b

4 .

PX -70-49

Partide Characterization

A. h. VUMCAN

JULY t AUGUST, SEPTEMBER

PANTEX PLANT Amarills,Texas

Foh

U S e Atomic Energy Commission Albuquergtre Operations Office

Portions of this document may be illegible in electronic image pxmdncts. h a g s are produced from the best avaiiable original dOcUI I len t

PARTICI E G-IARACTERI ZATION

A, A. Duncan

Ju ly , August, September 1970 Endeavor No. 117

Acct, NO, 22-2-44-02-317

I NTR ODUCT ION

The ef fec t of par t ic le s ize , shape, and surface on the behavior of a powder is continually being studied. In quali ty control of a powder, seldom i s a given parameter known well enough t o predict accurately overall behavior of a powder" Therefore, many par t ic le parameters must be evaluated t o determine the influ- encing factors , including width , lengthlwidth ra t io , volume, surface area, reentrant surface, bulk density, compressibility, surface roughness, pore volume, degree of sphericity, etc, , and the i r re1 ation t o extrudabi 1 i ty , pressabi l i ty , firing performance, e tc . Determining these t h i n g s i s called powder or par t ic le characterization,

DISCLAIMER

This report was prepared as an account of work sponsored by an agency of the United States Government. Neither the United States Government nor any agency thereof, nor any of their employees, makes any warranty, express or implied, or assumes any legal liability or responsi- bility for the accuracy, completeness, or usefulness of any information, apparatus, product, or process disclosed, or represents that its use would not infringe privately owned rights. Refcr- ence herein to any specific commercial product, process, or service by trade name, trademark, manufacturer, or otherwise does not necessarily constitute or imply its endorsement, recom- mendation, or favoring by the United States Government or any agency thereof. The views and opinions of authors expressed herein do not necessarily state or reflect those of the United States Government or any agency thereof.

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DISCUSSION

FowCer Characterization

Raw powders will have the following analysis performed on then before formulation,

de t cna to r packing, pressing, e tc .

I , Bulk Property Analysis

A. Density - Determined by Helium - Air Pycnometer B . B u l k Gensity C . Tap Density 0. Compressibility E. Surface Area

1 2, Volume-Specific Surface Area (cm2/cm3) Both weight and volume specif ic surface are2 are determined by the .f o 1 1 ow i na :

Weigh t-Specifi c Surface Area (cm2/g)

a. Air Permeabi7ity o r Air Permeametry

(1) Fisher Sub-sieve Sizer (Sp)

( 2 ) Blaine Fineness Tester (SB) 0

0

(3) Knudser Flow Permeameter is") 0

b . Microscopy Z (1) Zeiss Analyzer ( S o )

c . Gas Adsorption

(1) Perkin-Elmer Adsorptometer (S,") (Dynamic Flow System)

In addition t o specif ic surface area, average spherical diameter

i s calculated for each of the above determinations and pore volume

i s determined by gas absorption (,

by subtracting Sz from So,

substracting Sp from S,".

Surf ace roughness i s estimated P Reentrant surface i s determined by

0

0

-2-

F, Degree of Sphericity

S s where x = c - S

8 when x = 1 the powder consists of only spheres

S = surface area of a sphere of equal volume

S = surface area of the particle (determined by Zeiss) S

P I4 = number of particles

- 1 - - 1 arithmetic mean

of equivalent spherical diameter

I

X G o Index of Fineness = IF =

11. Particle Analysis

A. Sieve Analysis - Calculated distributions of the following: 1. Particle Size

a. Weight % retained bo Frequency % retained

2. Statistical Parameter Distributions

a, Surface area/particle b o Spherical diameter c Volume/parti cl e d o Cross-Sectional Area

For each of the above distributions, means, etc,, are also

calculated, This is further covered under microscopy,

B. Microscopy - Zeiss analysis is used to calculate the following parameter from dimensional measurements of individual particles,

where the parameters are calculated according to particle shape,

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1- Length 2 Width 3, Length/Width ratio 4, Volume 5, Surface area/ParticTe 6, Cross-Sectional Area 7, Equivalent spherical diameter

For each parameter, both frequency and weight distributions are

calculated with the following statistical evaluation:

a, Powder limits

(1)

(2) Mid-Range =

Range, and lowest and highest value lowest value + highest value

2 (3) Mode = Most frequently occurring value

b , Distribution Means - cxi ni

1 - N (1)

( 2 ) Geometric Mean = G = ( X ~ X ~ X ~ ~ ~ ~ X ~ )

Arithmetic Mean = X =

or -

log F = 1 c(1og xi)

- 1 1 - L (3) Harmonic Mean = H = Ifi z [ f l ) l

c, Measure of Dispersjon

(1) Quartfles

(a)

( b )

Lower = Q: - - the 25th percentile size

Middle = Qz = the 50th percentile size

( c ) Upper = Q3 = the 75th percentile size

(d) - Q q + Q? 42

Percentile Estimate = Q, -

- Q; - Qi 2 (e) Semi-Interquartile Range = Qs -

-4-

50 ( f ) Kramer's Modulus = K = c o xi gi (or n i ) /

(9) Range from Median

[11 lower = Median [21 upper = Median

( h ) Median Deviation =

t o lowest value t o upper value

( 2 ) Standard Deviation = S = 4- cxi2ni

N - F' or s2 (3 ) Variance = V =

(4) Coefficient of Variation = v = d m = 1/2 ~2 -

(5) Harmonic Variation = \J = -

S X

or - -

d. Measure of Di s t r ibu t ion Skewness

- (1) Degree of Symmetry = S, - - - M -

X

where S, = 1 f o r normal d i s t r i b u t i o n

= <1 f o r skewed l e f t

= >1 for skewed r i g h t

-5-

- (2) Range from mean = X - lowest value

P 3 (3) Coefficient of skewness = y 1 = -

Y3

with p 3 = third moment about weighted mean

u3

20 (4) Momenta1 Skewness = = 3-

with CT = 6

( 5 ) Coefficient of Excess = y2 = -3 0 4

( 6 ) Kurtosis (Measure of Flatness) = B2 = = y2 + 3 0 4

e. Green Harmonic Mean Diameter calculated from

; to have the following calculated: volume surface area

eni di N (1) dl = arithmetical mean diameter

Eni di2

eni di

en. di3

mi di2 1

( 3 ) d, = used in determination of surface area

( 4 ) d4 =

(5) .+h = determination of surface area =

en. di4

mi di3 1

eni di2

-6-

(6) D = determination of N

(7) N =

mi di3 - - d- 1

p V' D3 S

(8) S: = specific surface area = a""1 or 01 A z , psd3

n o -

(9) Degree of Uniformity = U = a1

-7-

CONCLUSION

Many segments of the above analysis of a powder have been completed and used

to study various relationships; e.g.

vacuum stability, analysis of k factor and its influence on air permeability

surface area, etc,

particle size versus extrudabili ty and

The determination of surface area by air permeability (Fisher Sub-Sieve Sizer)

has been useful and widely used procedure by the AEC explosives laboratories.

One of its most widely used applications is in determining specific surface

area for detonator grade PETN.

is primarily due to its easy, rapid analysis of a powder,

absorption of a gas at low temperatures usually give higher surface area

numbers, often considered more accurate.

why air permeability measurements are lower than gas absorption.

many workers believe that air permeability's difficulties with irregular

shaped particles were due to streamline or non-contact flow, which includes

little of the area making up the cracks and pores within the body of porous

particles, Others believe the shape of the particles influence the air flow

through the bed; e.g., cylindrical particles placed parallel to the air flow

offer less resistance than particles placed perpendicular to the flow,

influences of these factors are considered in the equations on which Gooden-

Smith based their analysis from which the FSSS was designed,

The Fisher Sub-sieve Sizer (FSSS) popularity

Measurements by

Many explanations were made as to

Presently

The

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The initial theory was based on Poiseville's equation for fluid flow through

capillaries..

described the flow o f a fluid through a bed o f divided material, from wh-ich

Carman developed the Kozeny-Carman equation for determining surface area of

a powder, From these experimentors and Henry Green, Gooden-Smith developed

the air permeability instrument known as the Fisher Sub-sieve Siter.

Kozeny developed an equation, using Poiseville's equation, which

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Surface Area from Permeametry

Basically a permeability apparatus consists of a chamber containing the powder

to be measured, a pump or other device with which a fluid is made to flow through

the powder, and gages to indicate the rate of flow and the accompanying pressure

drop across the chamber.

area is calculated from consideration of the powder bed dimensions, the degree

of packing, the properties of the flowing fluid, and the resistance to flow

encountered .

The flow may be either streamlined or not. Surface

Permeability indicates the surface area that contributes to the pressure drop.

With streamline flow this surface area is the non-contact area over which the

fluid passes and includes little of the area making up the walls of cracks and

pores within the body of porous particles.

what might be called the external surface area of particle materials.

and gases, at or near atmospheric pressure, are primarily employed as the

flowing fluids.

In the reduced pressure state the flow is considered molecular streaming or

Knudsen flow where the resistance is due primarily to molecular collision

with particles and passage walls (reentrant surface).

Streamline flow results indicate

Liquids

Newer developments utilize gases at greatly reduced pressures,

Streamline flow relations are primarily applicable to relatively coarse

powders with a resultant surface area equivalent to an envelope surface area.

Molecular streaming relations permit determinations for materials having a

mean surface diameter down to %0.1 1.1 with a surface area comparable to gas

absorption or total surface area. I

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. . . .. - .

Theory of A i r Permeabi 1 i ty

Gooden-Smith1 s t a t e , " I t has been pointed o u t by Green2 and by Carmen t h a t , of

the many kinds of average par t ic le diameters for a powder, the most important

i s the average that i s equal t o the diameter of a sphere equivalent i n specif ic

surface to the sample as a whole, For spherical par t ic les this i s simply an

average dl'ameter by surface weighing; f o r par t ic les of any shape i t i s twice

the average normal rad ius by surface weighing,

e t e r , e i ther f o r a single par t ic le or for a group, i s s ix times the total volume

d i v i d e d by the total surface regardless of par t ic le shape or s ize dis t r ibut ion,"

The value of t h i s average diam-

Green expressed specif ic surface area as a surface area per gram of material,

Expressing this i n the form of a general equation i t gives:

= Surface area/uni t weight (cm2/gm)

= Part ic le density (gm/cm3)

V = Volume of each par t ic le ( a n 3 )

S = Surface of each par t ic le (cm2)

n = Frequency

p.s

When geometrical s imilar i ty ex is t s i t follows tha t i f the par t ic le volume i s

made proportional t o the cube of some arbi t rary diameter and the surface

proportional to the same diameter, then the proportionality factors are

constant for the en t i re mass of par t ic les , Therefore, i n equation 1 we

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may substitute V = y'd3 and s = old2 where yl and 0' are the proportionality

For this special class of materials, equation 2 is less general constants.

- U'/Y' p ( cnd3/cnd2) sw - S

than equat I m Equation 2 holds, however, for any particle shape, for non-

uniformity and for any fixed diameter with the only limitation being geometrical

s i mi 1 ari ty

In order to deviate from geometrical similarity we must restrict the particle

diameters to a diameter which will be equivalent in each shape tested.

harmonic mean diameter dm is equal to 6 V/S which gives,

The

The diameter of a sphere, the edge of a cube, and the harmonic mean diameter

of the three edges of a rectangular parallelpiped are each equal to 6 V/S.

This diameter is evidently a kind of "natural" one, for its introduction,

as will' be seen, simplifies matters considerably.

equation 3 reduces to the well-known expression for specific surface,

At infinite uniformity,

sw = 6/Psdm

The next step behind the theory of air permeability is how can dm be

determined from the resistance offer to a flowing fluid by a column of

packed particles of random shape.

(4)

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Viscous Flow: Streamline Flow Permeametry

The equation describing the flow of a f l u id t h r o u g h a bed of divided material

was given by Kozeny3 and Fair and Hatch4, We shall use as a basis for der i -

vation the hydraulic rad ius defined as the cross-sectlonal area o f a conduit

derived by the perimeter wetted by a f lu id , the procedure used by Fair and

Hatch. Thus , f o r a c i rcular tube f i l l e d w i t h a f lu id , the hydraulic radius i s :

Rh = D/4

Rh i s hydraulic radius D i s the diameter of the tube

For a packing of length L and porosity E ,

- Cross-sectional area of flow Wetted perimeter

Rh -

/

Volume of voids Void (or par t ic le ) surface area

Rh =

V with V, = V f V

S

where V, i s to ta l volume

Vs i s volume of solid

V v is volume of voids

from which porosity is determined by the equation:

E = Vv/Vt

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(7 )

from this Rh may be found by the equation:

where S i s sol id surface area (cm2)

Sv i s surface area per uni t volume of solid (cm2/cm3)

Dc i s equivalent t o the diameter of a capil lary th rough the packing (cm)

b Since S, = Psdm

6 then Sv = dm

DC 1 E therefore i f 4 = r(=) then: V

Dc - = 2/3 (2) and dm 3Dc( 1-E) dm = 2E

A gas near atmospheric pressure and flowing a t a moderate velocity moves along

a channel in w h a t i s called viscous flow. This condition prevails i n s t ra ight

capi l lary tubes as well as along the i r regular channels formed among confined

particles. Therefore, Dc, the equivalent diameter of a capil lary th rough the

powder bed, must be found. Poiseville flow for capillary tube can be used t o

determi ne Dc :

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Ap is pressure difference across powder bed (gm/cm2)

L is length of packing (cm)

q is viscosity of fluid (poises)

Vc is velocity through the capillary (cm/sec)

g, is gravitational constant in cm/sec2

J L32nU ' C

C gcAP then D

After finding Dc then dm can be found from equation 13 and S or Sv from

equations 4 and 11, respectively. W

To find other parameters pertaining to air-permeabili ty surface area which

leads to determining Sv and Sw with and/or without finding Dc the following

equations are applicable.

When a fluid flows through a capillary tube because of a pressure difference

at the opposite ends, the volume per unit time is gjven by the equation:

V is volume of flow per unit time (ml)

t is time of flow (sec)

r is radius of capillary tube (cm)

R is length of capillary tube (cm)

0 is viscosity of fluid (poises)

Ap is pressure difference (gm/cm2)

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The equation i s valid only i f the flow i s laminar, which may n o t exceed flow

Reynol ds number 2000.

To determine the length of the capi l lary th rough the powder pack Poiseville

equation can be used t o give:

In this equation R i s a l so equal t o the tortuous patch Le through the packing.

If the f low i s streamline, we may inse r t the value of Dc i n the Poiseville

equation and thus obtain for the pressure drop th rough the packing the

equation :

2u u s2 (1-E)2 - c v A P 32u uc

L gCD: 9,

- = - E 2

where 1-1 is velocity of f lu id (ml/sec)

is gravitational constant (cm/sec2) 9, and i f we use the formula

where Uc is velocity through capi l lary (cm/sec)

L i s length of tortous path t h r o u g h the packing (cm)

L i s length o f packing (cm)

U is approach velocity (cm/sec)

e

- 16-

. '

€ 3 AP

gCL 2l.l UL (TI -m then S: =

e

and since Sv = p, Sw then S$ would be:

Carman later showed that the surface area,of powders forming a granular bed

is related to the porosity'and the permeability of the bed by the equations:

where K is proportionately constants representing

the permeability of the porous medium

Based on the fluid flow law, K1 can be expressed by:

where Q1 is the rate of the flowing fluid in ml/sec

A is the cross-sectional area of the porous medium in cm2

q is the viscosity of the fluid in poises

Ap is the pressure difference driving the fluid through the medium in gm/cm

L is the thickness of the porous medium in cm

Also the relationship may be expressed by

E 3 9, 5rl S;(l-E)Z

K =

-17-

from which equation 17 can be expressed by

where k i s a proportionately constant of 5 5 0.5

K i s a permeability constant, representing apparent l inear velocity per u n i t hydraulic gradient expressed i n cm/sec

y i s Kinematic viscosity of the f lu id i n Stokes (cm/sec) density)

( r a t i o of viscosity t o

Carmen i n his work with irregular par t ic les showed tha t for many powders the

r a t i o of L /L was

aspect factor and found by equation:

2.5. The factor k used i n equation 25 i s called the e

e L L k = 2 - = 5 k 0.5

In th i s equation Carmen was concerned w i t h the capillary

pa,h which i s a function of shape; b u t means of determin

par t ic les i s extremely d i f f i c u l t t o achieve.

Fowler and Hertel

the material used

i n turn, being re

forming the tor tuous

ng shape for irregular

have a l so pointed out t h a t the value of k depends upon b o t h

and the favored orientation of any par t ic les , the orientation,

ated t o the porosity. They show the value of k t o be ? equal t o

(27) k = Q m 3 sin 4 av

where (Sin2+)av i s the mean of the sin of the angle between the direction of

over-all flow and the normal of the par t ic le surface elements.

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. . .. - -

Fisher Sub-sieve Sizer

Gooden and Smith changed the equation f o r the use w i t h a i r currents by replacing

i n the equation

Ky with K2q i n which TI i s viscosity i n poises (gm/cm/sec) and K2 i s permeability

expressed as apparent l inear velocity per u n i t pressure gradient (cmL/gm/sec) e

By apparent l inear velocity i s meant the volume ra te of delivery of air form the

apparatus a t atmospheric pressure divided by the internal cross-sectional area

o f the sample tube,

expressing K2 and TI i n terms of the observational data required for the i r deter-

By substi tuting f o r Sv the equivalent diameter 6/dm, and

mination, simplifying terms and changing the

the formula

60000 dm = 14

u n i t of diameter there i s obtained

where d i s average diameter i n microns

q i s viscosity of air i n poises (dynes-sec/cm2)

C i s conductance of the flowmeter resistance i n cd/sec/uni t pressure (g/cm2)

i s density of sample i n gm/cc p

L i s length of height of the compacted sample cm

M

V

i s mass o f sample i n grams

i s apparent volume i n cc of compacted sample

- 19-

P

Ap i s pressure difference in gm/cm2 across flowmeter resistance

i s overall a i r pressure i n grams/cm2

therefore;

If the sample weight i s standardized a t a value numerically equal t o p , then

the equation can be simplified t o the form

where c = an instrument constant tha t combines factors i n equation 2

c = 60000 14 = (3.80)

If the flowmeter resistance is a capil lary tube of suitable dimensions, C i s

given by a simple form of Poiseville 's equation

where r i s radius of capillary

11 i s length of capillary

g i s gravitational constant

TI i s viscosity of air

By the expedience o f u s i n g a sample weight equal i n grams t o the control

density of material, packing the sample t o a known degree, selecting and

fixing several of the variables i n the equation, i t may be simplified t o the

extent tha t the average par t ic le diameter i s indicated by only the value of P;

i o e d , as f a r as the instrument i s concerned, by the height of a column of liquid

i n a glass tube. In the Sub-sieve Sizer i t i s n o t necessary t o make an actual

measurement of the height of the liquid column, Instead, by proper use o f the

calculator chart , the average par t ic le diameter and given porosity may be read

d i rec t ly from the chart,

6 x IO4 - - 6 x 10% dm = SP psw 0

6 x l o 4 therefore; SE = dmP

where dm i s the average diameter i n p

Sp i s the specif ic surface area 0

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( 5 )

EX P E R I M ENTA L

Samples of PETN which varied greatly i n d i s t r i b u t i o n and shape were measured

by the Zeiss analyzer t o see the i r e f f f ec t s on the surface area determined,

The 25 samples' surface area were r u n i n duplicates. The following simple

correlations w i t h surface area a l so measured by FSSS were calculated:

Parameter

Average length

Average w i d t h

Average volume

Average area/particl e

Average cross-sectional area

Average spherical diameter

Average L/W r a t i o

Correlation Coefficient

-t .88974

- .29001

i- .46565

- .33731

-t .07208

- .66837

- .66837

Twenty-seven powders w i t h i r regular shapes and specif ic surface areas deter-

mined by gas absorption and FSSS ranged from 1714 t o 27230 cm2/g,

are shown i n the following table.

Results

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Sampl e

8073 8075 8075-2 8121-03 8121-06 8148 8306P 83060 8320 1069- 140 1069- 146 1069- 154 1069-160 1069-167 1069- 174 1069- 181 1069- 188 1069- 195 1069-202 1069-210 1069-230

5-43- 1 5-43-8 5-43-11A 5-43-11B 5-43-11C

8220

Fisher Sub-sieve Si zer SP

0

( Cm2/ gm 1 6519 69 18 5926 5794 5467 6000 6 186 4808 65 19 6141 6119 6 108 6277 7369 6032 6420 6336 6520 6 190 6220 630 1

19939 1225 2515 1244 132 1 1311

Total

Average Deviation 27 Samples

Fisher A v o Par t jc le

D i ame t e r h 1 5,40 4.90 5,72 5,85 6,20 5.65 5.48 7.05 5,20 5.52 5,54 5,55 5.40 4,60 5,62 5,28 5,35 5,20 5,48 5,45 5,38 1,70

27,6 13,6 27,4 25,8 26,O

-23-

Gas Absorption SA

( Cm2/ gm 1 0

8822 7937 9058 8785 6101 7903 7968 6410 9088 8284 9302 87 18

10365 11041 8700 8246 8817 8759 9360 9458 8410

27230 1786 2856 17 14 22 12 2062

2303 10 19 3 132 299 1

634 1903 1782 1602 2569 2143 3 183 2610 4088 3672 2668 1826 2397 2239 3170 3208 2 109 729 1

561 341 470 88 1 75 1

6 1543 2279

Extex

Many parameters of a powder have been analyzed and used in the extrudability

o f Extex study, as determined by a Rossi-Peakes instrument,

Analysis

1, Fisher Sub-sieve Sizer (Sp)

2, Gas Absorption (SA)

3, Zeiss Average Width

4. Zeiss Average Volume

5, Zeiss Average Area/Particle

6, Zeiss Avg, Cross-Sectional Area

7, Zeiss Average Length

0

0

Number of

Observa t i ons

60

25

25

25

25

25

25

Correl ati on Coeffi cient

+O .63766

-0 ., 77589

-0 66665

-0 66087

-0 8039 1

-0 73072

+O 43096

Since the significance of these correlations are above 0,999 cm (except the

last, which is %0,98 cm) the relationships to the problems of extrudability

appear evident.,

was Zeiss arithmetic,

and harmonic means, etc, may lead to a better understanding of problems

connected with the extrudabi 1 i ty o f Extex,

When this study was made, the only calculated means available

Further analysis of distribution skewness, geometric

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