ASTM E799-03(2020)e1

This international standard was developed in accordance with internationally recognized principles on standardization established in the Decision on Principles for the
Development of International Standards, Guides and Recommendations issued by the World Trade Organization Technical Barriers to Trade (TBT) Committee.
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Designation: E799 − 03 (Reapproved 2020)
Standard Practice for Determining
Data Criteria and Processing for Liquid Drop Size Analysis
This standard is issued under the fixed designation E799; the number immediately following the designation indicates the year of
original adoption or, in the case of revision, the year of last revision.Anumber in parentheses indicates the year of last reapproval.A
superscript epsilon (´) indicates an editorial change since the last revision or reapproval.
ε NOTE—Keywords were added editorially in April 2020.
1. Scope 2.2 ISO Standards:
ISO13320–1ParticleSizeAnalysis-LaserDiffractionMeth-
1.1 This practice gives procedures for determining appro-
ods
priate sample size, size class widths, characteristic drop sizes,
ISO 9276–1Representation of Results of Particle Size
and dispersion measure of drop size distribution.The accuracy
Analysis-Graphical Representation
of and correction procedures for measurements of drops using
ISO9272–2CalculationofAverageParticleSizes/Diameters
particular equipment are not part of this practice. Attention is
and Moments from Particle Size Distribution
drawn to the types of sampling (spatial, flux-sensitive, or
neither) with a note on conversion required (methods not
3. Terminology
specified).Thedataareassumedtobecountsbydropsize.The
3.1 Definitions of Terms Specific to This Standard:
drop size is assumed to be the diameter of a sphere of
3.1.1 flux-sensitive, adj—describes the observation of mea-
equivalent volume.
surement of the traffic of drops through a fixed area during
1.2 The values stated in SI units are to be regarded as
intervals of time. Examples of flux-sensitive sampling are the
standard. No other units of measurement are included in this
collection for a period of time on a stationary slide or in a
standard.
sampling cell, or the measurement of drops passing through a
1.3 The analysis applies to all liquid drop distributions
plane (gate) with a shadowing on photodiodes or by using
except where specific restrictions are stated.
capacitance changes.An example that may be characterized as
neither flux-sensitive nor spatial is a collection on a slide
1.4 This international standard was developed in accor-
movingsothatthereismeasurablesettlingofdropsontheslide
dance with internationally recognized principles on standard-
in addition to the collection by the motion of the slide through
ization established in the Decision on Principles for the
the swept volume. Optical scattering devices sensing continu-
Development of International Standards, Guides and Recom-
ously may be difficult to identify as flux-sensitive, spatial, or
mendations issued by the World Trade Organization Technical
neither due to instantaneous sampling of the sensors and the
Barriers to Trade (TBT) Committee.
measurable accumulation and relaxation time of the sensors.
For widely spaced particles sampling may resemble temporal
2. Referenced Documents
2 and for closely spaced particles it may resemble spatial. A
2.1 ASTM Standards:
flux-sensitivesetofdataisproportionaltofluxdensity:number
E1296Terminology for Liquid Particle Statistics (With-
3 per (unit area×unit time).
drawn 1997)
3.1.2 local, adj—indicates observations of a very small part
(volume or area) of a larger region of concern.
ThispracticeisunderthejurisdictionofASTMCommitteeE29onParticleand
3.1.3 representative, adj—indicates that sufficient data have
Spray Characterization and is the direct responsibility of Subcommittee E29.02 on
been obtained to make the effect of random fluctuations
Non-Sieving Methods.
acceptably small. For temporal observations this requires
Current edition approved April 1, 2020. Published April 2020. Originally
sufficienttimedurationorsufficienttotaloftimedurations.For
approved in 1981. Last previous edition approved in 2015 as E799–03 (2015).
DOI: 10.1520/E0799-03R20E01.
spatial observations this requires a sufficient number of obser-
For referenced ASTM standards, visit the ASTM website, www.astm.org, or
vations.Aspatialsampleofoneflashphotographisusuallynot
contact ASTM Customer Service at service@astm.org. For Annual Book of ASTM
Standards volume information, refer to the standard’s Document Summary page on
the ASTM website.
3 4
The last approved version of this historical standard is referenced on Available fromAmerican National Standards Institute (ANSI), 25 W. 43rd St.,
www.astm.org. 4th Floor, New York, NY 10036, http://www.ansi.org.
Copyright © ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959. United States
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E799 − 03 (2020)
representative since the drop population distribution fluctuates where:
with time. 1000 such photographs exhibiting no correlation ¯ ¯
D = the overbar in D designates an averaging
withthefluctuationswouldmostprobablyberepresentative.A
process,
¯
temporal sample observed over a total of periods of time that
(p−q)p>q = the algebraic power of D ,
pq
is long compared to the time lapse between extreme fluctua- p and q = the integers 1, 2, 3 or 4,
D = the diameter of the ith drop, and
tions would most probably be representative.
i
p q
∑ = the summation of D or D , representing
i i i
3.1.4 spatial, adj—describes the observation or measure-
all drops in the sample.
mentofdropscontainedinavolumeofspaceduringsuchshort
0=p and q = values 0, 1, 2, 3, or 4.
intervals of time that the contents of the volume observed do
∑D is the total number of drops in the sample, and some
i i
not change during any single observation. Examples of spatial
of the more common representative diameters are:
samplingaresingleflashphotographyorlaserholography.Any
sum of such photographs would also constitute spatial sam-
¯
D = linear (arithmetic) mean diameter,
pling. A spatial set of data is proportional to concentration:
¯
D = surface area mean diameter,
number per unit volume. ¯
D = volume mean diameter,
¯
D = volume/surface mean diameter (Sauter), and
3.2 Symbols—Representative Diameters:
¯
D = meandiameterovervolume(DeBroukereorHerdan).
¯
3.2.1 (D ) is defined to be such that:
pq
See Table 1 for numerical examples.
p
D
(i i
3.2.2 D ,D ,D , and D are diameters such that the
¯ ~p2q!
Nf Lf Af Vf
D 5 (1)
pq
q
D
fraction, f, of the total number, length of diameters, surface
(i i
area,andvolumeofdrops,respectively,containpreciselyallof
the drops of smaller diameter. Some examples are:
D = number median diameter,
N0.5
D = length median diameter,
L0.5
This notation follows: Mugele, R.A., and Evans, H.D., “Droplet Size Distri-
bution in Sprays,” Industrial and Engineering Chemistry, Vol 43, No. 6, 1951, pp.
1317–1324.
TABLE 1 Sample Data Calculation Table
r A
Size Class Bounds No. of Sum of D in Each Size Class
i
Class Vol. % Cum. %
(Diameter Drops in
B
Width 2 3 4 in Class by Vol.
D D D D
in Micrometres) Class i i i i
3 6 9 12
240–360 120 65 19.5 × 10 5.9×10 1.8×10 1. × 10 0.005 0.005
360–450 90 119 48.2 19.6 8.0 3 0.021 0.026
450–562.5 112.5 232 117.4 59.7 30.5 16 0.081 0.107
562.5–703 140.5 410 259.4 164.8 105.2 67 0.280 0.387
703–878 175 629 497.2 394.7 314.5 252 0.837 1.224
878–1097 219 849 838.4 831.3 827.6 827 2.202 3.426
1097–1371 274 990 1221.7 1513.7 1883.2 2352 5.010 8.436
1371–1713 342 981 1512.7 2342.1 3641.1 5683 9.687 18.123
1713–2141 428 825 1589.8 3076.1 5976.2 11657 15.900 34.023
2141–2676 535 579 1394.5 3372.5 8189.2 19965 21.788 55.811
2676–3345 669 297 894.1 2702.8 8203.5 24999 21.826 77.637
3345–4181 836 111 417.7 1578.2 5987.6 22807 15.930 93.567
4181–5226 1045 21 98.8 466.5 2212.1 10532 5.885 99.453
5226–6532 1306 1 5.9 34.7 348.5 1534 0.547 100.000
r 3 6 9 12
Totals of D in ^κ = 6109 8915.3 × 10 16562.6 × 10 37729.0 × 10 100695 × 10
i
¯ ¯ ¯ ¯
entire sample D = 1300 D =1460 D =1860 D =2280 D =2670
N0.5 10 21 32 43
¯ ¯
D =1650 D =2060
20 31
¯
D = 1830
D = 2540 Worst case class width
V0.5
348.5 669
5 0.009 Relative Span 5 sD 2 D d/D 5 s3900 2 14200d/2530 5 0.98 3 0.21826 5 0.024
V0.9 V0.5 V0.5
37729 267613345
Less than 1 %, adequate sample size Adequate class sizes
A
The individual entries are the values for each κ as used in 5.2.1 (Eq 1) for summing by size class.
B 3 3
SUM D in size class divided by SUM D in entire sample.
i i
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E799 − 03 (2020)
where:
D = surface area median diameter,
A0.5
D = volume median diameter, and
f = 1−1⁄e ≈ 0.6321, and
V0.5
D = drop diameter such that 90% of the total liquid
D = Rosin-Rammler Diameter fitting the Rosin-Rammler
V0.9
RR
volume is in drops of smaller diameter.
distribution factor (see Terminology E1296).
See Table 2 for numerical examples.
3.2.5 D =upper-boundary diameter of drops in the kth
kub
3.2.3
size class.
¯
log~D ! 5 log D /n (2)
~ ! 3.2.6 D =lower-boundary diameter of drops in the kth
gm (i i klb
size class.
where:
n = number of drops,
¯
D = the geometric mean diameter
gm
3.2.4
D 5 D (3)
RR VF
TABLE 2 Example of Log Normal Curve with Upper Bound
Data Collected May 2, 1979 Computer Analysis May 2, 1979
Upper Bound Diameter (µm) Normal Curve, % Adjusted Data, % Data, %
360.00 0.006 0.005 0.005
450.00 0.027 0.027 0.026
562.50 0.109 0.108 0.107
703.00 0.389 0.387 0.387
878.00 1.227 1.224 1.224
1097.00 3.421 3.426 3.426
1371.00 8.407 8.437 8.436
1713.00 18.109 18.124 18.123
2141.00 34.080 34.024 34.023
2676.00 55.551 55.811 55.811
3345.00 77.828 77.637 77.637
4181.00 93.648 93.568 93.567
5226.00 99.481 99.453 99.453
6532.00 100.000 100.000 100.000
For Computing Curve Averages
Largest drop diameter = 6532.00 µm
Small
...