Correlation of the smoking tendency of materials

Fire Research, 1 (1977) 3 - 9 © Elsevier Sequoia S.A., Lausanne -- Printed in the Netherlands

3

Correlation of the Smoking Tendency of Materials

J. D. SEADER and S. S. OU Department of Chemical Engineering, University of Utah, Salt Lake City, Utah 84112 (U.S.A.) (Received February 26, 1976)

SUMMARY Physical aspects of smoke produced in an NBS Aminco Smoke-density Chamber are considered. A theory based on light scattering, light absorption, and particulate coagulation is developed in detail and calculated results are presented to relate the optical density to particulate size and mass concentration. Both flaming and nonflaming modes of material degradation are treated. The theory involves the particulate optical density (POD), a smoke parameter which is the ratio of the optical density per unit length of light path to the particulate mass concentration. Values of POD calculated theoretically for each mode do not vary widely and are in good agreement with measured values for a number of different natural and synthetic polymers. Separate correlations of POD for the two modes enable the prediction of specific optical density provided that particulate mass concentration is known or can be estimated.

INTRODUCTION The NBS Aminco Smoke-density Chamber [1] is the most widely accepted apparatus for characterizing the smoke-generation tendency of materials. A sample can be subjected to either nonflaming (smoldering) or flaming conditions. The smoke produced is generally confined to the chamber space and light obscuration is measured as a function of time until a maximum is attained. The data m a y be reported in terms of any one of several smoke parameters with specific optical density being the most common:

Ds =-

log10

(1)

whereDs is the specific optical density, V the

chamber volume, A the exposed area of sample, L the length of light path and T the percent light transmittance. An important aspect of the specific optical density is its scientific basis in radiative transport theory. Seader and Chien [2] applied this theory to produce a smoke development model for predicting specific optical density from particulate mass concentration and particulate properties. The most important particulate property is the size (diameter or radius), which can be estimated from coagulation theory. This paper presents a comparison of calculations based on the smoke model to experimental data obtained on a variety of natural and synthetic polymers with the NBS Aminco Smoke-density Chamber.

LIGHT SCATTERING AND ABSORPTION THEORY In the NBS Aminco chamber, a collimated beam of light is passed vertically up through a gas containing particulate matter. The initial light intensity is attenuated by light scattering and/or absorption phenomena. If the following assumptions are made: (1) monochromatic light source; (2) uniform, stable, and monodisperse particulate system of spherical particles or droplets; (3) independent and single scattering; then, from equations given by Chien and Seader [3] the optical density is: D = - l o g \(100)T =0"651XCSLpp-~

(2)

w h e r e D is the optical density, X the efficiency factor for scattering and absorption, C s the particulate mass concentration, pp the particulate density, and d the particulate diameter. It is convenient to utilize the particulate optical density (POD) defined by Seader and Chien [2] as

(D/L)

POD -- ~

(3)

C~

Combining eqns. (2) and (3) gives POD -

o

(4) Pp Equation (3) can be used to c o m p u t e values of POD from experimental measurements of D/L and C~. Equation (4) permits theoretical estimations of POD from the efficiency factor for light scattering and absorption and the particulate properties pp and d. The efficiency factor, X, depends upon (1) the complex refractive index, n; (2) diameter, d, of the particulates; and (3) the wavelength of the light beam, X, and is given quantitatively by the Mie theory [4]. For spherical particles that scatter and/or absorb light, X=~-~

~

(2m+l) Re(a,,+b",}

(5)

",=1

where a is the particle size parameter (= 7rd/k), m is an integer, Re is the real part of a complex value, +

Am

-

Re(W",}--Re{W",_1} , (7)

m

+

--A",_

1

1-1

(8)

,

nol

Ao -

(X S is the efficiency factor for scattering). Suppose the wavelength of the light is 0.547 pm (this wavelength was used in experiments by Chien and Seader [3] and is a reasonable average for white light); then calculations using eqns. (5) - (13) give the curves shown in Fig. 1. For wavelengths less than 0.547 um the curves shift to the left, since

, (6)

(nA",+ m) =

X=Xs

Re(Win} -- Re{Win-l}

a", =

Dr,,

Equations (5) - (13) are readily programmed for computation on a digital computer. For small values of a (< 1), convergence of the infinite series given by eqn. (5) is fairly rapid. For larger values of a, m a n y terms in eqn. (5) may be required for adequate convergence. In eqns. (6) and (7), values of A,, and W", are calculated recursively from eqns. (8) - (12). Smoke generated in the nonflaming mode is composed generally of liquid droplets that do n o t absorb light. For nonabsorbing chemical species, the refractive index has only a real part that varies from 1.4 to 1.5 and represents light scattering; thus,

sin p cos p + i sinh q cosh q sin2p + sinh 2 q

•

,

(9)

(10 \

O~

]

Wo = sin a + i cos a,

(11)

W_x = cos a -- i sin a,

(12)

i = imaginary number = x / - ~ , and p and q are obtained from na = p -- iq.

(13)

a sl~ift to the right occurs for h > 0.547 pm. For carbon soot particles, typical of smoke produced by the flaming mode, both absorption and scattering are important. For amorphous carbon the equation of Stull and Plass [5] gives a complex refractive index of 1.79 -0.79 i for a wavelength of 0.547 pm. Tien, Doornink, and Rafferty [6] preferred to use a complex refractive index at 0.547 ~m of 1.5 -- 0.5 i based on soot containing some hydrogen as obtained from burning propane. Unfortunately, accepted data on the complex refractive index of soot from burning of polymeric materials are not available. It might be expected that soot from the burning of polymeric materials, with a H/C ratio between that of amorphous carbon and propane, might have a refractive index between the two values cited above. Curves of efficiency for light extinction based on these two complex refractive indices are shown in Fig. 2 as computed from eqns. (5) - (13). Again, the curves shift to the left and to the right for values of less than and more than 0.547 pm, respectively.

I

I

=~

I

I

n=15

~

"~

X"~

~l/lllllltllN =1.4 2

~k= 0.547p.

~'%~

/

l 1/I I

Oq

I

0.2

I

0.4

I

0.6

0.8

1.0

DROPLETDIAMETER(micron) Fig. 1. Light scattering efficiency factor for nonabsorbing spherical particles. 14

12

I

t

I

~

I

~.=0.547~

I0

n = 1.79 -0.79i

4

2

0

0

I

0.2

I

0.4

I

0.6 PARTICLEDIAMETER(micron)

I

0.8

1.0

Fig. 2. Efficiency factor for light attenuation by spherical soot particles. COAGULATION THEORY

The modified biparticle collision theory of Smoluchowski [7] can be applied to estimate particulate diameter. The relation is [2] [ 6KCst] 1/3 d = d30 + (14)

ent values of p, at an aging time of five minutes. Over the three-fold range of Cs shown, particulate diameters range from somewhat more than 0.1 pm to somewhat more than 1.0/~m. Plots similar to Fig. 3 are readily prepared for other assumed aging times.

~Pp

where d o is the initial diameter of particulate, K = 3.06 × 10 -8 cmS/min, and t is the aging time. Assume d o < 0.05 pm. After approximately two minutes, particulate diameter, d, changes only slowly with aging time. Figure 3 is a plot of particulate diameter as a function of particulate mass concentration, C~, for several differ-

THEORETICAL PREDICTIONS OF PARTICULATE OPTICAL DENSITY

Figures 1 and 2 can be used in conjunction with eqns. (4) and (14) to predict values of POD for various conditions of particulate concentration and aging time. Calculated curw.~ for the nonflaming mode with nonabsorbing

I01 d o < O.05micron t = 5rain

2

.o E nhi I" I,U I0C ~E

pp = 1.0 g/cm 3 - - x

pp 2

0

g

/

c

m

3

~

,

,

1,1.1 .J t-

. , ....

I0 -I

I01

L

,

,

,

I ....

102

I

,,

103

... 104

PARTICULATE CONCENTRATION (rnglrn 3)

Fig. 3. Predicted values of particle diameter by coagulation theory.

tO5

~,o"j

----

/ / "

~,-,~g/cm~

// ///

~03

I01

/

~

102

103

I0 4

P A R T I C U L A T E CONCENTRATION (rng/rn 3)

Fig. 4. Theoretical curves of particulate optical density for nonabsorbing particles at an ageing time of five minutes.

d r o p l e t s are s h o w n in Fig. 4 f o r p a r t i c u l a t e densities o f 1.0 a n d 1.5 g / c m 3 a n d f o r refractive indices o f 1.4 t o 1.5 a t an aging t i m e o f five m i n u t e s . T h e e f f e c t o f t i m e is s h o w n in Fig. 5. A f t e r t h e first few m i n u t e s P O D increases o n l y slowly w i t h t i m e . For the flaming mode, assuming a density o f 2.0 g / c m 3 f o r c a r b o n a c e o u s s o o t particles, c a l c u l a t e d curves o f P O D are s h o w n in Fig. 6 for t w o d i f f e r e n t c o m p l e x r e f r a c t i v e indices a n d an aging t i m e o f five m i n u t e s . T h e e f f e c t o f aging t i m e s h o w n in Fig. 7 is r e l a t i v e l y small, and POD can a c t u a l l y d e c r e a s e w i t h time.

EXPERIMENTAL DATA FOR POD E x p e r i m e n t a l values o f P O D m a y be determ i n e d f r o m eqn. (3) w h e n m e a s u r e m e n t s o f D/L a n d C s are available. S u c h m e a s u r e m e n t s have b e e n r e p o r t e d b y King [8] and Chien a n d S e a d e r [3, 9] using NBS S m o k e - d e n s i t y C h a m b e r s o p e r a t i n g at 2.5 W / c m 2. A d d i t i o n a l d a t a w e r e o b t a i n e d as p a r t o f t h e s t u d y rep o r t e d h e r e using t h e e x p e r i m e n t a l t e c h n i q u e discussed b y Chien a n d S e a d e r [ 3 ] . T h e d a t a o f all t h r e e investigations are p r e s e n t e d as p l o t s of D/L as a f u n c t i o n o f C s in Fig. 8 f o r t h e n o n f l a m i n g and f l a m i n g m o d e s , respectively.

105

i

i

,

,

i

I

n =1.5~__.

E iO4

£3 0 (1.

//

i0 3

/

NON-ABSORBING AEROSOL

///

Pp= l~glcm3

/

- --'-..... I 2

0

I 4

I I 6 8 T I M E (minutes)

(a)

Cs = 50rng/m 3 Cs = IOOmg/m 3 Cs = 5 0 0 m g / r n 3 I I0

I 12

105

n = 1.5--~_.

¢J

~

// 104

/../

. ---"*"

.~"

//

/" 0.

/" /

"

f

//

:/// /

~ /

NONFLAMING MODE NON-ABSORBING AEROSOL pp = i.Sg/cm 3

k__n=l. 4 .....

J," / I0 3 0

C= - 5Omgl m3 I 2

..... I I 6 8 T I M E (minutes)

I 4

(b)

C s , IOOmg/m s C, • 500rag/m s I I I0 12

14

Fig. 5. Effect of aging time on particulate optical density for nonabsorbing particles of 1.0 specific gravity (a) and 1.5 specific gravity (b), respectively. IO5

I

....

I

FLAMING MODE CARBONACEOUS SOOT

O D.

i0'101

*

J

,

I

,

,

~ ~ I 102

,

,

,

I

, 103

P A R T I C U L A T E C O N C E N T R A T I O N ( m g / m 3)

Fig. 6. Theoretical curves of particulate optical density for soot particles at an aging time of five minutes.

The data in Fig. 8(a) include various w o o d s and synthetic polymers covering a wide particulate concentration range of 25 to 2,750 mg/m a. Depending on the particulate density, Fig. 3 for an aging time of five minutes indi-

cates a corresponding predicted particulate diameter range from 0.17 to 0.93 pm. The experimental data in Fig. 8(a) are correlated reasonably well by the single solid line, whic5 represents a least-squares fit of the data to a

i

105

,

i

,

i

q

n = 1.79 - 0 . 7 9 i

-

. . . . .

E

.

n= 1.5-0.5i

104 __

.

.

-.

J

C3 0

F L A M I N G MODE C A R B O N A C E O U S SOOT pp = 2 . 0 g / c m 3

I03

I 2

0

I 4

Cs = 5 0 r a g / m

----

Cs = I O O m g / m S

.....

Cs = 5 0 0 m g / m

l

I 6

I I0

8

TIME

F i g . 7.

- -

3 3 I 12

14

(minutes)

Effect o f aging time o n particulate optical d e n s i t y for s o o t particles.

401

I01

• l .... I

" '

....

I

/

"J"

/

_J ~

I0 C

I00

I-t,g

=E

)

I--

j ~

Z W

v/"

~

L

v,¢,

I'--

xF:L2. ~ G t s / e r a 2

MODE FLAMING HEAT FLUX : 2.Swo1ts/cm 2

5 ASS

_1 ~ I0 °q I.-0

¢.) IC

"

~G~/~ ~0~/" V

/g/.

o /

"

o

;• VINYL ::X.ooo URETHANE • . . . . . . . .

I0-~101

-

_~

~ ALPHA CELLULOSE ID OOUSLAS Fm

i 102

,

RIGID URETHANE ALPHA CELLULOSE

p OOU~AS~,R 103

I0

PARTICULATE CONCENTRATION (mg/m 3)

(a)

.

I01

104

. I . .

.

L . . I0 z

PARTICULATE

A

RIGID PVC

o

PLAST'C,ZEOPvc

~ RED OAK • POLYSTYRENE DATA OF CHiEN AND SEADER IR ALPHA CELLULOSE DATA OF THIS WORK • RIGID URETHANE • VINYL URETHANE • DOUGLASFIR . [ .... I I 103 CONCENTRATION

(mg/m

i •

.. 104

3)

(b)

Fig. 8. Correlation o f e x p e r i m e n t a l data on particulate optical d e n s i t y for n o n f l a m i n g m o d e (a) and flaming m o d e ( b ) , respectively.

POD value of 19,000 cm2/g. This value is close to the value of 17,000 cm2/g suggested by Seader and Chien [ 2 ] . The experimental data in Fig. 8(a) correspond to a POD range from approximately 8,000 to 32,000 cm2/g. This range is not significantly different from the ranges covered in Fig. 5 for aging times greater than a few minutes. Thus, experiment and theory are in reasonably good agreement for the assumed ranges of particulate density and refractive index. Figure 8(b) for the flaming mode includes data for two woods and several synthetic poly-

mers covering a particulate concentration range of 15 to 500 mg/m a. For a particulate density of 2.0 g/cm a, Fig. 3 indicates a corresponding predicted particulate diameter range from 0.12 to 0.42 pm. The experimental data are correlated reasonably well by the single solid line, which represents a least-squares fit of the data to a POD value of 33,000 cm2/g. Seader and Chien [2] suggested a value of 8,000 cm2/g based on a value of 1.5 -- 0.5 i for the refractive index and a particulate diameter of 1.0 pm. It is n o w believed that particulate diameters are more typically less than 0.5 pm as indicated in Fig. 3. Correspondingly,

as s h o w n in Fig. 7, P O D values are m u c h g r e a t e r t h a n 8 , 0 0 0 cm2/g. T h e e x p e r i m e n t a l d a t a in Fig. 8 ( b ) corres p o n d t o a P O D range f r o m a p p r o x i m a t e l y 2 6 , 0 0 0 to 4 2 , 0 0 0 cm2/g. This range is m u c h n a r r o w e r t h a n the d a t a s p r e a d in Fig. 8(a) and is c o n s i s t e n t w i t h t h e relatively n a r r o w range o f t h e o r e t i c a l P O D values s h o w n in Fig. 7, w h e r e t h e curves c o v e r a range o f 1 6 , 0 0 0 t o 4 2 , 0 0 0 cm2/g. Again, a g r e e m e n t b e t w e e n exp e r i m e n t a n d t h e o r y is r e a s o n a b l y g o o d . T h e c o r r e l a t i o n s o f e x p e r i m e n t a l d a t a given in Fig. 8 e n a b l e t h e p r e d i c t i o n o f specific optical d e n s i t y f o r a given g e o m e t r i c a l configur a t i o n , p r o v i d e d t h a t p a r t i c u l a t e mass c o n c e n t r a t i o n is k n o w n or can be e s t i m a t e d .

ACKNOWLEDGEMENTS T h e s t u d y r e p o r t e d h e r e was s u p p o r t e d b y Grants GI-33650 and ENV72-03406 A06 from the N a t i o n a l Science F o u n d a t i o n u n d e r its R A N N p r o g r a m . G r a t i t u d e is e x p r e s s e d to P r o f e s s o r I. N. E i n h o r n o f t h e U n i v e r s i t y o f U t a h f o r his i n t e r e s t a n d e n c o u r a g e m e n t . T h e NBS S m o k e - d e n s i t y C h a m b e r was m a d e available f o r o u r use b y t h e A m e r i c a n I n s t r u m e n t Company (AMINCO) through Samuel Greenberg. The synthetic polymeric materials

used in the tests w e r e supplied b y A r a p a h o e Chemicals, Inc., t h r o u g h R o d Legg. REFERENCES 1 T. G. Lee, Interlaboratory evaluation of smoke density chamber, NBS Tech. Note 708, U.S. Government Printing Office, Washington, D. C., December 1971. 2 J. D. Seader and W. P. Chien, Physical aspects of smoke development in an NBS Smoke-density Chamber, J. Fire Flammabil., 6 (1975) 294. 3 W. P. Chien and J. D. Seader, Predictions of specific optical density for smoke obscuration in an NBS Smoke-density Chamber, Fire Technol., 11 (3) (1975) 206. 4 H. C. Van de Hulst, Light-Scattering by Small Particles, Wiley, New York, 1957. 5 V. R. Stull and G. N. Plass, Emissivity of dispersed carbon particles, J. Opt. Soc. Am., 50 (2) (1960) 121 6 C. L. Tien, D. G. Doornink and D. A. Rafferty, Attenuation of visible radiation by carbon smokes, Comb. Sci. Tech., 6 (1972) 55. 7 H. L. Green and W. R. Lane, Particulate Clouds: Dust, Smokes and Mists, Van Nostrand, New York, 2nd edn., 1964. 8 T. Y. King, Empirical relationships between optical density and mass density of smoke, J. Fire Flammabil., 6 (1975) 222. 9 W. P. Chien and J. D. Seader, Smoke measurement in a modified NBS Smoke-density Chamber, FRC/UU-44, UTEC 75,055, Flammability Research Center, University of Utah, Salt Lake City, Utah (April 14, 1975).