ASTM E799-03(2015)
(Practice)Standard Practice for Determining Data Criteria and Processing for Liquid Drop Size Analysis
Standard Practice for Determining Data Criteria and Processing for Liquid Drop Size Analysis
SIGNIFICANCE AND USE
4.1 These criteria6 and procedures provide a uniform base for analysis of liquid drop data.
SCOPE
1.1 This practice gives procedures for determining appropriate sample size, size class widths, characteristic drop sizes, and dispersion measure of drop size distribution. The accuracy of and correction procedures for measurements of drops using particular equipment are not part of this practice. Attention is drawn to the types of sampling (spatial, flux-sensitive, or neither) with a note on conversion required (methods not specified). The data are assumed to be counts by drop size. The drop size is assumed to be the diameter of a sphere of equivalent volume.
1.2 The values stated in SI units are to be regarded as standard. No other units of measurement are included in this standard.
1.3 The analysis applies to all liquid drop distributions except where specific restrictions are stated.
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Designation: E799 − 03 (Reapproved 2015)
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.
1. Scope 9276–1Representation of Results of Particle SizeAnalysis-
Graphical Representation
1.1 This practice gives procedures for determining appro-
9272–2Calculation ofAverage Particle Sizes/Diameters and
priate sample size, size class widths, characteristic drop sizes,
Moments from Particle Size Distribution
and dispersion measure of drop size distribution.The accuracy
of and correction procedures for measurements of drops using
3. Terminology
particular equipment are not part of this practice. Attention is
drawn to the types of sampling (spatial, flux-sensitive, or 3.1 Definitions of Terms Specific to This Standard:
neither) with a note on conversion required (methods not
3.1.1 spatial, adj—describes the observation or measure-
specified).Thedataareassumedtobecountsbydropsize.The
mentofdropscontainedinavolumeofspaceduringsuchshort
drop size is assumed to be the diameter of a sphere of
intervals of time that the contents of the volume observed do
equivalent volume.
not change during any single observation. Examples of spatial
samplingaresingleflashphotographyorlaserholography.Any
1.2 The values stated in SI units are to be regarded as
sum of such photographs would also constitute spatial sam-
standard. No other units of measurement are included in this
pling. A spatial set of data is proportional to concentration:
standard.
number per unit volume.
1.3 The analysis applies to all liquid drop distributions
3.1.2 flux-sensitive, adj—describes the observation of mea-
except where specific restrictions are stated.
surement of the traffic of drops through a fixed area during
1.4 This international standard was developed in accor-
intervals of time. Examples of flux-sensitive sampling are the
dance with internationally recognized principles on standard-
collection for a period of time on a stationary slide or in a
ization established in the Decision on Principles for the
sampling cell, or the measurement of drops passing through a
Development of International Standards, Guides and Recom-
plane (gate) with a shadowing on photodiodes or by using
mendations issued by the World Trade Organization Technical
capacitance changes.An example that may be characterized as
Barriers to Trade (TBT) Committee.
neither flux-sensitive nor spatial is a collection on a slide
movingsothatthereismeasurablesettlingofdropsontheslide
2. Referenced Documents
in addition to the collection by the motion of the slide through
2.1 ASTM Standards:
the swept volume. Optical scattering devices sensing continu-
E1296Terminology for Liquid Particle Statistics (With-
ously may be difficult to identify as flux-sensitive, spatial, or
drawn 1997)
neither due to instantaneous sampling of the sensors and the
2.2 ISO Standards: measurable accumulation and relaxation time of the sensors.
13320–1Particle Size Analysis-Laser Diffraction Methods For widely spaced particles sampling may resemble temporal
and for closely spaced particles it may resemble spatial. A
flux-sensitivesetofdataisproportionaltofluxdensity:number
1 per (unit area×unit time).
ThispracticeisunderthejurisdictionofASTMCommitteeE29onParticleand
Spray Characterization and is the direct responsibility of Subcommittee E29.02 on
3.1.3 representative, adj—indicates that sufficient data have
Non-Sieving Methods.
been obtained to make the effect of random fluctuations
Current edition approved March 1, 2015. Published March 2015. Originally
approved in 1981. Last previous edition approved in 2009 as E799–03 (2009).
acceptably small. For temporal observations this requires
DOI: 10.1520/E0799-03R15.
sufficienttimedurationorsufficienttotaloftimedurations.For
For referenced ASTM standards, visit the ASTM website, www.astm.org, or
spatial observations this requires a sufficient number of obser-
contact ASTM Customer Service at service@astm.org. For Annual Book of ASTM
vations.Aspatialsampleofoneflashphotographisusuallynot
Standards volume information, refer to the standard’s Document Summary page on
the ASTM website.
representative since the drop population distribution fluctuates
The last approved version of this historical standard is referenced on
with time. 1000 such photographs exhibiting no correlation
www.astm.org.
with the fluctuations would most probably be representative.A
Available fromAmerican National Standards Institute (ANSI), 25 W. 43rd St.,
4th Floor, New York, NY 10036, http://www.ansi.org. temporal sample observed over a total of periods of time that
Copyright © ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959. United States
E799 − 03 (2015)
is long compared to the time lapse between extreme fluctua- See Table 1 for numerical examples.
tions would most probably be representative. 3.2.2 D ,D ,D , and D are diameters such that the
Nf Lf Af Vf
fraction, f, of the total number, length of diameters, surface
3.1.4 local, adj—indicates observations of a very small part
area,andvolumeofdrops,respectively,containpreciselyallof
(volume or area) of a larger region of concern.
the drops of smaller diameter. Some examples are:
3.2 Symbols—Representative Diameters:
¯
3.2.1 (D ) is defined to be such that:
D = number median diameter,
pq
N0.5
D = length median diameter,
p
L0.5
D
(i i
p2q
¯ ~ !
D = surface area median diameter,
D 5 (1)
A0.5
pq
q
D
i D = volume median diameter, and
(i
V0.5
D = drop diameter such that 90% of the total liquid
V0.9
where:
volume is in drops of smaller diameter.
¯ ¯
D = the overbar in D designates an averaging
See Table 2 for numerical examples.
process,
¯ 3.2.3
(p−q)p>q = the algebraic power of D ,
pq
p and q = the integers 1, 2, 3 or 4,
¯
log~D ! 5 log~D !/n (2)
gm (i i
D = the diameter of the ith drop, and
i
p q
∑ = the summation of D or D , representing
where:
i i i
all drops in the sample.
n = number of drops,
0=p and q = values 0, 1, 2, 3, or 4.
¯
D = the geometric mean diameter
gm
∑D is the total number of drops in the sample, and some
i i
3.2.4
of the more common representative diameters are:
D 5 D (3)
RR VF
¯
D = linear (arithmetic) mean diameter,
where:
¯
D = surface area mean diameter,
¯ f = 1−1⁄e ≈ 0.6321, and
D = volume mean diameter,
¯
D = Rosin-Rammler Diameter fitting the Rosin-Rammler
D = volume/surface mean diameter (Sauter), and
RR
¯
distribution factor (see Terminology E1296).
D = meandiameterovervolume(DeBroukereorHerdan).
3.2.5 D =upper-boundary diameter of drops in the kth
kub
size class.
This notation follows: Mugele, R.A., and Evans, H.D., “Droplet Size Distri-
3.2.6 D =lower-boundary diameter of drops in the kth
klb
bution in Sprays,” Industrial and Engineering Chemistry, Vol 43, No. 6, 1951, pp.
size class.
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
E799 − 03 (2015)
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
Smallest drop diameter = 240.00 µm
Fra
...
This document is not an ASTM standard and is intended only to provide the user of an ASTM standard an indication of what changes have been made to the previous version. Because
it may not be technically possible to adequately depict all changes accurately, ASTM recommends that users consult prior editions as appropriate. In all cases only the current version
of the standard as published by ASTM is to be considered the official document.
Designation: E799 − 03 (Reapproved 2009) E799 − 03 (Reapproved 2015)
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. A number in parentheses indicates the year of last reapproval. A
superscript epsilon (´) indicates an editorial change since the last revision or reapproval.
1. Scope
1.1 This practice gives procedures for determining appropriate sample size, size class widths, characteristic drop sizes, and
dispersion measure of drop size distribution. The accuracy of and correction procedures for measurements of drops using particular
equipment are not part of this practice. Attention is drawn to the types of sampling (spatial, flux-sensitive, or neither) with a note
on conversion required (methods not specified). The data are assumed to be counts by drop size. The drop size is assumed to be
the diameter of a sphere of equivalent volume.
1.2 The values stated in SI units are to be regarded as standard. No other units of measurement are included in this standard.
1.3 The analysis applies to all liquid drop distributions except where specific restrictions are stated.
2. Referenced Documents
2.1 ASTM Standards:
E1296 Terminology for Liquid Particle Statistics (Withdrawn 1997)
2.2 ISO Standards:
13320–1 Particle Size Analysis-Laser Diffraction Methods
9276–1 Representation of Results of Particle Size Analysis-Graphical Representation
9272–2 Calculation of Average Particle Sizes/ Diameters Sizes/Diameters and Moments from Particle Size Distribution
3. Terminology
3.1 Definitions of Terms Specific to This Standard:
3.1.1 spatial, adj—describes the observation or measurement of drops contained in a volume of space during such short intervals
of time that the contents of the volume observed do not change during any single observation. Examples of spatial sampling are
single flash photography or laser holography. Any sum of such photographs would also constitute spatial sampling. A spatial set
of data is proportional to concentration: number per unit volume.
3.1.2 flux-sensitive, adj—describes the observation of measurement of the traffic of drops through a fixed area during intervals
of time. Examples of flux-sensitive sampling are the collection for a period of time on a stationary slide or in a sampling cell, or
the measurement of drops passing through a plane (gate) with a shadowing on photodiodes or by using capacitance changes. An
example that may be characterized as neither flux-sensitive nor spatial is a collection on a slide moving so that there is measurable
settling of drops on the slide in addition to the collection by the motion of the slide through the swept volume. Optical scattering
devices sensing continuously may be difficult to identify as flux-sensitive, spatial, or neither due to instantaneous sampling of the
sensors and the measurable accumulation and relaxation time of the sensors. For widely spaced particles sampling may resemble
temporal and for closely spaced particles it may resemble spatial. A flux-sensitive set of data is proportional to flux density: number
per (unit area × unit time).
3.1.3 representative, adj—indicates that sufficient data have been obtained to make the effect of random fluctuations acceptably
small. For temporal observations this requires sufficient time duration or sufficient total of time durations. For spatial observations
this requires a sufficient number of observations. A spatial sample of one flash photograph is usually not representative since the
This practice is under the jurisdiction of ASTM Committee E29 on Particle and Spray Characterization and is the direct responsibility of Subcommittee E29.02 on
Non-Sieving Methods.
Current edition approved Nov. 1, 2009March 1, 2015. Published February 2010March 2015. Originally approved in 1981. Last previous edition approved in 20032009
as E799 – 03.E799 – 03 (2009). DOI: 10.1520/E0799-03R09.10.1520/E0799-03R15.
For referenced ASTM standards, visit the ASTM website, www.astm.org, or 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.
The last approved version of this historical standard is referenced on www.astm.org.
Available from American National Standards Institute (ANSI), 25 W. 43rd St., 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
E799 − 03 (2015)
drop population distribution fluctuates with time. 1000 such photographs exhibiting no correlation with the fluctuations would most
probably be representative. A temporal sample observed over a total of periods of time that is long compared to the time lapse
between extreme fluctuations would most probably be representative.
3.1.4 local, adj—indicates observations of a very small part (volume or area) of a larger region of concern.
3.2 Symbols—Representative Diameters:
3.2.1 (D¯ ) is defined to be such that:
pq
p
D
(i i
¯ ~p2q!
D 5 (1)
pq
q
D
i
(i
where:
D¯ = the overbar in D¯ designates an averaging process,
(p − q) p > q = the algebraic power of D¯ ,
pq
p and q = the integers 1, 2, 3 or 4,
D = the diameter of the ith drop, and
i
p q
∑ = the summation of D or D , representing all drops in the sample.
i i i
0 = p and q = values 0, 1, 2, 3, or 4.
∑ D is the total number of drops in the sample, and some of the more common representative diameters are:
i i
D¯ = linear (arithmetic) mean diameter,
D¯ = surface area mean diameter,
D¯ = volume mean diameter,
D¯ = volume/surface mean diameter (Sauter), and
D¯ = mean diameter over volume (De Broukere or Herdan).
See Table 1 for numerical examples.
3.2.2 D , D , D , and D are diameters such that the fraction, f, of the total number, length of diameters, surface area, and
Nf Lf Af Vf
volume of drops, respectively, contain precisely all of the drops of smaller diameter. Some examples are:
D = number median diameter,
N0.5
This notation follows: Mugele, R.A. and Evans, H.D., “Droplet Size Distribution in Sprays,” Ind. Engnrg. Chem., Vol 43, No. 6, 1951, pp. 1317–1324.This notation
follows: Mugele, R.A., and Evans, H.D., “Droplet Size Distribution 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
50.009 Relative Span 5 sD 2D d/D 5 s3900 2 14200d/2530 50.98 30.21826 50.024
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
E799 − 03 (2015)
D = length median diameter,
L0.5
D = surface area median diameter,
A0.5
D = volume median diameter, and
V0.5
D = drop diameter such that 90 % of the total liquid volume is in drops of smaller diameter.
V0.9
See Table 2 for numerical examples.
3.2.3
¯
log~D ! 5 log D /n (2)
~ !
gm (i i
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
Smallest drop diameter = 240.00 μm
Fraction of normal curve = 0.999995
Normal Curve Simple Calculation
(Gaussian Limits—4.55457 to 4.53257)
D = 1464.91 1459.37 μm (length mean diameter)
D = 1646.44 1646.57 μm (surface mean diameter)
D = 1824.85 1832.39 μm (volume mean diameter)
D = 1850.45 1857.79 μm (surface/length mean diameter)
D = 2036.73 2053.27 μm (volume/length mean diameter)
D = 2241.75 2269.32 μm (sauter mean diameter)
D = 2615.67 2670.75 μm (mean diameter over volume)
D = 2534.53 2533.31 μm (volume median diameter)
V0.5
D = 1303.62
...
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