In Situ light scattering dissymmetry measurements of the evolution of the aerosol size distribution in flames

In Situ Light Scattering Dissymmetry Measurements of the Evolution of the Aerosol Size Distribution in Flames HYUKSANG CHANG AND PRATIM BISWAS 1 Department of Civil and Environmental Engineering, University of Cincinnati, Cincinnati, Ohio 45221-0071 Received April 4, 1991; accepted March 11, 1992 A light scattering system using angular dissymmetry is used to map out the evolution of the size distribution of a nonabsorbing aerosol in a controlled methane-air fiat flame. Silicon tetrachloride vapor is generated by bubbling argon through a pool of silicon tetrachloride (SiCI4) liquid and fed in controlled amounts into the flame, wherein silica (SIO2) particles are formed by oxidation of the SIC14 vapor. A fractal analysis of light scattering data indicates that the particles are close to spherical. The scattered light intensity data at three different angular positions is inverted using the Mie light scattering expressions to determine the effective spherical aerosol size distribution assuming that the distribution can be described by a lognormal function. The results are compared to monodisperse inversion techniques and the predictions of a 1-D lognormal model. © 1992AcademicPress,Inc. INTRODUCTION

product aerosol characteristics in these systems Aerosol processing provides a means of (6, 7, 8). Flame aerosol reactors are used to produce producing fine particles with well-prescribed powders of great industrial significance such physicochemical properties. In industry, aeroas fumed silica for use as a thickening, reinsol reactors have been used to make particulate forcing, and free flow agent, and titania as a commodities such as carbon black and pigbase in pigments. Powders must be produced ments, and material for high technology apwith unique structural, optical, magnetic, and plications such as optical waveguides and electrical properties. Often it is desirable to powders for advanced ceramics ( 1). Aerosol produce submicrometer particles of known processes are used whenever high purity is of size, polydispersity, and shape, and to relate importance such as in the fabrication of optical final powder characteristics to process condiwaveguides for telecommunication (2). Curtions. In other combustion environments, such rently, research is also under way to use these as boilers and incinerators, it is necessary to systems to produce high temperature superunderstand particle formation from an enviconducting powders ( 3, 4). Frequently, in industrial aerosol processes the focus is on op- ronmental standpoint. Ulrich and co-workers timization of a specific characteristic of the (9, 10, 11 ) have performed experiments aimed product aerosol such as deposition efficiency at understanding silica particle formation in in lightguide fabrication, size uniformity in the flames. They concluded that coagulation conmanufacture of powders for advanced ceram- trolled growth of the particles in flames. Zaics, or opacity per unit mass in production of chariah et al. (12) used a counter diffusion pigments (5). Basic studies on aerosol reactors flame burner developed by Chung and Katz have increased the understanding of the rela- (13) to study silica particle nucleation and tionship between operating variables and precursor chemistry in silane laden H2/O2 flames. Bautista et al. (14) have studied flame deposition of silica-germania particles in the ' To whom correspondence should be addressed. OVD and VAD process for optical waveguide 157

Journalof Colloidand lntef['aceScience,Vol. 153,No. 1, October1, 1992

0021-9797/92 $5.00 Copyright© 1992by AcademicPress,Inc. All rightsof reproductionin any formreserved.

158

CHANG AND BISWAS

manufacture. They used dynamic light scattering techniques to probe particle sizes. Metallic particle formation in flame incinerators has been studied by Sethi and Biswas ( 15 ) and by Lin et al. (16). They determined that lead vaporizes in the high temperature of the flame region and then nucleates to form submicrometer sized particles at the cooler downstream regions. Condensation and coagulation are the dominant growth mechanisms once the seed nuclei are formed. A variety of diagnostic techniques have been used to measure particle sizes in flames. Thermophoretic sampling techniques have been used by Megaridis and Dobbins (17) to deposit particles on a cold probe and then examine them by electron microscopy. Dilution sampiing probes have been used by Biswas and co-workers (8, 16 ) to measure the aerosol size distribution using real time instruments. Many optical techniques have also been used, and they provide in situ, nonintrusive measurements with great spatial resolution. Two techniques that have been used are elastic light scattering (ELS) and dynamic light scattering (DLS) (18 ). DLS and ELS techniques have been compared by various researchers ( 18, 19)

and good agreement was obtained on mean particle diameters. Santoro et al. (20, 21 ) used a combination of scattering and extinction measurements to infer sizes of light absorbing particles (soot) in diffusion flames. Most of the studies on in situ measurement of particle size by light scattering (18, 19, 21 ) have assumed that the aerosol is monodisperse, and then have computed mean particle diameters. Using this mean particle diameter, a number concentration of the aerosol was determined. In this paper we present a technique to determine the aerosol size distribution from in situ, multiple angle light scattering dissymmetry measurements for a nonabsorbing aerosol. The routine developed is used to obtain the aerosol size distribution of silica particles formed in a flat flame burner. EXPERIMENTAL SYSTEM

Silica particle formation by oxidation of SIC14 in a methane-air flame has been studied. A premixed methane-air fiat flame supported on a burner nozzle (diameter 25.4 mm) packed with capillary tubes was used in this study (Fig. 1 ). This arrangement maintained a steady, nearly one-dimensional flow field, and provided controlled conditions to study Z aerosol formation and dynamics. Flame temperatures were measured using an uncoated Pt-Pt/13% Rd thermocouple (wire diameter 0.051 ram). The flow rate of methane and air Flow (filtered) supplied to the burner was controlled and measured. SiCI4 vapor was entrained in an argon stream, passed through a bubbler (8), and fed into the flame region as shown in Fig. 2. The optical system to carry out the light , !~uuulJ scattering measurements is shown in Fig. 3. A Capillary Tubes He-Ne laser (polarized, 5 roW) was used as (Ig .64ram, 0g .89mm) the light source. The laser beam was mechanically chopped at 1500 Hz, and passed through a beam splitter to divide the beam into two I 5iCI4 parts. One beam was directed through the reAir CH4 gion of the flame for the light scattering meaFIG. I. Schematicof the burner head (z: axialdistance, surements. The other beam was directed to a photodiode connected to a lock-in amplifier r: radial distance). I lIHtllllll

r Ilil[llllfl

Journal of Colloid and Inle@,ce Science, Vol. 153, No. 1, October 1, 1992

159

L I G H T SCATTERING OF FLAME AEROSOLS Loser Beam

~urnef

Rolometer FlowController CH4

Arg00

b,.r

FIG. 2. Schematic of the air, fuel, and reactant supply system.

(Oriel 70707) to obtain a reference signal and thus distinguish the scattered light intensity signal from the unchopped background noise. The scattered signal from the probe volume was measured using a photomultiplier tube ( P M T ) (Oriel 77344) connected to a lock-in amplifier for signal conditioning. Two slits on the P M T allowed for a very small scattering volume to be defined (diameter 0.8 m m , length 1 m m ) , thus enhancing spatial resolution. A laser line filter centered at ), = 632.8 n m (A)t = 1 nm) was also mounted on the P M T to reject extraneous signals from flame emissions. Before the b e a m was passed through the measuring region in the flame, it

a_2 _%_ 4~s 14tz~ 7 , . I-- -~,~.... lu................ ,~.. ............

I I

zh

I

I

i',

/

I

88. ,," I

-.

88 "-./~

was sent through a polarizer to maintain it perpendicular to the scattering plane. A polarizer was also used before the P M T to ensure that the scattered light corresponded to the incident beam. The P M T was installed on a rotator so that it could measure the scattered light intensities at various angles. The axis for the rotation of the P M T passed through the center point of the measuring volume. The position of the measuring volume in the flame was changed by moving the burner. The burner was installed on a movable system which could be traversed vertically with respect to the fixed measurement system. The output signal from the lock-in amplifier was digitized with an A / D converter, and sent to a microcomputer for data storage and processing. The experimental parameters used in this study are listed in Table I. The scattered beam intensities at various spatial positions were measured at 60 ° , 90 ° , and 120 ° in the forward scattering direction (Table II). To test the sphericity of the particles, a fractal analysis was carried out using light scattering measurements made at 5 ° intervals from 25 ° to 125 ° (22). Measurements were done along the axis of flow (r = 0 ram) from 1 m m to 50 ram. The axial distance was measured from the surface of burner. TEST OF SPHERICITY

Flame generated particles such as soot (23) and silica (24) have been reported to have an agglomerate structure. Fractal dimensions have been used to describe the aggregates (23, 24, 25, 26). A wide range of the fractal di-

I>/9 TABLE I Experimental Parameters Used in This Study

FIG. 3. Schematic of the light scattering measurement system: 1. laser, 2. chopper, 3. beam splitter, 4. spatial filter, 5. polarizer, 6. photodiode, 7. light trap, 8. slit, 9. laser line filter, 10. photomultiplier, 11. lock-in amplifier, 12. A / D converter, 13. computer, 14. burner.

Peak temperature CH4 flow rate Total flow rate (at burner nozzle) Equivalence raito (4) SIC14concentration (at flame front) Argon flow rate through SiCl4 bubbler

1750 K 250 cm3/min 3.5 L/min 0.75 2.87 × 10-4 mol/L 45 cm3/min

Journal of Colloid and Interface Science, Vol. 153,No. 1, October 1, 1992

160

CHANG AND BISWAS TABLE II

Scattered Light Intensities, Mean Volumetric Diameters, Standard Deviations, and Number Concentrations, and Volume Concentrations at Different Axial Positions S~(O,)

S~(02)

S~(03)

z (mm) 2 3 4 5 6 7 8 9 10 12 14 16 18 20 24 28 32 36 40 45 50

S~(Ox)SR(02) S~(02)SR(O0

(V) 0.0091 0.0514 0.0763 0.0938 0.1169 0.1249 0.1412 0.1509 0.1637 0.1776 0.1893 0.1928 0.2063 0.2151 0.2289 0.2378 0.2502 0.2502 0.2589 0.2739 0.2663

0.0183 0.0496 0.0649 0.0782 0.0871 0.0935 0.1010 0.1070 0.1096 0.1164 0.1177 0.1224 0.1304 0.1364 0.1367 0.1409 0.1460 0.1469 0.1455 0.1510 0.1520

0,0185 0,0480 0.0581 0.0641 0.0705 0.0762 0.0833 0.0870 0.0878 0.1009 0.1019 0.1095 0.1123 0.1135 0.1175 0.1180 0.1174 0.1187 0.1203 0.1239 0.1262

1.21 2.52 2.86 2.92 3.27 3.25 3.40 3.43 3.64 3.71 3.92 3.84 3.85 3.84 4.08 4.11 4.17 4.15 4.33 4.42 4.27

S~(Ox)SR(O~) S~(03)SR(O~) 1.69 3.67 4.50 5.01 5.68 5.62 5.80 5.94 6.38 6.03 6.36 6.03 6.29 6.49 6.67 6.90 7.30 7.22 7.37 7.57 7.22

Note: SR(01) = 4 . 3 8 1 X 10 -8 V c m s t e r a d i a n , SR(O1)/SR(02) =

dpv (#m)

a

0.025 0.126 0.156 0.170 0.557 0.616 0.515 0.5l l 0.497 0.528 0.520 0.520 0.518 0.512 0.507 0.505 0.495 0.481 0.492 0.488 0.500

2.18 2.02 2.22 2.36 1.90 1.88 1.60 1.56 1.43 1.36 1.30 1.31 1.33 1.33 1.34 1.29 1.29 1.30 1.28 1,26 1,26

,41o

M~

(#/era 3)

(cm3/cm s )

6.7 3.5 2.7 2.3 1.3 1.1 1.4 1.5 1.6 1.5 1.5 1.6 1.7 1.8 1.9 1.9 2.1 2.2 2.1 2.3 2.2

x × N x × X X X X X X X × X X X X X X X X

10 x~ 109 109 109 108 108 108 108 lO 8 108 108 108 108 108 108 108 108 108 108 108 108

5.21 3.69 5.27 7.07 1.18 1.39 9.95 1.06 1.01 1.12 1.11 1.23 1.26 1.23 1.28 1.28 1.3t 1.31 1.34 1.37 t.41

× x X N X X X X X X X X X X X X X X X X X

10 -6 10 -6 10 -6 10 -6 10 -5 lO -5 10 -6 10 -5 10 -5 10 -5 10 -5 10 -8 10 -8 10 -5 10 -5 10 -3 10 -5 10 -5 10 -5 10 -5 10 -8

0 . 4 1 0 8 0 , SR(O1)/SR(O3) = 0 . 2 9 2 0 5 , 0~ = 6 0 °, 02

= 9 0 °, a n d 09 = 120 °.

mension has been reported for flame generated silica particles. Schaefer et aI. (25) reported the fractal dimension of a colloidal aggregate of silica particles in solution to be 2.12. Martin et al. (26) dispersed flame generated silica into a solution and determined a mean fractal dimension of 1.84 by static light scattering measurements. Freltoft et al. (27) reported fractal dimensions in the range of 2 to 2.6 determined from neutron scattering measurements. Hurd and Flower (24) carried out in situ measurements of silica formation in a premixed, lean methane-air flame by oxidation of hexamethyldisiloxane. They reported a fractal dimension of 1.49 at a distance of 14 m m from the flame front. This fractal dimension was assumed to be constant at other axial positions, and they computed a radius of gyration of 0.08 #m at 6 m m (3 ms residence time) and 0.153 #m at 14 m m (30 ms residence time) above the flame front. Journal of Colloidand InterfaceScience, Vol. 153, No. 1, October I, 1992

An approach similar to that of Hurd and Flower (24) was used to determine the radius of gyration and fractal dimension. Details of the conditions for these experiments are provided in Chang (22). For the analysis of the scattering intensities from the flame generated agglomerates, the Rayleigh-Debye scattering theory (24, 25, 28) was used. A plot of the scattering intensity as a function of the scattering wave vector, q ( = 4 ~s i n ( 0 / 2 ) / × ) is shown in Fig. 4 for measurements at different axial positions. The slope of the curve at larger values of q in Fig. 4 is equal to - D r, the fractal dimension. At small q, S(q) has a parabolic dependence on q (29), and fitting the data yields a value of Ra, the radius of gyration. These were determined at different axial locations and the results listed in Table III. The radius of gyration increased with distance away from the flame front due to growth of the agglomerate. As most of the

LIGHT SCATTERING OF FLAME AEROSOLS

161

to obtain information about the polydispersity of the aerosol.

1(~1-:

INVERSION TECHNIQUE

03 --2 ....

-..~....:~..

The intensity of the scattered light from the particles is a function of the angle, the refracx:l -e.. ,t .'~-~e" tive index of the particle, and particle size in ~o-3 the Mie scattering regime. The relation beO3 tween the particle size and the scattering intensity is well established as described by van 16~04 de Hulst (30). The Mie theory is only appliq (cm-') cable for spherical particles, and hence an efPIG. 4. Scatteringintensityas a function of the scattering fective spherical diameter is obtained by this wave vector q at different axial positions from the burner inversion technique. face: (O) 10, (11) 20, (A) 30, (O) 40, and ([~) 50 ram. The incident b e a m and scattered b e a m are resolved into two independent polarized components, one with electric vector perpendicular particle growth had occurred near the flame to the scattering plane (subscript v) and one front, the increase in RG was not very signifparallel to the scattering plane (subscript H ) . icant beyond I 0 m m . The fractal dimension In the experiments, the measured intensity increased with axial position, indicating that of the scattered light, Svv, is given by (30) coalescence led to a more spherical shape being Svv = QvvnAVAflIo .... [11 obtained. This was also observed in the scanning electron micrographs obtained at differwhere Io is the incident b e a m flux, A~2 is the ent axial locations (22). The particles at solid angle aperture of the collection optics, greater distances away from the burner face AV is the measuring volume, n is the efficiency appeared to be more coalesced. The fractal diof optical elements, the subscript v denotes mension obtained in this work at 50 m m (65 the polarization state, and the double subscript ms residence time) was 2.8, greater than that indicates the states of polarization of incident reported ( 1.49) by Hurd and Flower (24). This and scattered beams. Q~v is the differential m a y be due to a n u m b e r o f reasons. The disscattering coefficient, and for a size distributance from the flame front is greater in this tion of particles, is given by study (residence time of 65 ms as compared to 30 ms), allowing more time for coalescence. Qvv(O) = f C~v(X, O)n(v)dv, [2] Ulrich and Subramanian (10) also reported d that coalescence increases with residence time and temperature. The other difference between TABLE lII this work and that of H u r d and Flower (24) o_ _

-.

.-4~.

was that the reactants were different. Thus, the morphology of flame generated particles is system dependent. The inversion of the light scattering data indicates relatively large fractal dimensions, and hence an inversion technique based on angular dissymmetry using the Mie scattering theory is justified. The intent o f this study, therefore, was to extend the data inversion analysis clone on dissymmetry measurements

The Radius of Gyration and Fractal Dimension of the Silica Particles at Different Axial Positions in the Flame" z(mm)

Ro(~m)

Df

10 20 30 40 50

0.292 ± 0.02 0.300 ± 0.025 0.301 +__0.023 0,303 ± 0.026 0.302 ± 0.024

2.17 ± 0.08 2.50 ± 0.06 2.67 -+ 0.07 2.76 + 0.06 2.80 ± 0.11

a Experimental conditions are listed in Chang (22). Journal qfColloid and Inter.lace Science Vol. 153, No. 1, October 1, 1992

I62

CHANG AND BISWAS

where Cw(X, 0) is the scattering cross section in the Mie regime (30), n(v) is the aerosol number concentration, X( = rcdp/)~) is the optical particle size parameter, and )~ is the wavelength of the incident light beam. The scattering cross section of the vertically polarized beam has angular dependence in the Mie regime (X > 0.3). Equation [1] can be rewritten by combining the system parameters into a single parameter, SR (0), thus Svv(0) = Qvv(O)SR(O),

[31

SR(O) = ~TaVA~210,vv.

[41

where

The shape of the aerosol size distribution is assumed to be lognormal, this being used widely in describing aerosols (8, 31 ) M0 n ( v ) - 3 2V~ln

exp

ISUM(0i, Vg, a)

= £~ Gv(X' v Oi)

SR(02) Svv(02) $1¢(0~)

Svv(01 ) f12(vg, a) = - -

ISUM(0I, Vg, O') = 0 ISUM (02, Vg, ~)

Svv(01) SR(03) Svv(03) SR(O,) ISUM(01, Vg, a) = 0, ISUM(03, vg, o')

In 2 (V/Vg)

'v

i-8W7) a , [81

and where v, (volume corresponding to minimum particle size) and v2 (volume corresponding to maximum particle size) are the limiting particle volumes in the aerosol size distribution. These limiting volumes are based on the limits of applicability of the Mie size regime. Eqs. [6] and [7] are a set of coupled equations which can be solved for the unknowns Vg and a. From the light scattering and calibration experiments, the ratios R1 and R2, defined as

In 2 (v/vg)] 1 ~ 1-~ ~- J v ' [5]

where M0 is the total number concentration, vg is the particle geometric mean volume, and a is the geometric standard deviation. Three parameters (M0, a, Vg) describe the aerosol size distribution completely, and hence three equations (as Eq. [3 ]) would be needed to determine these values. By measuring the scattered intensity at three different angles, 01, 02, and 03, three such equations can be developed. The left hand side (Sv,(O)) of Eq. [3] would be known from measurements and SR(O) would be known from the calibration tests. Writing Eq. [ 3 ] for the three angular positions, and using Eqs. [2] and [5], and by simple algebraic manipulations, we obtain

f13(Vg, ~) =

where

R 1 =

Svv(OI)SR(02) Svv(O2)SR(OI)

[9]

R2 =

Sw(O1)SR(03) Svv(O3)SR(01) '

[lOl

and

are determined. The topographical plot (Fig. 5 ), which is obtained by calculating ISUM (0i, Vg, or) in Eq. [8], shows constant R1 and R2 lines as a function of the geometric mean diameter and standard deviation. The intersection point of the measured values of R1 and R2 (Table II) determine the value of dog and ~r at the measurement point. The number concentration, M0, is obtained by back substitution into Eq. [ 3 ] and by using the value of the system parameter, SR (Oi), determined from calibration experiments. The lower limit of the dimensionless size parameter, X, is 0.3 in the Mie regime (30). For a He-Ne laser beam, ~,, the wavelength is [61 0.6328 tzm. Hence the lower limit of the particle size is 0.06 ~tm (corresponding to vl --1.16 × 10-4/zm3). We chose the upper limit of the particle size to be 1.5 #m (corresponding to v2 = 1.767 #m 3) based on our experience with silica particle formation in aerosol reac[71 tors (8). Sensitivity tests were carried out by

Journal of Colloid and lmerface Science, Vol. 153, No. 1, October I, 1992

LIGHT SCATTERING OF FLAME AEROSOLS

163

1.95

1.85

Eb

r~.~

.............................

i.s5

~."~.,*.. -,",4 ~ - . . . , , . ~

,., 1,35

",

o 1,5,1, " 1.05

I O. 15

I

"-,

"',-,",

"-, .,.¢ ",

',

..- .~ ,_. ........... ....... ...... --.4..--...~.. ~ ,..--\ ........... :::....;: ..... ...... -.... ~.. \~",

;

"'~-

"""%""~;~'~~;"'~ ~':;"~?!k:"4:" !~,~\

]

1

I I 0.20

0.25

' ' "1 ' ' 0.30

....

i\,~i

"-~

- .".' -., . . .

"',

,,

",

,"

,,,,,,

I 0.35

I 0.40

0.45

0.50

0.55

Geometric Mean Diameter ~ m ) FIG. 5. Topographical map of Rt and R2 (Eq 8) as a function of geometric standard deviation, ~r, and geometric mean diameter, dpg[( RI( = ISUM(01, vg, a)/ISUM(02, vg, a), --- R2( = ISUM(01, Vg, a)/ ISUM(03, vg, a)].

varying v2, a n d no difference was o b t a i n e d in the results. T h e s u b r o u t i n e D A M I E ( 3 2 ) was used to calculate Cvv(X, 0), the scattering cross section o f silica particles (refractive i n d e x m = 1.46). RESULTS AND DISCUSSION T h e t e m p e r a t u r e history in the zone o f interest is m e a s u r e d b y a fine R - t y p e t h e r m o couple a n d is shown in Fig. 6. T h e equivalence ratio was m a i n t a i n e d at 0.75 to ensure excess oxygen for o x i d a t i o n o f SIC14. T h e p e a k t e m perature was a r o u n d 1750 K at the flame front, a n d decreased to a b o u t 1400 K at a distance o f 50 m m away f r o m the flame front. U n d e r these c o n d i t i o n s it is expected t h a t m o s t o f the silicon t e t r a c h l o r i d e will be oxidized very rapidly close to the flame front. G a s m o l e c u l a r scattering is a c o m m o n l y used m e t h o d to d e t e r m i n e the system p a r a m -

eter SR(Oi) (18, 2 0 ) . In o u r system, the m o lecular scattering signal from the p r o b e v o l u m e h a d a high s i g n a l / n o i s e ratio. H e n c e , SR(Oi ) was d e t e r m i n e d b y m e a s u r i n g the scattered intensities o f aerosols o f k n o w n size distributions. T w o aerosols were used: m o n o d i s p e r s e D O P a n d p o l y d i s p e r s e d f u m e d silica aerosol.

2000

~1800 eL = 1600

& 140C

1200 . 0.0

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

10.0

20.0 30.0 Ax]m Distance ( m m )

40.0

50.0

FIG. 6. Centerline temperature variation as a function of the axial distance, z (~ = 0.75, CH4 flow rate = 250 cm3/ rain ). Journal of Colloid and Interface Science, VoL 153, No. 1, October 1, 1992

164

CHANG AND BISWAS

In case of the fumed silica aerosol, the size distribution was measured by a Differential Mobility Particle Sizer ( D M P S ) . Using Eq. [2], Q ~ ( O i ) was calculated using the known size distribution, n (v). The scattered light intensity S ~ (0~) was measured using the optical system, and S R ( O i ) was then determined using Eq. [3]. This experiment was repeated a n u m b e r of times to obtain average values of S R ( O ~ ) . Both calibration methods yielded similar values of the system parameter, S R ( O i ) . The average S R ( 0 1 ) , S R ( 0 2 ) , and S R ( 0 3 ) values are listed in Table II. The optical system was then used to measure the scattered light intensity at different axial locations, at three different angles; the data are listed in Table II for a SIC14 feed rate of 2.87 × 10 -4 tool/liter. As described earlier, the ratios ( S v v ( O i ) S R ( O : ) ) / ( S v v ( O : ) S R (0i)) are determined and listed in Table II. Using the topographical m a p (Fig. 5), a and dpv(= dpgexp( 1.5 In 2 ~r)) were determined as described earlier, and these values are also listed for different axial positions in Table II. The aerosol n u m b e r concentration, M0, and aerosol volume, M l , were then computed and are also listed. The variation of dpv with axial position is shown in Fig. 7. The volumetric mean diameter increases from about 0.02 # m to 0.5

'~

2.50

"o 2,00

"E

"°%'d ...... a'a'.d....... ~e'.~....... ;o'.d....... 20'.d....... g0.o Axial

Orstance

(ram)

FIG. 8. Variation of measured standard deviation, (r, as

a function of axial position on the center line (r = 0 mm): (©) lognormal inversion technique; (O) DMPS. Solid line is a prediction ofa 1-D lognormal model (8), and dashed line is a fit to inverted data.

/~m. As stated earlier, the lower limit of particle size in the Mie regime for the optical system is 0.06 ~tm. The data point at z = 2 m m (dpv = 0.02/~m) was thus obtained by extrapolation in Fig. 5. All data points after z = 2 m m are in the Mie regime. As silica particles formed initially are very small (order of a few angstroms) and the number concentration is high, they coagulate rapidly and a sharp size increase is observed. This is consistent with isothermal reactor oxidation of SIC14 (8). A dilution probe in conjunction with the DMPS (16) was used to measure the size distribution, and the data are also shown in Fig. 6. The solid line is the prediction of the silica size distribution evo0.80 lution in the flame reactor using a one-dimensional lognormal model (8). The model underpredicts the mean size (dpv), and this is 0.60 o o o ---t ~ . . . . . . . _o. . . . ~ - . . . . . . . . due to the overpredicfion of the n u m b e r con'~°° i centration and underprediction of the volume concentration. Past light scattering dissymmetry studies ( 12, 18 ) have assumed the aerosol to be monodisperse, and the results are shown by solid symbols. As three angular 000 .... ' ......... ' ......... r • 0.0 10,0 20,0 30.0 40.0 50.0 measurements were done, two monodisperse Axial Distance (ram) diameters can be computed, and are shown in FIG. 7. Variation of measured particle volume mean Fig. 7. Different values are obtained, further diameter, dp~,as a function of axial position on the center indicating that the aerosol is indeed polydisline (r = 0 ram): (O) lognorrnal inversion technique; (e) DMPS; (•) monodisperse (60 °-90 ° ); ( • ) monodisperse perse. Similar data are shown in Fig. 8 for the (60°-120 ° ). Solid line is a prediction of a 1-D lognormal geometric standard deviation. Closer agreemodel (8), and dashed line is a fit to inverted data. ment of the measured data is obtained between o.4o

F

, ..j=...-

•

.

.

•

.

•

•

•

•

•

•

.

Journal of Colloid and Intedace Science, Vol. 153, No. 1, October l, 1992

LIGHT SCATTERING OF FLAME AEROSOLS theoretically predicted and D M P S measured values. The asymptotic geometric standard deviation from the experimental data appears to be between 1.34 and 1.26 (Table II), and this is close to the asymptotic value of 1.33 for lognormally distributed aerosols ( 31 ). Due to the short residence times, the theoretically predicted value of the geometric standard deviation is around 1.5; however, it slowly approaches the limiting value of 1.33. The variation of the total particle n u m b e r (Mo) and the total particle volume concentration (M~) as a function of axial distance is shown in Figs. 9a and 9b, The n u m b e r concentration predicted by the model is an order o f magnitude higher at locations close to the inlet. At these locations, there is a large concentration of small particles that m a y not be detected by the light scattering system used in this study. As particles coagulate and increase in size, there is a better agreement between measured and predicted values. The DMPS measurement is an order of magnitude lower and m a y be attributed to losses and nonidealities in the sampling probe. An interesting comparison of the monodisperse inversion technique (18) and the inversion technique developed in this paper can be made from the results in Figs. 9a and 9b. When the standard deviation is higher (at low z), as expected the difference

~.

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Axiol D i s t c n c e ( m r n )

FIG. 9b. Variation of particle volume concentration, M1, as a function of axial position on the center line (r = 0 ram): (O) lognormal inversion technique; (O) DMPS; (•) monodisperse (60°-90 ° ); (•) monodisperse (60 °120°). Solid line is a prediction ofa 1-D lognormalmodel (8), and dashed line is a fit to inverted data. between the results of the two inversion techniques is significant. The volume concentration reaches its peak value close to the burner face, indicating that most of the conversion occurs rapidly, and further growth occurs by coagulation (no further increase in particle volume). The final volume concentration as measured by the light scattering technique ( 1.41 × I0-5 c m 3 / c m 3) corresponds to an inlet SIC14 feed rate of 5.3 × 10-4 mol/liter, higher than the measured inlet feed rate of 2.87 × 10 -4 tool/liter (Table I). CONCLUSIONS

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.

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•

•

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Axial D i s t a n c e ( r n m )

FiG. 9a. Variation of particle number concentration, M0, as a function of axial position on the center line (r = 0 mm): (O) lognormal inversion technique; (O) DMPS; (l) monodisperse (60°-90°); (a) monodisperse (60°120° ). Solidline is a prediction ofa I-D lognormalmodel (8), and dashed line is a fit to inverted data.

Multiangle light scattering dissymmetry measurements were used to determine the three parameters, M0, ~, and dpg describing the aerosol size distribution. The technique was demonstrated by applying it to silica particle formation by oxidation in a flat flame burner, assuming that the particles were effectively spherical. A fractal analysis of light scattering data indicated that the particles appeared to coalesce to form spherical shapes. The results were compared to measurements made by a differential mobility particle sizer and the predictions of a lognormal aerosol model. G o o d agreement was obtained a m o n g the various results with the in situ optical system being better able to m a p the size distriJournal of Colloid and Interface Science, V o l .

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CHANG AND BISWAS

bution close to the flame front. This is a viable technique to determine effective spherical aerosol size distributions, and can be extended to examine multicomponent systems. ACKNOWLEDGMENTS This work was supported by National Science Foundation Grant CBT 8808813. REFERENCES 1. Ulrich, G. D., Chem. Engr. News 62, 22 (1984). 2. Nagel, S. R., Z Lightwave Technol, LT-2 (6) (1984). 3. Kodas, T. T.,Angew. Chem. Int. Ed. Engl. Adv. Mater. 28, 794 (1989). 4. Biswas, P., Zhou, D., Zitkovsky, I., Blue, C., and Boolchand, P., Mater. Lett. 8, 223 (1989). 5. Pratsinis, S. E., and Mastranjelo, S. V. R., Chem. Eng. Prog. 62 (1989). 6. Pratsinis, S. E., Kodas, T. T., Dudukovic, M. P., and Friedlander, S. K., lnd. Eng. Chem. Process Des. Dev. 25, 634 (1986). 7. Wu, J. J., and Flagan, R. C., J. Appl. Phys. 61, 1365 (1987). 8. Biswas, P., Li, X., and Pratsinis, S. E., J. Appl, Phys. 65, 2445 (1989). 9. Ulrich, G. D., Milnes, B. A., and Subramanian, N. S., Combust. Sci. Technol, 14, 243 (1976). 10. Ulrich, G. D., and Subramanian, N. S., Combust. Sci. Technol, 17, 119 (1977). 11. Ulrich, G. D., and Riehl, J. W., J. Colloid Interface Sci. 87, 257 (1982). 12. Zachariah, M. R., Chin, D., and Semerjian, H. G., Cornbust. Flame 78, 287 (1989). 13. Chung, S. L., and Katz, J. L., Combust. Flame 61, 271 (1985). 14. Bautista, J. R., Potkay, E., and Scatton, D. L., Mater. Res. Soc. Syrup. Proc. 17, 151 (1988).

Journalof ColloidandInterfaceScience.Vol. 153,No. 1, October1. 1992

15. Sethi, V., and Biswas, P., J. Air Waste Manage. Assoc. 40, 42 (1990). 16. Lin, W. Y., Sethi, V., and Biswas, P., Aerosol Sci. Technol. 117, 119 (1992). 17. Megaridis, C. M., and Dobbins, R. A., Combust. Sci. Technol. 66, 1 (1989). 18. Zachariah, M. R., Chin, D., Semerjian, H. G, and Katz, J. L., Appl. Opt. 28(3), 530 (1989). 19. Flower, W. L., Phys. Rev. Lett. 51, 2287 (1983). 20. Santoro, R. J., Semerjian, H. G., and Dobbins, R. A., Combust. Flame 51, 203 (1983). 21. Santoro, R. J., Yeh, T. T., Horvath, J. J., and Semerjian, H. G., Combust. Sci. Technol. 53, 89 (1987). 22. Chang, H., "Particle Characterization in Flames by In-Situ Light Scattering Measurements." Ph.D. Thesis, University of Cincinnati, 1991. 23. Megaridis, C. M., and Dobbins, R. A., Comb. Sci. Technol. 711, 95 (1990). 24. Hurd, A. J., and Flower, W. L., J. Colloid Interface Sci. 1122, 178 (1988). 25. Schaefer, D. W., Martin, J. E., Wiltzius, P., and Cannell, D. S., Phys. Rev. Lett. 52, 2371 (1987). 26. Martin, J. E., Schaefer, D. W., and Hurd, A. J., Phys. Rev. A 33, 3540 (1986). 27. Freltoft, T., Kjems, J. K., and Sinha, S. K., Phys. Rev. B, 269 (1986), 28. Mountain, R. D., and Mulholland, G. W., Langrnuir 4, 1321 (1988). 29. Berne, B. R., and Pecora, R., "Dynamic Light Scattering," Chap. 8. Wiley, New York, 1976. 30. Van de Hulst, H. C., "Light Scattering by Small Particles." Dover, New York, 1981. 31. Lee, K. W, and Chert, H., Aerosol. Sci. Technol. 3, 327 (1984). 32. Dave, J. V., "Subroutine for Computing the Parameters of the Electromagnetic Radiation Scattered by a Sphere." IBM Scientific Center Report No. 320-3237 (1968).