image Analysis instead of sieves.

Page 29: Particle Shape of Micronized Powders

© 2013 HORIBA, Ltd. All rights reserved.

Solid particles 20 mm – 125 mm Low equipment cost Some automation/calculation available

More information available through www.retsch.com

Sieves

Difficult to tell when sieve results are “drifting” due to wear

Results depend on nature of “shaking” leading to operator to operator variations in results.

Limited information

Page 30: Particle Shape of Micronized Powders

© 2013 HORIBA, Ltd. All rights reserved.

Advantage of Image Analysis

Better size analysis due to understanding of particle shape:Length, Width, Average Diameter

Page 31: Particle Shape of Micronized Powders

© 2013 HORIBA, Ltd. All rights reserved.

Shape Analysis with CAMSIZER XT

31

© Retsch Technology GmbH

area of the particle

perimeter of the particle

circle with same area as

particle

diameter of circle of same

area

2

4

P

ASPHT

max

min

Fe

c

x

x

l

w

l

b

b/l0.4 0.5 0.6 0.7 0.80

10

20

30

40

50

60

70

80

90

Q3 [%]

Pharma-Product-1-30kPa-bonne-forme-_xc_min_009.rdfPharma-Product-1-30kPa_Vitesse-Adaption_xc_min_008.rdf

lactose-30kPa_xFemax_003.rdfPharma-Product-2-460_xc_min_008.rdf

SPHT0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.90

10

20

30

40

50

60

70

80

90

Q3 [%]

Pharma-Product-1-30kPa-bonne-forme-_xc_min_009.rdfPharma-Product-1-30kPa_Vitesse-Adaption_xc_min_008.rdf

lactose-30kPa_xFemax_003.rdfPharma-Product-2-460_xc_min_008.rdf

Page 32: Particle Shape of Micronized Powders

© 2013 HORIBA, Ltd. All rights reserved.

X-Jet Dry Powder Dispersion

Sample: PMMA Beads

Detection of oversized particles

x c _ m i n [ µ m ]8 1 0 1 2 1 4 1 60

1 0

2 0

3 0

4 0

5 0

6 0

7 0

8 0

9 0

Q 3 [ % ]

C A 1 0 F e e d 4 5 0 k p a _ x c _ m i n _ 0 0 7 . r d fC A 1 0 F e e d 4 5 0 k p a _ x c _ m i n _ 0 0 8 . r d fC A 1 0 T 1 8 C 4 5 0 k p a _ x c _ m i n _ 0 0 4 . r d fC A 1 0 T 1 8 C 4 5 0 k p a _ x c _ m i n _ 0 0 5 . r d fC A 1 0 T 1 8 F - A 4 5 0 k p a _ x c _ m i n _ 0 0 1 . r d fC A 1 0 T 1 8 F - A 4 5 0 k p a _ x c _ m i n _ 0 0 2 . r d fC A 1 0 T 1 8 F - B 4 5 0 k p a _ x c _ m i n _ 0 0 1 . r d fC A 1 0 T 1 8 F - B 4 5 0 k p a _ x c _ m i n _ 0 0 2 . r d f

G r a p h o f m e a s u r e m e n t r e s u l t s :C : \ . . . C a m s i z e r 4 3 1 9 X T \ C A M D A T \ R T 1 6 9 4 M i c r o b e a d s \ C A 1 0 F e e d 4 5 0 k p a _ x c _ m i n _ 0 0 7 . r d fT a s k f i l e : R T 1 6 9 4 P M M A 4 5 0 . a f g

Cu

mu

lati

ve D

istr

ibu

tio

n

Particle size [µm]

4 Samples:RedGreenBlueViolet

x c _ m i n [ µ m ]1 3 1 4 1 5 1 6 1 7 1 8

9 9 . 0

9 9 . 2

9 9 . 4

9 9 . 6

9 9 . 8

1 0 0 . 0

Q 3 [ % ]

C A 1 0 F e e d 4 5 0 k p a _ x c _ m i n _ a v . r d fC A 1 0 T 1 8 F - B 4 5 0 k p a _ x c _ m i n _ a v . r d fC A 1 0 T 1 8 C 4 5 0 k p a _ x c _ m i n _ a v . r d fC A 1 0 T 1 8 F - A 4 5 0 k p a _ x c _ m i n _ a v . r d f

G r a p h o f m e a s u r e m e n t r e s u l t s : M e a n v a l u e s , t a s k R T 1 6 9 4 P M M A 4 5 0 . a f g C : \ . . . C a m s i z e r 4 3 1 9 X T \ C A M D A T \ R T 1 6 9 4 M i c r o b e a d s \C A 1 0 F e e d 4 5 0 k p a _ x c _ m i n _ 0 0 8 . r d f , C A 1 0 F e e d 4 5 0 k p a _ x c _ m i n _ 0 0 7 . r d f

Δ ~ approx 0.5% Vol.

Red with oversized particlesGreen without oversizeBlue with oversized particlesViolet without oversize

Page 33: Particle Shape of Micronized Powders

© 2013 HORIBA, Ltd. All rights reserved.

Dispersing a SampleWant to spread particles out so that they

don’t touch.No Yes

Page 34: Particle Shape of Micronized Powders

© 2013 HORIBA, Ltd. All rights reserved.

Want to spread particles out so that they don’t touch.

Use % of field of view that is covered in order to control feed rate. Try 1% at first.

Control feed rate.

Feeding Too fast Good

Page 35: Particle Shape of Micronized Powders

© 2013 HORIBA, Ltd. All rights reserved.

SMALL PARTICLESPOTENTIALLY SMALL

EXTRACTION ERRORS (A)POTENTIALLY LARGE

SAMPLE PREP ERRORS (C)

LARGE PARTICLESPOTENTIALLY LARGE

EXTRACTION ERRORS (B)POTENTIALLY SMALL

SAMPLE PREP ERRORS (D)

INSTRUMENT ERROR IS SMALL AND RELATIVELY CONSTANT

PARTICLE SIZE

SAMPLE PREPARATION SAMPLE EXTRACTION

INSTRUMENT ERROR

%

E

R

R

O

R A

B

C

D

Measurement Error Sources

Page 36: Particle Shape of Micronized Powders

© 2013 HORIBA, Ltd. All rights reserved.

Want to spread particles out so that they don’t touch.

Small and sticky particles will stay clumped together. Need to use energy to separate particles. That means air dispersion or liquid dispersion.

Micronized Powders

Feeding Too fastNot enough dispersion energy Good

Page 37: Particle Shape of Micronized Powders

© 2013 HORIBA, Ltd. All rights reserved.

Modular "X-Change" ConceptFlexible configuration for a wide application range

simple • safe • fast

Page 38: Particle Shape of Micronized Powders

© 2013 HORIBA, Ltd. All rights reserved.

Measurement principle – X-Jet

Page 39: Particle Shape of Micronized Powders

© 2013 HORIBA, Ltd. All rights reserved.

X-Jet Measurement ResultsInfluence of dispersion on shape parameters

Milk powder with X-Jet at 30, 60, 120, 200, 300 kPa

Milk powder_30kPa_xc_min_001.rdfMilk powder_60kPa_xc_min_002.rdfMilk powder_120kPa_xc_min_003.rdfMilk powder_200kPa_xc_min_004.rdfMilk powder_300kPa_xc_min_005.rdf

Page 40: Particle Shape of Micronized Powders

© 2013 HORIBA, Ltd. All rights reserved.

CCD - Basic CCD - Zoom

Measuring Principle

CAMSIZER XT 14µm 1µm

CAMSIZER

Resolution Difference

30 µm -> 30 mm1 µm-> 3 mm

Size Range

Detection of particles

One pixel is element of a projection when at least half of the pixel is covered.

Page 41: Particle Shape of Micronized Powders

© 2013 HORIBA, Ltd. All rights reserved.

Measurement Range

Large particles cannot been measured properly even they fit in the frame.

Page 42: Particle Shape of Micronized Powders

© 2013 HORIBA, Ltd. All rights reserved.

Measurement RangeThe probability of large particles touching the edge of the frame is higher than for smaller particles.

=> Large particles cannot been measured sufficiently

Upper limit of measurement range

Page 43: Particle Shape of Micronized Powders

© 2013 HORIBA, Ltd. All rights reserved.

Two-Camera-System

Basic

Zoom

Basic-Camera Zoom-Camera

43© Retsch Technology GmbH

Page 44: Particle Shape of Micronized Powders

© 2013 HORIBA, Ltd. All rights reserved.

comparison

CAMSIZER-measurement xarea (red)and sieving * (blue)

A

A‘ = A

xare

a

xarea

“diametervia projection surface”

Digital Image ProcessingArea Measurement Sieving

44© Retsch Technology GmbH

Page 45: Particle Shape of Micronized Powders

© 2013 HORIBA, Ltd. All rights reserved.

Feret diam. 1

Feret diam. 2

Longest diam.

to longest┴

Equivalentsphericaldiam

Size Descriptors

Page 46: Particle Shape of Micronized Powders

© 2013 HORIBA, Ltd. All rights reserved.

Feret diam. 1

Feret diam. 2

Longest diam.

to longest┴

Aspect ratio

= shortest diam longest diam

= to longest diam longest diam

= shortest Feret diam longest Feret diam

= three different numbers!

Shape: Aspect Ratio

Page 47: Particle Shape of Micronized Powders

© 2013 HORIBA, Ltd. All rights reserved.

More Shape Descriptors

Page 48: Particle Shape of Micronized Powders

© 2013 HORIBA, Ltd. All rights reserved.

Optical Process Controlanalysis for size and shape

Measurement Results

Page 49: Particle Shape of Micronized Powders

© 2013 HORIBA, Ltd. All rights reserved.

Number of Particles

Error bars are one standard deviation from repeated measurements of the same number of particles from different parts of the sample.

The error bars get smaller as you evaluate more particles.

Page 50: Particle Shape of Micronized Powders

© 2013 HORIBA, Ltd. All rights reserved.

Measurement of very broad particle distributions (due to speed and two cameras)

Direct particle definition by width (analogue to sieving) by length or projection surface

Two camera system for more accuracy and reproducibility

Easy operation Fail-safe, robust Ideal for particle shape analyses Measurement of density, counting of

particles

Measurement Results

50© Retsch Technology GmbH

CAMSIZER Advantages

Page 51: Particle Shape of Micronized Powders

© 2013 HORIBA, Ltd. All rights reserved.

Watch out for:

Sample preparationImage qualityMeasure enough particles

Page 52: Particle Shape of Micronized Powders

© 2013 HORIBA, Ltd. All rights reserved.

What we’ll talk about

Importance of particle shape

Dynamic image analysis principles

Examples

Q&A

Page 53: Particle Shape of Micronized Powders

© 2013 HORIBA, Ltd. All rights reserved.

Product PerformanceSome products perform better when

more sphericalGlass beads for highway paintProppants

Some products perform better when less sphericalAbrasivesCatalysts

Finding particles by shape

Page 54: Particle Shape of Micronized Powders

© 2013 HORIBA, Ltd. All rights reserved.

Glass Beads for Highway Paint

Size and shape critical to reflective properties

More round = more reflectivity back to source

CAMSIZER uses b/l ratio to quantify roundness

Dry In paint

Page 55: Particle Shape of Micronized Powders

© 2013 HORIBA, Ltd. All rights reserved.

Defects from round particles

Oval

Satellites

Pointed

Aggregates

Glass Beads for Highway Paint

Quantified by Camsizer

Page 56: Particle Shape of Micronized Powders

© 2013 HORIBA, Ltd. All rights reserved.

Proppant Packing

Page 57: Particle Shape of Micronized Powders

© 2013 HORIBA, Ltd. All rights reserved.

Shape Comparison

A s p c t R a t i o0 . 3 0 . 4 0 . 5 0 . 6 0 . 7 0 . 80

1 0

2 0

3 0

4 0

5 0

6 0

7 0

8 0

9 0

Q 3 [ % ]C e r a m i c - P r o p - E P - 2 0 - 4 0 - M e s h - 4 0 . r d fC e r a m i c - P r o p - S B - 2 0 - 4 0 - M e s h 1 . r d fC e r a m i c - P r o p - S G - V - 1 . r d fS a n d - P r o p - S I B - 2 0 - 4 0 - M I S - 9 . r d fN a t u r a l - B r o w n - S a n d - C - 2 0 - 4 0 . r d fW h i t e - S a n d - P r o p - U N F - 2 0 - 4 0 - 1 7 . r d fW h i t e - S a n d - P r o p - S I B - 2 0 - 4 0 - C H F - 1 0 . r d fW h i t e - S a n d - P r o p - U N F - 2 0 - 4 0 - 1 . r d fW h i t e - S a n d - P r o p - U N F - 2 0 - 4 0 - 8 . r d f

G r a p h o f m e a s u r e m e n t r e s u l t s : M e a n v a l u e s , t a s k P r o p p a n t s - C a d r e . a f g D : \ . . . - P r o p p a n t \I m e r y s - E l - P r o p - # 2 0 - # 4 0 - 1 8 m m - Z _ x c _ m i n _ 2 0 1 2 _ 0 2 _ 1 4 _ 2 3 _ 5 5 _ 5 3 _ 0 4 2 . r d f , I m e r y s - E l - P r o p - # 2 0 - # 4 0 - 1 8 m m - Z _ x c _ m i n _ 2 0 1 2 _ 0 2 _ 1 5 _ 0 0 _ 3 0 _ 3 4 _ 0 4 1 . r d f

l

w

Shape comparison between natural sand proppants and ceramic proppants. There are two clearly different ranges of Aspect Ratio (Krumbein’s Sphericity). Analysis of other shape parameters are possible as well (Convexity for ceramic bead twins, Symmetry for good and broken ceramic beads, Krumbein’s Roundness etc.)

Page 58: Particle Shape of Micronized Powders

© 2013 HORIBA, Ltd. All rights reserved.

Proppants

Traditional method CAMSIZER

Page 59: Particle Shape of Micronized Powders

© 2013 HORIBA, Ltd. All rights reserved.

Abrasion Mechanics

Difference in hardness between the two substances: a much harder abrasive will cut faster and deeper

Grain size (grit size): larger grains will cut faster as they also cut deeper

Grain shape: sharp corners help some mechanisms

Compactness helps in others

Page 60: Particle Shape of Micronized Powders

© 2013 HORIBA, Ltd. All rights reserved.

Dynamic Image AnalysisBy choosing proper size parameter, Xc min, results can match historic sieve Data. Also generates shape data provenTo correlate with abrasive performance.

Page 61: Particle Shape of Micronized Powders

© 2013 HORIBA, Ltd. All rights reserved.

Sand: Round vs. “Edgy”

Similar in size.Shape difference seenin b/l and sphericity.Edgy would makebetter abrasive.

Sphericity

Breadth/length (b/l)

Page 62: Particle Shape of Micronized Powders

© 2013 HORIBA, Ltd. All rights reserved.

Catalysts Size/Shape by CAMSIZER

Spherical catalysts Easy, no special effort

Cylindrical catalystsLength, width

Bended extrudatesUse other parameters 2

min2

max )()( cFelength xxx

mincstretch x

Ax

Page 63: Particle Shape of Micronized Powders

© 2013 HORIBA, Ltd. All rights reserved.

Catalysts Size/Shape by CAMSIZER

Tri & quadralobePossible to distinguish

between different diameters

Shorter green distribution = length

Taller maroon distribution= width

Size helps define shape

Quadralobe catalysts

Trilobe catalysts

Page 64: Particle Shape of Micronized Powders

© 2013 HORIBA, Ltd. All rights reserved.

32.8%

67.2%

xFe max

xc min

Measurement Results

Q3 (round particles) =

Find the componentsof Ion Exchanger

and Charcoal in a mixture

Page 65: Particle Shape of Micronized Powders

© 2013 HORIBA, Ltd. All rights reserved.

What we’ll talk about

Importance of particle shape

Dynamic image analysis principles

Examples

Q&A

Page 66: Particle Shape of Micronized Powders

© 2013 HORIBA, Ltd. All rights reserved.

Danke Merci

Gracias

Большое спасибо

Grazie<اُشْك? ر

Σας ευχαριστούμε

감사합니다 Obrigado

Tacka dig

谢谢 ขอบคุ�ณคุรั�บ

Thank youありがとうございました

धन्यवा�दநன்ற

Page 67: Particle Shape of Micronized Powders

© 2013 HORIBA, Ltd. All rights reserved.

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