NBSIR 76-1037

Integral Measurement

Procedures for Determining

Particle Size in Aerosols

F. J. Kraus

Institute for Electronic Communication

Technology of the Rheinisch-Westfalian

Technical College

Aachen, West Germany

Translated for:

Center for Fire Research

Institute for Applied Technology

National Bureau of Standards

Washington, D. C. 20234

May 1 976

Final Report

U S. DEPARTMENT OF COHMEIICE

NATIONAL BUREAU OF STANDAIIOS

NBSIR 76-1037

INTEGRAL MEASUREMENT

PROCEDURES FOR DETERMINING

PARTICLE SIZE IN AEROSOLS

F. J. Kraus

Institute for Electronic Communication

Technology of the Rheinisch-Westfalian

Technical College

Aachen, West Germany

Translated for:

Center for Fire Research

Institute for Applied Technology

National Bureau of Standards

Washington, D. C. 20234

May 1 976

Final Report

U.S. DEPARTMENT OF COMMERCE, Elliot L. Richardson, S^cfetmy

James A. Baker, III, Under Secretary

Dr. Betsy Ancker-Johnson, Assistant Secretary for Science and Technology

NATIONAL BUREAU OF STANDARDS, Ernest Ambler. Acting Director

PREFACE

This report is a translation of a paper prepared by Mr. F. J. Kraus and presented by him at

the Colloquium on Aerosol Measurement Techniques

held March 4, 1975, in Aachen, West Germany. The

Colloquium was presented by the Institute for

Electronic Communication Technology of the

Rheinish-Westfalian Technical College, Aachen

in conjunction with the Gesamthochschule in

Duisburg.

This translation has been prepared to disseminate useful information to interested fire

research personnel on a need-to-know basis and

is not an original work of the Center for Fire

Research.

We express our appreciation to the author,

Mr. F. J. Kraus, for his permission and assistance

in making this information available.

We also express our appreciation to the

Joint Publication Research Service, Arlington,

Virginia, who provided the translation of the

original paper.

Richard G. Bright

Program for Fire Detection

and Control Systems

Center for Fire Research
CONTENTS

Page

PREFACE iii

LIST OF FIGURES vi

LIST OF TABLES vi

Abstract 1

1. INTRODUCTION 1

2. SMOKE MEASUREMENT DEVICES 2

2.1. Extinction Measurement Device 2

2.2. Scattered-Light Measurement Device 4

2.3. Measurement Device According to the Small

Ion Accumulation Effect 5

3. EXPERIMENTAL TEST 5

3.1. Remarks Concerning the Logarithmic Normal

Distribution 9

3.2. Determination of the Distribution Parameters

of a Polydisperse Aerosol 12

3.3. Application of the Procedure to Determine

the Distribution of a Paraffin Oil Mist. . . 16

4. LIMITS OF THE MEASURING RANGE 17

5. FINAL REMARKS 19

6. REFERENCES 21

V
LIST OF FIGURES

Page

Figure 1. Relation between m and y for monodisperse

aerosols 22

Figure 2. Relation between u and y for monodisperse

aerosols 23

Figure 3. C^/d as function of d 24

Figure 4. i/d as function of d 25

Figure 5. A as function of C and A 26

Figure 6. B as function of ^ and A 27

Figure 7. Curves to locate characteristic values,

for the determination of C and A 28

Figure 8. Particle size distribution of an oil

mist 29

Figure 9. Limits of measuring range 30

Figure 10. Limits of measuring range 31

Figure 11. Limits of measuring range 32

LIST OF TABLES

Table 1. Limits of Measuring Range 18

vi

INTEGRAL MEASUREMENT PROCEDURES FOR DETERMINING

PARTICLE SIZE IN AEROSOLS

F. J. Kraus

Abstract

In assessing the performance of smoke detectors in the laboratory, it is necessary to have

standardized smoke measurement devices which

function according to the same principles as the

smoke detectors under test. In developing these

measurement devices, a need exists to determine,

as precisely as possible, the effects of the

smoke characteristics on the measurement devices.

This paper presents the correlation between smoke

characteristics and comparative measuring devices

important in smoke detector test work and how

these measuring devices can also be used as aerosol

measuring devices.

Key words: Aerosols; ionization chambers; light

attenuation; scattered light; smoke detectors;

test methods.

1. INTRODUCTION

In the USA in 1972, property valued in the amount of

2.7 billion dollars was destroyed by fire. About 12,000

persons yearly die in the USA by fire, most of them from the

effects of smoke and noxious gases [1]-^. The problems of

automatic fire detection increase in significance more and

more. What is required for automatic fire detection is a

measuring device which reacts to a definite fire characteristic and initiates an alarm signal when this characteristic

exceeds a prescribed threshold. A frequently used fire characteristic is smoke which, as a rule, results from fires.

There already exists a number of automatic smoke detectors, working according to different functional principles.

The common characteristic of all smoke detectors is the

transformation of certain characteristics of smoke into an

electrical quantity, which makes possible comparisons with a

threshold value. Smoke detectors are, as a rule, subjected

to technical tests, which are supposed to investigate whether

Bracketed numbers refer to references listed at the end of

this paper.

1
the detector is (1) sufficiently sensitive for the planned

application, (2) already able to detect a fire at an early

stage, and (3) whether the smoke detector retains this

property unchanged over a sufficiently long period of time.

These tests are, in practice, performed with artificial

aerosols and with smoke from real test fires. It has turned

out that smoke detectors react quite differently to different types of smoke. To obtain a norm for the sensitivity of

a smoke detector, standardized smoke measurement devices

have been developed, which work according to different

functional principles, just like the smoke detectors themselves. The objective is always to compare a smoke detector

under test with a standard measurement device which works

according to the same functional principle as the smoke

detector under test itself.

In developing these standard measuring devices, the

task consisted in determining as accurately as possible the

transformation properties between the smoke characteristics

and the electrical quantity of measurement. In this paper

it will be shown how the connection between smoke characteristics and the electrical quantity of measurement was determined for comparative measuring devices important in testing

smoke detectors and what opportunities resulted therefrom

for using these comparative measuring devices as aerosol

measuring devices.

2. SMOKE MEASUREMENT DEVICES

In the following three sections, the three smoke measurement devices used in testing smoke detectors are described,

and a theoretical hypothesis is derived for the connection

between the electrical quantities of measurement and the

parameters of the aerosol. To simplify the mathematical description, we first start with the measurements of monodisperse aerosols with spherical particles.

2.1. Extinction Measurement Device

With the extinction measurement device, attenuation of

a parallel monochromatic light beam by aerosol particles is

measured. In the practical design of the measurement device,

it was found appropriate to use a so-called double-beam

process. With this double-beam process, a light ray penetrates the measurement distance, homogeneously filled with

aerosol, while a second light ray is directed through a

mirror system directly on an optical receiver, without traversing the measuring distance. Both light rays are generated from the same light source and are focused on the same

2
receiver. By differentially modulating the two light rays,

the associated signals can be separated electrically, and

the degree of transmission of the measuring distance filled

with aerosol can be directly measured by forming a quotient.

When the adjustment is correct, the following is valid for

the output signal (u) of the measuring device:

u = T (1)

Here, ^ is the degree of transmission of the aerosol.

According to the law of Bouguer and Lambert [2,3], the

following is valid for this degree of transmission:

T = exp [- a • 1] (2)

Here <^ is the extinction modulus of the aerosol and 1 is the

length of the measurement path. The extinction modulus a can

now be expressed according to Beer's law in terms of the

particle concentration z (number concentration) and the

extinction cross section C„ . of an aerosol particle:

" = ^ • <^Ext

=Ext = '=Ext S) (3)

The extinction cross section C^^^ is a function of the wavelength ^„ of the measured light, of the particle diameter d,

Ci and of the complex index of refraction m of the aerosol

particle.

From equations (1), (2), and (3), there follows:

u = exp [- z • Cg^^ • 1] (4)

Simple solution of this equation leads to:

0.434 1

Here and below, m designates the measured value of the

extinction measurement device. The extinction device used

3
in measurements to be described later works with monochromatic light of wavelength A„ = 0.8 ym. The effective hi length of the measuring path is 1 = 76 cm. The measured

value m has the dimension [1/length] . The connection between

the measured value m and the parameters of the aerosol are

described by the assumption

2.2. Scattered-Light Measurement Device

The scattered-light measurement device used in testing

smoke detectors measures a collectivity of aerosol particles,

just like the extinction measurement device. The boundary

condition existing in its development was the practical

design of a scattering volume open on all sides. This was

to ensure that the aerosol should, as much as possible, not

be influenced by the measurement process. The developed

measuring device operates with a pulsed semiconductor laser

at a wavelength of 0.905 ym and a mean scattering angle of

15° with respect to the forward direction. The limiting

values for the scattering angle lie at 12° and 18°. The

following assumption was made for the connection between the

aerosol parameters influencing the measurement and the electrical output signal u of the scattered light measurement

device

:

u = • z • i

i = i(0Q/ Ag, d, m) (7)

Here, i is the sum of the Mie intensity functions, and

it depends on the scattering angle, the wavelength of the

measured light, the particle diameter, and the complex index

of refraction. The term z is the number concentration of

the aerosol particles and K2 is a device constant. The integration of the intensity function over the solid angle was

taken into account in the device constant K2 because of the

small effective angular range.

4
2.3. Measurement Device According to the Small

Ion Accumulation Effect

The measurement device according to the small ion accumulation effect, hereafter called the I-chamber for short, is

in principle embodied in a cylindrical electric condenser

arrangement, in which flows an ion stream. When there are

smoke particles in the I-chamber, small ions accumulate at

these smoke particles, which are larger by orders of magnitude,

and thereby effect a measurable reduction of the ion current

[4,5]. The I-chamber is continuously traversed by the aerosol contained in the surrounding air so that a continuous

measurement of the collectivity of aerosol particles is possible. The following assumption is valid for the connection

between the relevant aerosol parameters and the electrical

output signal y of the measurement device:

y = . z • d (8)

To justify this assumption, see references [6] and [7]

.

All three measurement devices described measure a collectivity of aerosol particles. The measurement volumes are

all constructed as open as possible, so that the aerosol

reaches the individual measurement zones uninfluenced. A

close grouping of the measurement devices during measurement

can achieve simultaneous measurement of the same particle

concentration z by all three measurement devices. The measurement process is continuous in time. The connections cited

for the individual measurement devices, between the aerosol

parameters and the electrical output quantities of the measurement devices (equations 6-8) , are to be understood as

hypotheses, which require experimental verification.

3. EXPERIMENTAL TEST

To test the characteristic equations (6-8) of the measurement devices experimentally, all three measurement devices

were installed in an aerosol channel and were exposed to a

temporal rise in aerosol concentration. The measured values

m (extinction measurement device) , u (scattered-light measurement device) and y (I-chamber) are continuously recorded with

time. Monodisperse paraffin oil mist was used as a test aerosol and it was produced by a La-Mer generator. The particle

size of the test aerosol was determined by means of an "owl"

(Tyndall colors) . Computed results from the Mie theory were

used to connect the position of the Tyndall colors and the

geometric particle diameter d. The index of refraction of

5
the oil droplets was m = 1.41 - i0.15. For evaluation, the

always-simultaneously measured values, m and u, were plotted

as functions of y. Figures 1 and 2 show that directly proportional relationships between m and y and between u and y always result. From the hypothetical assumptions (equations

6-8) there follows:

m =

A'

u = K^z (10)

B'

Since the aerosol itself was constant during the entire

time of the experiment, as could be confirmed by checking

with the Tyndall colors, all the measuring devices must have

measured the same particle concentrations. If this were not

the case, the proportionality factors A' and B' from equations (9) and (10) could not be constant, and no directly

proportional relationship between the individual measured

quantities could have resulted from the experiments. Information concerning the particle size of the aerosol is contained in the proportionality factors A' and B'.

I _ m

Y

1

K. (11)

B' = ^

Y d

(12)

It will now be shown that the interpretation of factors

A' and B' given in equations (11) and (12) , can be confirmed

experimentally. For this purpose, experiments were performed

in the manner described above, using several monodisperse

aerosols, and the characteristic quantities A' and B' were

determined each time. The experimental result obtained

the characteristic quantities A'

6

and B' as functions of

IS

the
particle diameter d. These experimentally determined relationships A' (d) and B' (d) are then compared with C /d as

a function of d and with i/d as a function of d, the dependences of both fractions being calculated from Mie theory.

These theoretically calculated relationships are shown in

figures 3 and 4. The drawn points (x) are measured values

for the relationships A' and B' respectively. By fitting the

ordinate scales for the measured functions A' (d) and B' (d)

to the calculated functions C^/d and i/d as functions of d,

the device constants K^^ and could be determined.

A'

d.

1 = 1 13 (13)

K.

B'

d.

1 = 1 ... 9 (14)

Here, i designates the individual measurements with monodisperse aerosols of different particle diameters. From these

measurements, the following values result for the device

constants

:

K. = (2.6 0.1) 10 -2

cm' (15)

^ = ^^'^ t 0.5)

^

(16)

Actual constants resulted from the experimentally found data,

that is the values and K^/K^i could be determined with an

accuracy of 4% and 6% respectively — independent of the

particle diameter d. Consequently, the relations cited in

equations (6) -(8) can be reqarded as experimentally confirmed,

The following relations are therefore valid for the connection between the relevant aerosol parameters and the

electrical output quantities of the three integral measurement procedures which have been mentioned

:

Extinction measurement: m = z • C„ (17)

I-chamber measurement: y = 2.6 • 10" • z • d • cm^ (18)

Scattered-light measurement: u = 0.3 • z . i yVcm^ (19)

7
In the form in which they are given, equations (17) -(19) are

valid for monodisperse aerosols, i.e. for aerosols whose

particles all have the same diameter d. On passing to polydisperse aerosols, all quantities in equations (17)-(19),

which depend on the random variable d (particle diameter)

,

are to be replaced by their expectation values.

This means:

Cg-- Cg = /JCg(d) . p(d) dd (20)

i - i = // i (d) . p(d) dd (21)

/

d -> d = / d • p(d) dd (22)

Here, p (d) is the probability density function for the

particle diameter d of a polydisperse aerosol.

The equations for the measuring device, which form the

starting point for the discussion below, take into account

the relations given in equations (20) -(22), and are as follows

m = z • Cg (23)

y = • z • d (24)

with Kj^ = 2.6 • lO"^ cm2

u = K2 • z • T (25)

with K2 = 0.3 pVcm3

These equations are now generally valid for polydisperse

aerosols. The specified device constants K^^ and K2 are

valid specifically for the measurement devices described

above.

8
3.1. Remarks Concerning the

Logarithmic Normal Distribution

Mutually divergent relationships are frequently cited

for the probability density function of a logarithmic normal

distribution. For this reason, some derivations and conceptual clarifications will be given at this point. The

difference between the logarithm to base ten and the natural

logarithm is frequently disregarded in the literature.

The following holds:

Logarithm to base 10: log a

Natural logarithm (base e) : In a

log a = M • In a; M = log e 0.43429

If X is a random variable, then

i|;(x) = J: • exp {- ^^"^^

>; y ^l>ix)dK = /2T a 12

describes the probability density function of a Gaussian or

normal distribution. The equation for the normalized Gaussian

or normal distribution is as follows:

= exp T-} '* u - —

/27

The following holds for the cumulative probability distribution:

/-x

(|)(x) = y ij;(s)ds; d4)(x) = 4)(x)dx

The distributions to be investigated later refer to

the random variable particle diameter d (d = x) . It has

turned out that, with most condensation aerosols, the particle diameters themselves are not distributed normally, but

only the logarithms of the particle diameters follow a normal distribution. The base according to which the logarithms are determined is here in the first instance unimportant. But if the normal distribution is to be described

9
by definite characteristic values (mean value, deviation)

,

precise attention must be paid to which random variable is

being considered.

The following holds:

Let X be a random variable

Let u = f (x) be a transformed random variable with

a normal distribution.

The probability density function p(x) of the random variable

X is sought.

Since the random variable u is distributed normally,

the following assumption can be made for the cumulative

probability function:

<l)(u) = <t'(f(x)) = P(x)

dP(x) = p(x)dx = ^{f{x)) df(x)

From this follows:

p(x) = 'l'(f(x))

df (X)

dx

P(x) = exp f(x)2( df (X)

dx

In many practical cases, a transformation of the following type can be assumed for the transformation f(x):

Here, g(x) is a new random variable, which is normally distributed about the constant mean value g (

, with a standard

deviation o.

A random variable has a logarithmic normal distribution, when the logarithm of the random variables

is distributed normally.

10
There thus results the following possibilities for describing

a logarithmic normal distribution; (x > 0)

1. g(x) = log x;

2. g(x) = M • In x;

3. g(x) = In x;

df (x) ^ _M

dx ax

df (x) ^ _M

dx ax

df (x) ^ _1

dx ax

, . In df (X) 1

4. g(x) = 7T log x; —5-^

^ ^ - = — M ^ dx ax

The associated probability density functions are:

1. p(x) = exp'j- M log ^ - 0'

/27 ax

M

/27 ax

1

/27 aX

1

/27 aX

;a

, V M , J (In X - Inr) 2 m^i

2. p(x) = • exp'<-

^

^ [- (In X - InQ^ l 3. p(x) = • exp

A t \ 1 ^ ) (log X - logr)

4. p(x) = • exp' {- 2 2^

2a2 m2

2

Now since all four probability density functions describe the same physical state of affairs, all four functions

must also yield the same values. This is only possible with

the consideration that the deviation a is not numerically

the same in all cases. In case 1 and 2, gives the variance of log X (logarithm to base ten) , while in case 3 and

4, a 2 gives the variance of In x (natural logarithm). The

relationship between the deviation a is given by

a ] log x> = M • a Un X [ ; M = log e = 0.43429

11
The subsequent discussion is always based on the transformation for the logarithmic normal distribution specified

in case 3. There thus results for the probability density

function

:

1 In —

p(d) = exp' - \ (26)

/2tt ad 2a2

As already mentioned, is here the variance of In d, and

C is the median value of the random variables d.

The width A is used as another parameter in describing

the log-normal distribution:

= Modus (d) = ^'^P' f°'l '27)

The expectation value of d can be described in terms of K and

A. The following holds:

d

• 2

p(d)dd = C • expMy- ?/A (28)

3.2. Determination of the Distribution

Parameters of a Polydisperse Aerosol

In determining the particle size distribution of a polydisperse aerosol of an arbitrary type, determination of an

unlimited number of parameters is required. This is experimentally impossible. A customary approximation in the solution of the problem consists in dividing the particle size

distribution into a limited number of intervals based on the

particle diameter. Each interval is here described by a

parameter to be determined by technical measurement (histogram) .

In the case treated here, only three integral measurement procedures are available, and thus, at most, three

unknown parameters can be determined. Consequently, another

approximation must be made in order to determine the particle size distribution of a polydisperse aerosol. The starting

point must be that the type of particle size distribution is

known in advance, and can be analytically represented by two

free parameters.

12
To elucidate the measuring process, the discussion

below takes as its starting point that the particle diameters

of the aerosol under analysis have a logarithmic normal distribution. This assumption is always fulfilled with sufficient accuracy for aerosols of interest within the framework

of automatic fire detection. This is true because condensation aerosols are considered exclusively.

To analyze a polydisperse aerosol, for example, such as

that generated by the mist generators used in testing smoke

detectors, the following relationships are available:

m = z • Cg (29a)

u = K2 • z • i (29b)

y = • z . d (29c)

= iK, A, m, Ag) (29d)

i = i (u. A, m, Ag, ii^) (29e)

d = d (C, A) (29f)

The first three equations here refer to the measurement

technique, while equations (29d) and (29e) are given by Mie

theory. The following initial conditions are required to

solve this system of equations

:

1. The type of particle distribution must be known

a priori (here e.g., log-normal distribution), and

must be describable by two free parameters.

2. The aerosol particles must have a shape which is

accessible to the theoretical calculations of Mie

theory (e.g., homogeneous spheres, concentric

spherical shells, rods, etc.)

3. The complex index of refraction m of the aerosol

particles must be known a priori.

13
When the three initial conditions are fulfilled, and

when the properties of the measuring devices described further

above are taken into consideration, the following quantities

in the system of equations (29) are known:

Device constants: K, , K^, A X ij> i. Z tj s o

Aerosol parameters: m (complex index of refraction)

The following can be determined by technical measurement:

m, u, y

The following remain as unknown quantities in the system of

equations

:

z, C^, T, d, A

There thus remains the task of solving six equations with

six unknowns. Now unfortunately, equations (29d) and (29e)

cannot be represented analytically, and there thus exists no

possibility for a closed analytic solution of the system of

equations. To solve the problem, the following procedure

was used:

From (29a), (29b), and (29c), there follows:

(30)

(31)

The quantities A and B, defined by equations (30) and (31)

,

can be determined by technical measurement.

With equations (29d) through (29f )

, and equation (28)

,

it can be shown that A and B depend only on the two parameters C and A:

14
A = Cg( A )

5

• /a

(32)

B =

i (C/ A )

C

* /a

(33)

The two equations (32) and (33) can be solved numerically or graphically. The quantities A and B respectively,

corresponding to equations (32) and (33) are shown in figures

5 and 6, in the range 0.1 <_ C £ 0.7/ and for several special

A-values. These figures serve to make clear the quantities

A and B, which are derived from measured data when aerosol

parameters E, and A are prescribed. The original task, however, consists in determining the distribution parameters e, and A from the measured data A and B. For this a further

step is still necessary. If the lines A = constant and B = constant are drawn respectively in figures 5 and 6, the

(^, A) combinations possible for constant parameters A and B

are found.

From figure 5 follows: e, = ^{A) A = constant

From figure 6 follows: E. = E,{A) B = constant

These two functions are shown in figure 7. If the

diagram shown in figure 7 has once been calculated, the

desired distribution parameters ^ and A are found with the

two measured values A and B, at the intersection of the

associated curves A = constant and B = constant. If e, and

A are now_known, equation (28) yields the mean particle

diameter d, and thus equation (24) yields the number concentration z of the aerosol particles. Since the measured

quantities m, y, and u are continuously measured as functions

of time, temporal changes in the particle concentration and

in the particle size distribution can also be determined by

technical measurement in the manner cited.

15
3.3. Application of the Procedure to Determine

the Distribution of a Paraffin Oil Mist

As an example of the application of the described measurement process, the particle size distribution of a paraffin

oil mist will be determined. The paraffin oil mist was

generated with an aerosol generator of the Draeger firm.

This mist generator is, in practice, used to test automatic

smoke detectors and to test filter materials. With respect

to the functional principle of the generator it need only be

said that the aerosol is generated by a combined atomization

and condensation process. Further particulars are found in

the literature references [8-10] . Paraffin oil of the Merck

firm (Darmstadt), with specification number 7162, was used

as the basic substance. The aerosol generator was operated

at an atomizing pressure 2 kPa/cm^ , and a mixing air throughflow of 50 1/min. The aerosol was led into an aerosol

channel, and the measured values m, y, and u were continuously determined as functions of time.

At an arbitrarily-chosen point in time, the following

measured values occurred:

m = 0.2 meter

V = 1

u = 1.39 volt

From these measured values the quantities A and B were

determined

:

A = . - = 2.6 • 10 . — . ^^^^

= 0.52 ym

B = • - = 8.9 . MicT^ = 12.4 ym"^ K2 y 1

Using the quantities A = 0.52 ym and B = 12.4 ym , the

associated distribution parameters K and A are found from

the diagram shown in figure 7

:

? = 0.3 ym

A = 1.25

16
with these distribution parameters, the probability

density function for the geometric particle diameters is

determined. It is shown in figure 8.

A mean diameter of d = 0.336 ym results from d = 5

• /a. The number concentration of the aerosol particles

results from

K^d

During the experiment described here, a concentration range

of

0 £ z _< 2.86 • lO^cm"^

was traversed. At the time the particle sizes were determined, the concentration was:

z = 1.14 • lO^cm"^

Since factors A and B were constant at all times of the

experiment, the aerosol distribution functions given in

figure 8 did not change as the above-cited concentration

range was traversed.

In the Institute for Dust Research at Bonn, the particle

size was determined for aerosols of paraffin oil particles

generated with the same aerosol generator as described previously [11] . In these experiments, measurements were made

with an Andersen cascade impactor, and the median value of

the number distribution was calculated from the measured mass

distribution. The value thus calculated turned out to be

0.36 ym, which agrees quite well with the value determined

here.

4. LIMITS OF THE MEASURING RANGE

In this section, the limits of the concentration range,

which can be attained with the described measuring devices,

will be investigated. It should be particularly stressed

that the following considerations refer to the described

measurement devices, as these are used to test automatic

smoke detectors, and therefore should not be regarded as

absolute limits for the associated measurement principle.

17
This limitation is particularly valid for the "upper limits"

(high particle concentration and large particle diameters)

.

First of all, the limits of the measuring range for

measuring monodisperse aerosols will be determined. The

starting point is the previously-described constants of the

measuring device, and the value m = 1.41 - i0.15 (e.g. paraffin oil) is assumed as index of refraction. For the three

starting quantities m, u, and y, of the three measurement

devices, the measuring range limits specified in table 1

are valid.

Table 1. Limits of Measuring Range

Extinction Measuring Device

Scattered-Light Measuring

Device

I -chamber

Minimum Maximum

m 2.5-10~®vim~^ 5,2-10"^ym~^

u 0.08 V 10 V

V 0.025 2.5

Using the relations given in equations (17)-(19), and the

values from table 1, the following determining equations

result for the maximum or minimum obtainable particle concentration as a function of particle diameter:

^ . 5.2 • 10^ -3

Extinction Measuring Device ^max ~ ~ ~

[C„(d)/um2]

2.5 • 10*^ -3

z = cm min

[C (d)/ym2]

Scattered-Light Measuring 3 33 • lO'^ -3

Device z^^^ = • i(d)

2.7 • 10

5

^^-3

z = cm mm i(d)

18
I-chamber

:

9.6 10^ _ 3 Z cm

max [d/pm]

9.6 103 - 3 z cm min [d/ym]

The cited relationships are shown graphically in figure

9. The range in which all three measuring devices can be

utilized simultaneously is severely bounded. The lower

particle size limit lies at about 0.3 ym. The concentration

range lies between 10 cm" ^ and 10^ cm~^.

In the case of polydispersions , this measuring range

broadens primarily towards smaller particles. With polydispersions, integral mean values are measured with respect

to the extinction cross section and the intensity function.

Consequently, the only point is that these mean values lie

in the common measuring range of the three measuring devices.

To make this clear, we stress that the mean value with respect

to the three parameters C„, i, and d, is not formed in the

measuring devices themselves but, from a physical point of

view, takes place in the aerosol-filled measurement volume.

It thus becomes clear that, when the distributions are sufficiently broad, mean values less than 0.1 ym can certainly

still be attained, although the lower measurement lies at

about 0.3 ym for monodisperse aerosols. The measuring range

limits for polydisperse aerosols are plotted in figures 10

and 11. The boundary lines were determined as in the case

of monodisperse aerosols, only that now there occurs an

additional dependence of the width of the distribution

function (A). The range of mean values between 0.1 ym and

1 ym, which is of particular interest within the framework

of automatic fire detection is covered quite well.

The described procedure to determine distribution parameters of aerosols permits measurements that occur continuously in time, without influencing the aerosol in its natural

diffusion behavior by the extraction of samples. The measuring devices have relatively simple construction, so that

they can be produced in larger numbers to achieve a practical "grid of measuring points"; thus, changes of an aerosol

can be sensed while it is spreading out.

5. FINAL REMARKS

19
The measuring range of the individual measuring devices

is tailored to problems posed in the area of automatic fire

detection. However, the large number of param.eters of the

measurement devices easily permits practical design of substantial changes in the measuring range. Prior knowledge

of the type of particle size distribution of the aerosol

under analysis is required, but is not a very significant

limitation. If no prior information is available concerning

the type of particle distribution, preliminary analyses can

be performed with other measuring devices, which as a rule

"operate statically."

A limitation of the measuring process exists which, in

the first instance, is significant: Only particles can be

analyzed whose shape can be processed with the aid of Mie

theory. This means that the particles of the aerosol under

analysis must be spherical, prescinding from a few numericallydifficult exceptions.

With reference to real fire aerosols (i.e. smoke) , this

requirement for spherical aerosol particles is not fulfilled

with certainty; nevertheless, the procedure is to be applied

precisely to such aerosols: Interpretation of measured

results (distribution parameters) found in this way, must

take in account that the distribution parameters determined

by technical measurement do not characterize the particle

size distribution of the real fire aerosol, but the particle size distribution of a theoretical "equivalent aerosol"

with spherical particles. This "equivalent aerosol," determined in this way, affects the three physical measurement

principles, used during measurement, in the same manner as

the real fire aerosol itself. Since these measurement

principles generally agree with the measurement principles

of automatic fire detectors, the effects of a fire aerosol

on automatic fire detectors can likewise be described with

the parameters of the associated "equivalent aerosol."

20
6 . REFERENCES

[1] National Commission on Fire Prevention and Control,

America Burning, U.S. Government Printing Office,

Washington, D.C. (1973).

[2] Bauer, G., Measurements of Absorption, Transmission,

Scattering, Archive of Technical Measurements,

V 462-3 (Apr. 1959)

.

[3] DIN 1349, Light Absorption in Optically Clear

Materials, Sizes, and Designations (Feb. 1955) , further

new draft: DIN 1349, Bl.l, Penetration of Radiation

through Media-Optically Clear Materials (Sept. 1969)

.

[4] Hasenclever, D. and Siegmann, H. , New Methods in Measuring Dust by Means of Small Ion Accumulation, StaubReinhaltung der Luft, 20, No. 2, 1960.

[5] Coenen, W. , Dust Monitor for Operational Dust

. Monitoring, Staub-Reinhaltung der Luft 23, No. 2,

1963.

[6] Hosemann, J. P., Towards a Theory of Ionization Measurement Chambers, Considering Small Ion Recombination,

Staub-Reinhaltung der Luft 32, No. 7, 1972.

[7] Gilson, H. H., Hosemann, J. P., A Measuring Chamber

According to the Small Ion Accumulation Principle, for

Quantitative Detection of Aerosol Particles, Research

Report of the Province NordrheinWestfalen No. 2336,

West German Publishers, Cologne & Opladen (1973).

[8] Hasenclever, D., Concerning the Testing of Filters for

Eliminating Radioactive Aerosols, Staub-Reinhaltung

der Luft 19, No. 2 (1959).

[9] Draeger, H. and Draeger, B. , Draeger Mist Generators,

Construction Model VI Description, Draegerwerk, Lubeck

(1967) .

[10] Preliminary Guidelines for Testing Lifters to Eliminate

Suspended Materials, Staub-Reinhaltung der Luft 23,

No. 1 (1963).

[11] Riediger, G., Concerning the Utilization of the

Andersen-Cascade Impactor in Industrial Testing Technology for Hygiene, Especially to Determine the

Fraction Elimination Level, Staub-Reinhaltung der Luft

34, No. 8 (1974) .

USCOMM-NBS-DC

21
Figure 1. Relation between m and

y for monodisperse aerosols

22
d

T 1 1 1 ! 1 1 1 1 T 1 1 1 1 1 T

.8 1.0 1.2 1.4 1.6 1.8

I.E.N.T.

T.H. Aachen

Zusammenhang zwischen u und y

bci monodispersen Aerosolen flbb.-. 2j

K r 1975

Figure 2. Relation between u and y

for monodisperse aerosols

23
|xm

.

2. - in = 1.41 -i0.15

/ X

1.0; / X

Mie- Theorie

MeOwerte k x x

Measured Values

.5

x/

.3-

2-

0.1-

/ ' ' —1

1 1 1 1

1

1 1 1 ' 11

1

.5 1. 1.5

I.E.N.T.

T.H. Aachen

Ce/cJ als Funktion von d

flbb.. 3

Kr

19 7 5

Figure 3. C_/d as function of d

24
Figure 4. i/d as function of d

25
3.

2.

1. -

0.5 -

0.3

0.2 -

0.15 •

^ 2.5

^^"'^^^ 2.25

^^^^^^^^^^^^^^^

1.75

jyy^

/Xy''^\y^'^^ rn = 1.41- 10.15

//// / A«C^/d"

' 1 / / / ^.A. 1 r tin d/H /// / / PM)' ^ = exp{--——— j 11/ / y2TClnA d ' 2 InTV '

r 1 '1 ' ' ^

0.1 .2 .3 .A 0.5 .6 .7

I.E.N.T.

T.H.Aachen

A als Funktion von \ und A

Rbb -. b

Kr

1975

Figure 5. A as function of C and A

26
Figure 6. B as function of C and A

27
IE. NT Kennwertortskurven zur Bestimmung von Kr

T.H. Aachen I und A ^y^^, J

1975

Figure 7. Curves to locate characteristic

values, for the determination of C and A

28
p(d)

2.5

2.

1.5

1.

0.5

0

P(d)

%

p{d) =

Modusldj = 0. 24 tim

Median |dl = 0.3 \im

Mean |d} = 0.33 5 \xm

flr(log d) = 0.205

{in dj = 0.472

A = 1.2 5

y2n In A d

I.E.N.T.

T.H. Aachen

Parti kelgroflenvertei lung

eines Olnebels Bbb-"- 8

Kr

1975

Figure 8. Particle size distribution

of an oil mist

29
Kr

Messbereichsgrenzen 19 7 5

Rbb.-. 9

Figure 9. Limits of measuring range

30
10 -|- —

I

1 1—I I I r 1

1

1 I r—

Q .2 .3 .4 .7 ^ 2. 3. _L

Kr

Messbereichsgrenzen

Rbb.: AO

1975

Figure 10. Limits of measuring range

31
Figure 11. Limits of measuring range

32
NBS-114A (REV. 7-73)

U.S. DEPT. OF COMM.

BIBLIOGRAPHIC DATA

SHEET

1. PUBLICATION OR RIvPORT NO.

NBSIR 76-1037

2a Gov *r ArppQ^inn

No.

3. Rf^firMf^nt'c Afr'f*ccir»n NJi^

i TIT! F AND SUBTITI E

integral Measuremenu rroceaures lor

Determining Particle Size in Aerosols

5. Publication Date

May 1976

6. Performing Organization Code

7. AUTHOR(S)

F. J. Kraus

8. Performing Organ. Report No.

0 DpDPOnUTMn ORnAMI7ATinN NAMP AMD AHnRF^^

NATIONAL BUREAU OF STANDARDS

DEPARTMENT OF COMMERCE

WASHINGTON, D.C. 20234

10. Project/Task/Work Unit No.

4928677

11. Contract/Grant No.

12. Sponsoring Organization Name and Complete Address (Street, City, State, ZIP)

Same as No . 9

13. Type of Report & Period

Covered

Final Report

14. Sponsoring Agency Code

15. SUPPLEMENTARY NOTES

16. ABSTRACT (A 200-word or less factual suamary of moat significant information. If document includes a significant

bibliography or literature survey, mention it here.)

In assessing the performance of smoke detectors in the

laboratory, it is necessary to have standardized smoke measurement devices which function according to the same principles as

the smoke detectors under test. In developing these measurement devices, a need exists to determine, as precisely as

possible, the effects of the smoke characteristics on the

measurement devices. This paper presents the correlation

between smoke characteristics and comparative measuring devices

important in smoke detector test work and how these measuring

devices can also be used as aerosol measuring devices.

17. KEY WORDS (six to twelve entries; alphabetical order; capitalize only the first letter of the first key word unless a proper name; separated by semicolons) ^erosols; ionization chambers ; light attenuation;

scattered light; smoke detectors; test methods.

18, AVAILABILITY [X^ Unlimited 19. SECURITY CLASS

(THIS REPORT)

21. NO. OF PAGES

1

' For Official Distribution. Do Not Release to NTIS

UNCLASSIFIED 37

1

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Washington. D.C. 20402. SD Cat. No, C13

20. SECURITY CLASS

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22. Price

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USCOMM-DC 29042-P74