The Chemistry of Combustion Processes - American Chemical Society

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2 Quantitative Chemical Mechanism for Heterogeneous Growth of Soot Particles in Premixed Flames STEPHEN J. HARRIS Physical Chemistry Department, General Motors Research Laboratories, Warren, MI 48090

In this article we present the first quantitative chem­ ical mechanism for the heterogeneous growth of soot particles in premixed flames. We have found that the increased surface growth rate in sootier (richer) flames is due primarily to an increase in the surface area available for growth; the concentration of the gas phase growth species is similar from flame to flame. Growth decreases as the soot ages in the flame, but this is due to a decrease in the reac­ tivity of the soot and not to a depletion of growth species. Acetylene supplies nearly all of the mass for soot growth, and our data suggest that soot growth can be understood in terms of a first order decomposition reaction of acetylene on the soot surface. Soot f o r m a t i o n i n p r e m i x e d f l a m e s may b e d i v i d e d i n t o p a r t i c l e i n c e p t i o n ( " n u c l e a t i o n " ) and growth s t a g e s ( 1 ) . I n t h e n u c l e a t i o n s t a g e t i n y (1-2 nm) s o o t p a r t i c l e s a r e c r e a t e d , w h i l e d u r i n g the g r o w t h s t a g e t h e s o o t p a r t i c l e s c o a l e s c e and a l s o a c c r e t e h y d r o c a r b o n m o l e c u l e s ("growth s p e c i e s " ) f r o m t h e b u r n e d g a s e s . These g r o w t h s p e c i e s r e a c t c h e m i c a l l y w i t h a n d become i n c o r p o r a t e d i n t o t h e s o o t p a r t i c l e s i n a h e t e r o g e n e o u s p r o c e s s known a s s u r f a c e growth, and they account f o r n e a r l y a l l t h e f i n a l soot mass. G r e a t e f f o r t s h a v e b e e n made t o w a r d s u n d e r s t a n d i n g s o o t n u c l e a t i o n , and a number o f mechanisms h a v e b e e n p r o p o s e d ( 1 ) ; however, no c o m p a r a b l e e f f o r t h a s b e e n made t o w a r d s u n d e r s t a n d i n g s u r f a c e growth. I n t h i s a r t i c l e we p r o p o s e t h e f i r s t q u a n t i t a t i v e c h e m i c a l mechanism o f s o o t p a r t i c l e s u r f a c e g r o w t h i n p r e m i x e d f l a m e s . A more d e t a i l e d a c c o u n t o f t h i s w o r k w i l l b e p u b l i s h e d elsewhere ( 2 ) .

0097-6156/ 84/ 0249-0023506.00/ 0 © 1984 American Chemical Society

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Experimental Premixed flames of and a 79-21 m i x t u r e o f A r and 0^ were s t a b i l i z e d on a w a t e r - c o o l e d p o r o u s p l u g b u r n e r w i t h a n i t r o g e n shroud. B e c a u s e t h e f l a m e s were n e a r l y 1 - d i m e n s i o n a l , m e a s u r e ments made as a f u n c t i o n o f h e i g h t above t h e b u r n e r c o u l d be c o n v e r t e d i n t o measurements made as a f u n c t i o n o f t i m e f r o m knowl e d g e o f t h e h o t gas v e l o c i t y . S o o t was d e t e c t e d u s i n g s t a n d a r d R a y l e i g h s c a t t e r i n g and e x t i n c t i o n t e c h n i q u e s (3,4) u s i n g an a r g o n l a s e r , a l l o w i n g sc^ot number ^ d e n s i t y , mean p a r t i c l e d i a m e t e r , and volume f r a c t i o n (cm - s o o t / cm - f l a m e ) t o be d e t e r m i n e d . A l l measurements w e r e made f a r downstream f r o m t h e s o o t n u c l e a t i o n zone (The s m a l l e s t p a r t i c l e s d e t e c t e d had d i a m e t e r s o f a b o u t 8 nm.) i n a r e g i o n o f t h e f l a m e where r a d i c a l c o n c e n t r a t i o n s had d r o p p e d t o t h e i r e q u i l i b r i u m v a l u e s (5) and where s o o t g r o w t h was the main chemical process o c c u r r i n g . Temperatures, determined f r o m t h e b r i g h t n e s s and e m i s s i v i t y o f t h e s o o t , v a r i e d m a i n l y b e t w e e n 1650 and 1750 K. Samples o f b u r n e d g a s e s were c o l l e c t e d w i t h a w a t e r - c o o l e d q u a r t z m i c r o p r o b e and b a t c h a n a l y z e d f o r CO, CO^, C^H^, and CH. w i t h IR and mass s p e c t r o m e t r y . In the r e g i o n o f t h e f l a m e e x a m i n e d , A r , CO, C0«, H^, and H^O made up a b o u t 97% o f t h e gas p h a s e m a t e r i a l ; C o 2 ' CH^, and t r a c e amounts o f o t h e r h y d r o c a r b o n s made up t h e r e s t . S o o t and c o n d e n s a b l e hydrocarbons ( " v o l a t i l e s " ) w e r e c o l l e c t e d on a w a t e r - c o o l e d p l a t e and s u b j e c t e d t o t h e r m o g r a v i m e t r i c , e l e m e n t a l , and B.E.T. s u r f a c e a r e a analysis (B.E.T. a n a l y s i s d e t e r m i n e s t h e s u r f a c e a r e a o f f i n e l y d i s p e r s e d p a r t i c l e s by m e a s u r i n g t h e amount o f a d s o r b e d on t h e p a r t i c l e s a t 77 K.) H

Results Two d y n a m i c a l p r o c e s s e s o c c u r i n t h e b u r n e d gas r e g i o n o f p r e m i x e d f l a m e s ( 4 ) . F i r s t , s m a l l s p h e r i c a l s o o t p a r t i c l e s c o l l i d e and c o a l e s c e i n t o l a r g e s p h e r i c a l p a r t i c l e s , a process which reduces t h e t o t a l amount o f s u r f a c e a r e a w i t h o u t c h a n g i n g t h e t o t a l mass. The s e c o n d p r o c e s s i s s u r f a c e g r o w t h , w h i c h a c c o u n t s f o r an i n c r e a s e i n t h e t o t a l s o o t mass and adds s u r f a c e a r e a . The n e t e f f e c t i s t h a t w h i l e t h e number d e n s i t y f a l l s ajnd t h e mean d i a m e t e r r i s e s , t h e t o t a l s o o t s u r f a c e a r e a p e r cm o f f l a m e , meas u r e d o p t i c a l l y , changes v e r y l i t t l e as t h e s o o t a g e s . These e f f e c t s a r e d i s p l a y e d i n F i g u r e s 1 and 2. However, F i g u r e 2 shows t h a t t h e r e i s a s t e e p i n c r e a s e i n t h e s o o t s u r f a c e a r e a as t h e f l a m e s become r i c h e r . Curves i n the upper p a r t of F i g u r e 3 show s o o t volume f r a c t i o n s f o r f i v e f l a m e s w i t h d i f f e r e n t C/0 ( c a r b o n / o x y g e n ) r a t i o s as a f u n c t i o n o f t i m e ( s o o t a g e ) . A l l o f t h e i n c r e a s e i n mass i n e a c h f l a m e i s a t t r i b u t e d t o s u r f a c e growth. To o b t a i n s u r f a c e g r o w t h r a t e s we d i f f e r e n t i a t e t h e v o l u m e f r a c t i o n c u r v e s , c o n v e r t i n g v o l u m e t o mass u s i n g a d e n s i t y o f 1.8 g/cm . A l t h o u g h a l l t h e c u r v e s a p p e a r t o h a v e s i m i l a r s l o p e s

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Ε Λ 20 Β CD Ε CO Û V 10

c ω Ω k_ ω _Ω

Ε D Ζ

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F i g u r e 1. Mean d i a m e t e r a n d s o o t p a r t i c l e d e n s i t y as a f u n c t i o n o f t i m e ( h e i g h t above t h e b u r n e r ) f o r a t y p i c a l f l a m e .

1.4 1.2 CO Ε ο 1.0 \ ο ο 0.8

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2 3 Figure 2. T o t a l s o o t s u r f a c e a r e a (π < d > N) p e r cm o f f l a m e . The s y m b o l s r e f e r t o t h e s t o i c h i o m e t r y : ·, -C/0 = Ο . 7 6 ; , -0.82; and • , - 0 . 9 Λ . (Reproduced w i t h p e r m i s s i o n from R e f . 2 . Copy­ r i g h t 1 9 8 3 , Gordon a n d B r e a c h . ) m

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Figure 3. T o p , s o o t volume f r a c t i o n s f o r f l a m e s w i t h t h e ^ i n d i c a t e d C/0 r a t i o s ; a n d b o t t o m , s u r f a c e g r o w t h r a t e s p e r cm o f s o o t surface. (Reproduced w i t h p e r m i s s i o n from Ref. 2. C o p y r i g h t 19Ô3, Gordon and B r e a c h . )

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when p l o t t e d o n s e m i - l o g p a p e r , t h e d e r i v a t i v e s a r e a c t u a l l y q u i t e d i f f e r e n t a n d i n c r e a s e v e r y s u b s t a n t i a l l y w i t h t h e C/0 ratio. However, o f more f u n d a m e n t a l i n t e r e s t t h a n t h e t o t a ] , g r o w t h r a t e ( g / s ) i s t h e s p e c i f i c s u r f a c e g r o w t h r a t e (g/cm - s ) , which takes i n t o account the greater s u r f a c e area a v a i l a b l e f o r growth i n the r i c h e r ( s o o t i e r ) flames ( F i g u r e 2 ) . S p e c i f i c s u r f a c e g r o w t h r a t e s , p l o t t e d i n t h e l o w e r h a l f o f F i g u r e 3, v a r y r e l a t i v e l y w e a k l y w i t h C/0 r a t i o compared t o t h e t o t a l s u r f a c e growth r a t e s . Discussion In o r d e r t o i n t e r p r e t t h e s u r f a c e growth r e s u l t s we assume t h a t s u r f a c e g r o w t h i s d e s c r i b e d b y dM/dt = S Σ k . [

j

g i

] i

quantitatively,

(1)

where M i s t h e scjot mass c o n c e n t r a t i o n , S i s t h e t o t a l s o o t s u r ­ f a c e a r e a p e r cm o f f l a m e , [ g . ] i s t h e m o l e f r a c t i o n o f t h e i ' t h g r o w t h s p e c i e s , k^ i s t h e r a t e c o n s t a n t f o r t h e s u r f a c e r e a c t i o n w h i c h c o n v e r t s g. i n t o s o o t , a n d j . i s t h e r e a c t i o n o r d e r . The f a c t t h a t t h e s p e c i f i c s u r f a c e g r o w t h r a t e s ( 1 / S ) dM/dt a r e s i m i ­ l a r i n flames w h i c h have v e r y d i f f e r e n t t o t a l growth r a t e s and w h i c h p r o d u c e v e r y d i f f e r e n t amounts o f s o o t a l l o w s u s t o p l a c e s e v e r a l s i g n i f i c a n t c o n s t r a i n t s on the growth process and on the s u r f a c e growth s p e c i e s . ( i ) S u r f a c e g r o w t h i s much f a s t e r i n r i c h e r f l a m e s p r i m a r i l y b e c a u s e t h e r e i s more s u r f a c e a r e a a v a i l ­ a b l e f o r growth; thus, growth s p e c i e s c o n c e n t r a t i o n s a r e s i m i l a r i n the d i f f e r e n t flames. ( i i ) Growth r a t e s f a l l s t e e p l y as t h e s o o t a g e s , b u t t h i s f a l l i s n o t due t o d e p l e t i o n o f t h e g r o w t h species. The r e a s o n i s t h a t i f t h e [ g . ] a r e r o u g h l y i n d e p e n d e n t o f t h e s t o i c h i o m e t r y , a n d i f t h e y a r e èigh enough t o s u p p l y a l l o f t h e mass i n c r e a s e i n t h e r i c h e s t f l a m e , t h e n t h e r e must b e a n e x c e s s o f them i n a l l t h e l e a n e r f l a m e s , where t h e i n c r e a s e i n s o o t mass i s much l e s s . S i n c e the s p e c i f i c growth r a t e i n t h e r i c h e s t f l a m e i s a l m o s t t h e same a s i n t h e l e a n e r f l a m e s , t h e r e i s a l s o no d e p l e t i o n o f g r o w t h s p e c i e s i n t h e r i c h e s t f l a m e , ( i i i ) From t h e t o t a l amount o f s o o t mass p i c k e d up i n t h e r i c h e s t f l a m e , we c a l c u l a t e t h a t e i t h e r t h e g r o w t h s p e c i e s m o l e f r a c t i o n s t o t a l more t h a n 0.1/W, where W i s t h e (mean) m o l e c u l a r w e i g h t o f t h e g r o w t h s p e c i e s , o r t h a t t h e y a r e i n r a p i d (compared t o r e a c t i o n w i t h soot) e q u i l i b r i u m w i t h a r e s e r v o i r o f other species whose m o l e f r a c t i o n s t o t a l more t h a n 0.1/W. Among t h e h y d r o c a r bons i n t h e b u r n e d g a s e s , o n l y methane a n d a c e t y l e n e h a v e m o l e fractions that high. ( i v ) The y o u n g e s t s o o t p a r t i c l e s t h a t we d e t e c t h a v e d i a m e t e r s o f a b o u t 8 nm and m o l e c u l a r w e i g h t s w e l l above 100,000 b u t c o n t a i n o n l y o f t h e o r d e r o f 10 n u c l e i ( 6 , 7 ) . Thus t h e y a r e composed a l m o s t e n t i r e l y o f g r o w t h s p e c i e s . Since t h e r e i s no o b v i o u s way b y w h i c h t h e y o u n g g r o w i n g p a r t i c l e s c a n l o s e p u r e c a r b o n , t h e C/H ( c a r b o n / h y d r o g e n ) r a t i o o f t h e g r o w t h

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s p e c i e s c a n n o t be h i g h e r t h a n t h a t o f t h e young s o o t , a b o u t 2 t o 2 . 5 ( 3 ) . (As t h e s o o t ages i t s C/H r a t i o i n c r e a s e s t o a b o u t 8 (3).) To i d e n t i f y t h e g r o w t h s p e c i e s , we c o n s i d e r w h i c h h y d r o c a r bons i n t h e p o s t f l a m e g a s e s s a t i s f y t h e above c o n s t r a i n t s . The v o l a t i l e m a t e r i a l may e a s i l y be e l i m i n a t e d . F o r e x a m p l e , i t s c o n c e n t r a t i o n i s a b o u t 100 t i m e s h i g h e r i n b e n z e n e f l a m e s t h a n i n flames of a l i p h a t i c f u e l s ( 8 ) , but the growth r a t e s are n e a r l y i d e n t i c a l ( 9 ) . A l s o , t h e r e i s a l w a y s much l e s s v o l a t i l e m a t e r i a l t h a n s o o t i n t h e f l a m e ( 3 ) , so t h e r e c a n n o t be enough o f i t ( c o n s t r a i n t s ( i i ) and ( i i i ) ) t o a c c o u n t f o r t h e l a r g e i n c r e a s e i n s o o t mass w i t h age. P o l y a c e t y l e n e s (C,H to C H have been o b s e r v e d ) a r e e q u i l i b r a t e d w i t h a c e t y l e n e i n f l a m e s ( 1 0 ) . Bonne e t a l . (10) and Homann and Wagner (8) a r g u e d t h a t t h e l a r g e s t o f t h e s e a r e r e s p o n s i b l e f o r most o f t h e s u r f a c e g r o w t h , b u t t h e i r a r g u m e n t s were o n l y c o r r e l a t i o n s and w e r e t h e r e f o r e n o t c o n v i n c i n g . In f a c t , t h e e v i d e n c e shows t h a t t h e y a r e n o t i m p o r t a n t . For example, except f o r d i a c e t y l e n e ( C ^ t ^ ) , a l l of the p o l y a c e t y l e n e s v i o l a t e c o n s t r a i n t ( i v ) . Furthermore, i n order f o r the h i g h e r p o l y a c e t y l e n e s t o be as i m p o r t a n t as C^H^, their w o u l d h a v e t o be s u b s t a n t i a l l y h i g h e r s i n c e t h e i r c o n c e n t r a t i o n s a r e so much l o w e r (10). However, T e s n e r has f o u n d (11) t h a t i n any homologous s e r i e s o f h y d r o c a r b o n s an i n c r e a s e i n m o l e c u l a r w e i g h t l e a d s t o o n l y a " t i n y " i n c r e a s e i n the s u r f a c e growth r a t e s . Finally, deep i n t h e p o s t f l a m e g a s e s f a r b e y o n d t h e n u c l e a t i o n z o n e , o x y g e n has b e e n consumed and C^H^ w i l l be f o r m e d f r o m C^H^ by t h e p y r o l y s i s mechanism m o d e l l e d by Tanzawa and G a r d i n e r Î12)· F o r t h e r i c h e r f l a m e s t h e m o d e l g i v e s a C^H^ f o r m a t i o n r a t e o n l y 20% o f t h e peak m e a s u r e d r a t e o f s o o t f o r m a t i o n . This r e s u l t means t h a t d i a c e t y l e n e c a n n o t be r e s p o n s i b l e f o r s u r f a c e g r o w t h , s i n c e t h e e q u i l i b r i u m r e a c t i o n s c o n n e c t i n g C2H2 and C^H w o u l d be too slow to prevent d i a c e t y l e n e from b e i n g d e p l e t e d , v i o l a t i n g c o n s t r a i n t s ( i i ) and ( i i i ) . Even i f t h e m o d e l w e r e n o t a c c u r a t e enough t o e l i m i n a t e d i a c e t y l e n e on t h i s b a s i s a l o n e , i t a l s o makes an i m p o r t a n t q u a l i t a t i v e p r e d i c t i o n . I f d i a c e t y l e n e i s i m p o r t a n t l y i n v o l v e d i n soot growth, then d e s t r u c t i o n of d i a c e t y l e n e on t h e s o o t s u r f a c e w i l l s u b s t a n t i a l l y p e r t u r b t h e v a l u e o f t h e e q u i l i b r i u m r e l a t i o n s h i p b e t w e e n a c e t y l e n e and d i a c e t y l e n e , R = [ C , H ] [ H ] / [ C H ] . However, v a l u e s o f R measured i n h e a v i l y s o o t i n g (10) and i n n o n s o o t i n g (13) f l a m e s were e s s e n t i a l l y i d e n t i c a l , i m p l y i n g t h a t s u r f a c e growth i s i n f a c t a n e g l i g i b l e sink for C,H~. 2

2

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O n l y C j L and CH a r e p r e s e n t a t h i g h enough c o n c e n t r a t i o n to s a t i s f y c o n s t r a i n t ( i i i ) . However, g i v e n methane's c o n c e n t r a t i o n and t h e f a c t t h a t methane and a c e t y l e n e a r e n o t e q u i l i b r a t e d i n t h e f l a m e s ( 1 3 ) , CH, c o u l d n o t p r o v i d e a m a j o r f r a c t i o n o f t h e m a t e r i a l f o r soot growth w i t h o u t b e i n g s u b s t a n t i a l l y d e p l e t e d , v i o l a t i n g c o n s t r a i n t ( i i ) and c o n t r a d i c t i n g o u r c o n c e n t r a t i o n m e a s u r e m e n t s . T h u s , methane i s n o t i m p o r t a n t f o r s u r f a c e g r o w t h .

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( S i m i l a r l y , v i n y l a c e t y l e n e c o u l d not be important s i n c e i t t o o i s n o t e q u i l i b r a t e d w i t h a c e t y l e n e (13).) Therefore, whether o r n o t ^2^2 ^ - ^ a c t u a l l y decomposes o n t h e s o o t s u r f a c e , c o n s e r ­ v a t i o n o f mass r e q u i r e s t h a t p r a c t i c a l l y a l l o f t h e s o o t mass i s p r o v i d e d , d i r e c t l y o r i n d i r e c t l y , by the a c e t y l e n e i n the burned gases. I t remains t o determine whether s u r f a c e growth c a n be f u l l y a c c o u n t e d f o r by d i r e c t d e c o m p o s i t i o n o f C^R^. Bonne e t a l . ( 1 0 ) a r g u e d t h a t C^H^ c o u l d n o t be i m p o r t a n t s i n c e g r o w t h c e a s e d a t l o n g t i m e s w h i l e t h e ^2^2 i° remained h i g h . However, g r o w t h may c e a s e e v e n m t h e p r e s e n c e o f t h e g r o w t h s p e c i e s i f t h e s o o t becomes u n r e a c t i v e a s i t a g e s . The f a c t s t h a t a s i t ages s o o t l o s e s i t s r a d i c a l c h a r a c t e r (10) a n d t h a t i t s c h e m i c a l c o m p o s i t i o n becomes more g r a p h i t i c s u g g e s t t h a t i t s r e a c t i v i t y does i n d e e d f a l l . (Since t h e temperatures vary w i t h s t o i c h i o m e t r y by a s much a s 100 K, t h e s u b s t a n t i a l f a l l i n t h e r a t e c o n s t a n t w i t h t i m e i s n o t due p r i m a r i l y t o t h e d e c r e a s e i n t e m p e r a t u r e w i t h h e i g h t above t h e b u r n e r , w h i c h i s a l s o a b o u t 100 K.) I f we assume t h a t a c e t y l e n e i s t h e p r i n c i p a l g r o w t h s p e c i e s , t h e n a p l o t of l n ( s p e c i f i c growth r a t e ) vs lnfC^H^] g i v e s a r e a c t i o n order o f j=0.9±0.7 (2 s i g m a ) ; t h a t i s , t h e r e a c t i o n i s f i r s t o r d e r . The a p p a r e n t f i r s t o r d e r r a t e c o n s t a n t k may t h e n be d e t e r m i n e d , a n d i t i s p l o t t e d i n F i g u r e 4. The s p r e a d i n t h e d a t a w h i c h a p p e a r s i n the lower p a r t o f F i g u r e 3 i s l a r g e l y e l i m i n a t e d . I n d e p e n d e n t d a t a on s u r f a c e g r o w t h h a v e b e e n p r o v i d e d b y A r e | e v a e£ a l . ( 1 4 ) . A t 1700 Κ t h e y m e a s u r e d a r a t e c o n s t a n t o f 10 g/cm - s - a t m f o r s u r f a c e g r o w t h o n p u r e c a r b o n f r o m ^2^2* w h i c h i s s i m i l a r t o t h e r a t e c o n s t a n t t h a t we c a l c u l a t e f o r o l d ( h i g h C/H r a t i o ) s o o t i n o u r f l a m e . The agreement s u p p o r t s t h e c o n c l u s i o n t h a t s u r f a c e growth i s c o n t r i b u t e d p r i m a r i l y by a c e t y ­ lene. F i n a l l y , we n o t e t h a t s i n c e t h e s p e c i f i c g r o w t h r a t e s a r e s i m i l a r i n f l a m e s w h i c h p r o d u c e v e r y d i f f e r e n t amounts o f s o o t , t h e p r o c e s s e s c o n t r o l l i n g t h e u l t i m a t e s o o t l o a d i n g must o c c u r p r i o r t o the growth stage; t h a t i s , d u r i n g the n u c l e a t i o n stage. Thus, even though s u r f a c e growth i s r e s p o n s i b l e f o r p r a c t i c a l l y a l l o f t h e mass o f m a t u r e s o o t p a r t i c l e s , i t a p p e a r s t h a t r i c h e r f l a m e s p r o d u c e more s o o t b e c a u s e t h e y h a v e a h i g h e r n u c l e a t i o n r a t e and t h e r e f o r e more s u r f a c e a r e a f r o m t h e b e g i n n i n g o f t h e growth stage. t s e

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Summary a n d C o n c l u s i o n s (1) We h a v e f o u n d t h a t t h e i n c r e a s e d s u r f a c e g r o w t h i n r i c h e r flames i s accounted f o r p r i m a r i l y by t h e i n c r e a s e d s u r f a c e area a v a i l a b l e f o r growth i n t h e s e f l a m e s , and n o t by a h i g h e r con­ c e n t r a t i o n o f growth s p e c i e s . Thus, r i c h e r flames a r e s o o t i e r because they have a h i g h e r n u c l e a t i o n r a t e . (2) D e p l e t i o n o f g r o w t h s p e c i e s does n o t o c c u r i n o u r f l a m e s . T h e r e f o r e , t h e f i n a l s i z e r e a c h e d b y t h e s o o t p a r t i c l e s , when s u r -

CHEMISTRY OF COMBUSTION PROCESSES

30

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F i g u r e h. A p p a r e n t f i r s t - o r d e r r a t e c o n s t a n t f o r t h e r e a c t i o n converting acetylene t o soot. (Reproduced w i t h p e r m i s s i o n from Ref. 2 . C o p y r i g h t 1983, Gordon and Breach.)

f a c e growth has v i r t u a l l y ceased, i s n o t determined by d e p l e t i o n b u t r a t h e r by a d e c r e a s e i n t h e r e a c t i v i t y o f t h e s o o t . (3) We have shown t h a t t h e a c e t y l e n e i n t h e b u r n e d g a s e s i s t h e s o u r c e f o r most o f t h e mass o f m a t u r e s o o t p a r t i c l e s . Fur­ t h e r m o r e , we h a v e f o u n d t h a t t h e m e a s u r e d g r o w t h r a t e s a r e c o n s i s ­ tent w i t h the assumption that a f i r s t order decomposition r e a c t i o n o f a c e t y l e n e w i t h t h e s o o t s u r f a c e i s r e s p o n s i b l e f o r most o f t h e s o o t g r o w t h , a l t h o u g h d i a c e t y l e n e may a l s o p l a y some r o l e .

Literature Cited 1. 2. 3. 4. 5. 6. 7.

Gaydon, A. G.; Wolfhard, H. G. "Flames" 1979, Chapman and Hall, 4th edi., London. Harris, S. J . ; Weiner, A. M. Combustion Science and Technol­ ogy 1983, 31, 155. Ibid, 32, 267. D'Alessio, Α.; DiLorenzo, Α.; Sarofim, A. F.; Beretta, F.; Masi, S.; Venitozzi, C., 15th Symposium (International) on Combustion, The Combustion Institute, 1975, 1427. Haynes, Β.; Wagner, H. Gg. Energy and Combustion Science 1981, 7, 229. Millikan, R. C. J. Phys. Chem. 1962, 66, 794. Howard, J. B.; Wersborg, B. L.; Williams, C. G. in Faraday Symposium No. 7, Fogs and Smokes, Faraday Division, Chemical Society, Longon, 1973, 109. Smith, G. W. Combustion and Flame 1982, 48, 265.

2. 8. 9. 10. 11. 12. 13. 14.

HARRIS

Heterogeneous Growth of Soot Particles

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Homann, Κ. H.; Wagner, H. Gg., 11th Symposium (International) on Combustion, The Combustion Institute, 1967, 371. Haynes, B. S.; Jander, H.; Wagner, H. Gg. Ber. Bunsenges. Phys. Chem. 1980, 84, 585. Bonne, U.; Homann, Κ. H.; Wagner, H. Gg., 10th Symposium (International) on Combustion, The Combustion Institute, 1965, 503. Tesner, P. A. Comb. Expl. Shockwaves 1979, 15, 111. Tanzawa, T.; Gardiner, W. C. J. Phys. Chem. 1980, 84, 236. Bittner, J. P. Ph.D. Thesis, Massachusetts Institute of Technology, Department of Chemical Engineering, 1980. Arefeva, E. F.; Rafalkes, I. S.; Tesner, P. A. Khimiya Tverdogo Topliva (Solid Fuel Chemistry) 1977, 11, 113.

RECEIVED October 26,

1983