Soot diagnostics based on laser heating

Soot diagnostics based on laser heating

Lynn A. Melton

Through numerical calculations we have investigated the possibility of developing soot diagnostics basedon laser heating of the soot particles. Two strategies, one using the laser-modulated incandescence of the

particles, and the other using direct detection of the evaporated C2 molecules, were examined. Both strate-gies can yield size distribution and volume fraction information provided the laser wavelength is near thegraphite absorption band at 260 nm; otherwise, only volume fractions can be obtained.

1. Introduction

In 1977, Eckbreth showed that laser-modulated in-candescence from soot particles in a flame could easilyoverwhelm signals from Raman measurements, and herelated the time dependence of this interference to laserheating, heat transfer to the medium, particle vapor-ization, and indirectly to the particle size.' Recently,Greenhalgh has observed resonant CARS signals gen-erated from C2 molecules vaporized by the pulsed lasersused to generate the CARS signal,2 and Dasch hasstudied the flame perturbations caused by vaporizationof soot.3 Weeks and Duley have demonstrated that theincandescence from 2-jum particles can give character-istic size information.4 These experiments raise thepossibility of developing soot diagnostics based on thelaser heating of soot particles as the primary interaction;this paper examines on a computational basis potentialdiagnostic strategies based on laser-modulated incan-descence and on the measurement of C2 evaporatedfrom soot particles.

Starting with the optical constants for graphite in the200-1500-nm range and with the assumption of spher-ical particles, the Mie absorption equations have beensolved numerically. These solutions were then used innumerical solutions of the energy and mass balanceequations in which the temperature and particle radiusas a function of time were obtained. The expectedsignals for a particular experiment could then be cal-culated. In the laser-modulated incandescence strat-egies, a series of nonlinear least-squares fits was per-formed to test the extent to which the parameters of anassumed soot particle size distribution could be recov-ered.

The author is with University of Texas at Dallas, Box 830688,

Chemistry Department, Richardson, Texas 75080.Received 9 January 1984.0003-6935/84/132201-08$02.00/0.© 1984 Optical Society of America.

The results of this analysis may be summarized asfollows: both the laser-modulated incandescence(LMI) and C2 evaporation strategies (RECLAS) aresensitive to the soot particle size distribution in the0.02-0.2-,um diam range, and potentially either couldbe used to determine such a size distribution. Pre-liminary experiments with the LMI strategy indicatethat molecular fluorescence from the sooting flame willprobably eliminate it as a viable diagnostic. However,either diagnostic strategy can readily be made to givethe volume fraction of soot at a point in the flame, andin the long run, this use may be the most valuable re-sult.

II. Theoretical Development

A. Basic Equations

The Mie extinction, scattering, and absorption crosssections for a particle of radius a are related as fol-lows:

Cext = Cscat + Cabs, (1)

Kext = Kscat + Kabs, (2)

where K, the efficiency, is the cross section divided bythe geometric area 7ra2.5 Attenuation experimentsmeasure Kext, scattering experiments measure Kscat,and laser heating experiments measure Kabs. For smallparticles, i.e., a/X < 0.05,5 Kabs o- a 3 , and Kscat a6;hence, KabS provides a greater weighting for small par-ticles-as might be expected in nascent soot-than doesKscat-

B. Development of Energy and Mass Balance

Equations

In deriving the differential equations for the timedependence of the temperature (T) and radius (a) of alaser-heated spherical particle, we extend Eckbreth'streatment to include heat transfer to the medium as wellas radiation. These ideas are anticipated in several ofEckbreth's papers1 68 but have not been combined intoa single solution.

1 July 1984 / Vol. 23, No. 13 / APPLIED OPTICS 2201

Energy Balance:K8 b (a)7ra2q Ka (T - To)(4irl) AH, dM

a (1 + GK,) + W dt - yb(T4-To

4 dTX (47ra2) - ra 3 PCs d = 0.

3 dt (3)

The terms are, respectively, the laser energy ab-sorbed/sec, the rate of heat transfer to the medium(taken to be air at temperature T), the energy ex-pended in vaporization of the carbon, the rate of energyloss by blackbody radiation, and the rate of internalenergy rise. The symbols are listed in the Appendix,the symbol and value list. The particles are smallcompared to the mean free path (3500 A at 1-atmpressure and 2000 K), and the continuum heat transferexpression must be corrected; the factor (1 + GK)-1accounts for this. 9

In writing Eq. (3) we made use of Eckbreth's ap-proximate heat transfer calculations. He showed thatthe characteristic time for perturbation of the mediumis -35 nsec for particles with a = 0.005 gum and riseslinearly to 700 nsec for particles with a = 0.10 Azm. Inaddition, the particles may be assumed to have a uni-form internal temperature since the laser, which is as-sumed to have a triangular pulse of 10-nsec FWHM, ismuch longer than the characteristic time for internalgradient dissipation of 10-12 sec for a = 0.005 um and2 X 10-10 sec for a = 0.10 ,Am.6Continuity:

da-Ps da = puv- (4)dt

We assume with Eckbreth that the vapor velocity isgiven by the thermal velocity U = (RT/2 WV)1/2, thatthe vapor pressure of carbon is given by the Clapeyronequation

p(T) = p* exp (TT*)

and that the perfect gas equation holds.The soot particles will typically have a < 0.1 um =

10-5 cm, in which case the second term in the denomi-nator of the heat transfer term is dominant. Using thecontinuity equation to simplify the vaporization term,we have

8Ka (T - T) AHv 4Kabs(a)q- w pvU -4osB(T 4 -T )

4 dt-j PsCsa 7dt=0° (6)

We may examine Eq. (6) and note several qualitativefeatures. When the laser pulse is turned on, the tem-perature begins to rise linearly. Below 3300 K, heattransfer to the medium is the dominant energy lossmechanism; above 3700 K, vaporization is the dominantenergy loss path, and it severely limits the temperaturerise. Only at temperatures in excess of 10,000 K-notattained here-would the radiation term become im-portant. The heat loss to the medium, like the vapor-ization and radiation, is a function of T alone; it has no

explicit dependence on a. This lack of explicit a de-pendence coupled with a knowledge of the a depen-dence of Kabs will provide the basis for diagnosticstrategies based on laser heating.

Although Kabs may be easily evaluated with computerprograms, substantial physical insight may be obtainedby the use of the following analytic approximation10 :

IK _ M3m) a > ,abs a/ a <6,

1/[ 2(27r)k 12nf3'l(m)

X t4n2k2 - (n2 - k2 2)21

(7)

m = n - ik is the complex index of refraction, and ,(m)accounts for the Fresnel reflectivity of the sphericalparticle. Kabs rises linearly and levels off at a value nearunity. 6 may be considered as an absorption lengthparameter in which the bulk absorption depth B =[2(27r/X)k]-1 is modified for small particles by a factorof order unity. The break in the curve occurs at a 6.In the visible for soot particles, 0.1 m, and in theultraviolet (200-300-nm) region, 6 may be as small as0.01-0.02 im.

For small particles, for which Kabs is linear with a, themaximum temperature [dT/dt = 0 in Eq. (6)] is afunction of the product qa, but the initial rate of tem-perature rise depends on q only, i.e., all particles, re-gardless of size, increase their temperature at the samerate, but the smaller particles do not attain as high afinal temperature as the larger ones. For the particleswith a > 6 for which Kabs is approximately independentof a, the maximum temperature depends on q only, andthe initial rate of temperature rise depends on the ratioqia, i.e., small particles heat up faster, but all particlesattain the same final temperature. These differencesthen form the basis for diagnostic strategies which in-terrogate the size distribution: find a wavelength forwhich 6 is a minimum, heat the particle with a severalnanosecond pulsed laser at that wavelength, and detectthe temperature differences through measurements ofthe incandescence (LMI) or evaporated C2 (RECLAS).At early times the small particles will contribute mostheavily; at later times, the larger particles, with theirarea advantage, will dominate.

C. Calculation of Kabs

Given the complex indices of refraction for the me-dium and the particle, Kabs may be computed from theclosed-form solutions for electromagnetic scatteringfrom a spherical particle, the Mie equations. A FOR-TRAN11 program was used to compute Kext and Kscat;Kabs was calculated as Kext - Kscat-

The selection of values for the index of refraction ofsoot was difficult. The most commonly quoted valuesare those of Dalzell and Sarofim,2 although others havebeen proposed.13-16 Lee and Tien1 6 have used solid-state theory and the dispersion relations to fit experi-mental measurements in the visible and infrared andhave calculated n and k at 300, 1000, and 1450 K for the300-10000-nm wavelength range. Taft and Philipp17and Carter et al. 18 have made reflectancemeasurementson pyrolytic graphite in the 110-3000-nm wavelength

2202 APPLIED OPTICS / Vol. 23, No. 13 / 1 July 1984

range. The Lee and Tien theory does not reproducethese results, probably because it was fit to visible andinfrared measurements, and hence the graphite tran-sition at -260 nm played only a minor role in the overallfunction. Carbon black and presumably soot particlesdisplay this feature prominently.18 Because pyrolyticgraphite displays a microstructure of small graphiticregions laminarly arranged, 1 9 a characteristic of sootparticles also,20 we calculated Kabs using the results ofCarter et al. in the ultraviolet and those of Lee and Tienin the visible. The indices used are likely to be ade-quate for the numerical testing of the laser heatingmethods; subsequent use of the methods would requireindependent determination of the soot index of re-fraction under conditions approximating those of theactual experiment.

The calculated values of Kabs as a function of theparticle radius a are shown in Fig. 1 for the threewavelengths X = 220, 270, and 532 nm. The wave-lengths correspond, respectively, to the optimumwavelength, i.e., minimum 6, the fourth harmonic ofNd:YAG, and the second harmonic of Nd:YAG. Theindices of refraction and 6 values at these three wave-lengths are m = 0.78-1.61i (6 = 0.007 Aim), m = 1.73-2.26i (6 = 0.025 Am) and m = 1.92-0.51i (6 = 0.10 Am),respectively.

D. Prediction of Signals

Equations (4) and (6) may be numerically integratedto obtain T(t) and a(t) for a particular choice of Xex, theexcitation wavelength, q, To, and ao = a(t = 0). As ablackbody, the soot particle radiates isotropically intoa wavelength band AX centered at Xem according to thePlanck blackbody formula, where e is the emissivity,which in this case is equal to Kabs(a) at X = Xem2 1 :

Iem = Xe [exp(hc/Xemkt) - 1]'AX(e4ira2 ).em-

(8)

We may then define a response functionR(a,t,qXex,Xem,AX) as the incremental incandescentradiation received at time t in a bandwidth AX centeredat Xem for excitation of a particle of radius a at wave-length Xex with a triangular laser pulse of peak intensity,q and 10-nsec FWHM.

R(a,t,q,Xex,Xem,AX) = 2 a2 (t)Kabs(aXem)Xem

X 1[exp(hc/XemKT) - 11'

- [exp(hc/XemkTO) - 1]-1. (9)

The incandescence obtained from a distribution ofparticles is then

J(tqX exXemAX) = Np(a)R(atqXeXemAX)da, (10)

where N is the total number density, and p (a) is thenormalized probability density for a particle of radiusa.

As an approximate soot distribution, we have takenthe commonly used zero-order lognormal (ZOLN) dis-tribution in which

2.00-

KABS |=.3 1.50-

100- 270= .2701.00-

0 0.05 0.10 0.15 0.20 0.25

A( microns)

Fig. 1. Absorption efficiencies as a function of particle radius, Xex

- 220, 270, and 532 nm.

p(a) = [(27r)"/2amao exp( 0/2)1-1

X exp[-(loga - loga)2/2ao]. (11)

am is the radius at which p (a) is a maximum, and 00 isthe width parameter.5

To calculate the response function for the C2 mole-cules which are vaporized from the surface of the sootparticles, we calculate the rate of removal of mass fromthe particles:

R(a,t,q,Xex) = dM = pVUD(4ira 2 )f, (12)

where f is the mass fraction of the carbon vapor whichis C2, which, at these temperatures is 0.3.22 A resultanalogous to Eq. (10) is readily derived.

E. Relation to Soot Volume Fractions

Although it is of substantial interest to determine theparameters of the soot size distribution by measurementof integral J and subsequent least-squares fitting, moreimmediate results may be obtained by going to the limitof high laser power and the maximum particle tem-perature. In particular it can be shown that bothtechniques (LMI and RECLAS) give signals which areproportional to the volume fraction of soot at the laserfocus.

1. Laser-Modulated IncandescenceIn the limit of high laser power and maximum tem-

perature, Eq. (6) becomes

Kabs(a)q + \ H4p dt

Fora < 6,

aqlt - 1.22 X 10+8T-1/ 2 exp [23.9 (1 -)]

or

1 =_1 [- 1 log(aq/6)-I391 1ns3a9 n

(13)

(14a)

(14b)


where we have taken T112 to be slowly varying and have

approximated it as (4000)1/2.Inserting this result into Eqs. (9) and (10) we have

approximately

J= Ci NP(a)aXda, (15)

where

X = 3 + 0.154Xem.* (16)

a < is readily achieved by taking Xex large, i.e., in thevisible or infrared, and the deviation of the exponent ofa from 3 is minimized by taking Xem large. For Xem =

700 nm, the exponent has the value 3.22.

2. Direct Measurements of Vaporized C 2

As noted in Eq. (15), the response function for mea-surement of the vaporized C2 is simply dM/dt. Underhigh power, maximum temperature assumptions asbefore Eq. (3) imply that

Kab(a)q 7ra2+ dM 0, (17)

W dtor

J = j: n(a)Kab.(a)7ra2 q R da. (18)

For a < 6,

J irqWH J' n(a)a 3 da. (19)

F. Numerical ProceduresEquations (4) and (6) were integrated numerically to

obtain T(t) and a (t) for a given set of initial conditions.The program allowed a self-set variable step size formaximum efficiency, and integration error in the tem-

4500 0.10

4000 0.08

3500- 0.06

T(K) °\3000 0.04

0 20 40 60 80o 10TIME (nsec)

Fig. 2. Time evolution of particle properties -,a; --- laser in-tensity; .. . response function; and -, temperature. a 0.02 ,um,

To = 2000 K, q = 1.0 X 108 W/CM2.

perature is probably <5 K. Linear interpolation ofKabs(a), which was tabulated at intervals of 0.005 gm,was used to obtain Kabs for both excitation and emis-sion. The response function R was then evaluatedusing Eq. (9) with AX = 0.01 gim. The values of R at5(5)30 nsec, i.e., 5, 20, 15,... , 30 nsec, were obtained bylinear interpolation, involving an interpolation rangeof typically <1 nsec.

Integral J was evaluated using Simpson's rule witha step size of 0.0025 gm and an upper limit of 0.25 gm;the estimated error in this discrete sum is <0.5%.

To test realistically the recovery of the original pa-rameters by the least-squares fitting program, Gaussianrandom noise was added to the simulated data.

G. Nonlinear Least-Squares ProgramThe simulated experiments were fit with a nonlinear

least-squares program using the Marquardt conver-gence algorithm.23 After convergence the programcomputes a set of nonlinear confidence limits based onthe Fisher F test. We have set the statistic to corre-spond to -95% confidence levels.

111. Results and Discussion

In Fig. 2, the values of a(t), T(t), and R(t) are plottedalong with the triangular laser pulse. In this case, ao= 0.02 m, To = 2000 K, Qmax = 1 X 108 W/cM 2 . Thetemperature rises very rapidly, becomes limited by theenergy going into vaporization, and then falls with atime constant appropriate to thermal conduction to themedium. The particle radius decreases only -10%during the process. Similar curves are obtained forother initial conditions.

Figures 3-5 show the response function for LMI ob-tained for optimal laser excitation at X = 220 ni as afunction of the peak laser power q. Note that, at suc-cessively later times, the peak of the response functionshifts to larger particle radii. This is the result ofsmaller particles heating faster than larger particles.Note also that even the earliest distributions peak atparticle radii no smaller than 0.02um. Particles withradii smaller than 0.02 m have a < 6 and hence all heatat the same rate.

Figures 6-8 show similar results for ex = 270 nm.Figure 9 shows the calculated response function for

Xex = 532 nm. In this case, 6 0.1 m, and no peakingis seen in the a < 0.1-gm range.

The results obtained for the response function for C2vaporization (RECLAS) are qualitatively very similarto those obtained for LMI.

The response functions sample different portions ofthe size distribution function at successively later times.Hence, by measuring the laser-modulated incandes-cence as a function of time, one may be able to deter-mine the size distribution of the soot particles. We haverun such a numerical experiment to test the degree towhich the parameters of an assumed soot size distri-bution could be recovered.

Xex = 270 nm, em = 300 nin were taken as the bestresponse functions. These wavelengths correspond to


z0C') .1

0.0 0.5 01 .1 .0 020.5

A ( microns )

Fig. 3. Relative response functions: q = 1 106 W/CM2, Xex= 220

nm, em = 300 n. Maximum of response function = RM = 0.61 X10-4. - -, t =10nsec;- -- *, t =15 nsec;-, t =20 nsec.

0.0 0.05 0.10 0.15 0.20 0.25A ( microns)

ne as Fig. 3, q = 3 X 106 W/cm2

, RM = 0.65 X 10-3.

0.0 0.05 0.10 0.15A (microns)

0.20 0.25

Fig. 5. Same as Fig. 3, q = 1 X 107 W/cm2 , RM = 0.56 X 10-2.

wza

w0.5-

0.00.0 0.05 0.10 0.15 0.20 0.25

A ( microns)

Fig. 6. Relative response functions: q = 1 X 106 W/cm 2 , Xex = 270

nm, Xem = 300 nm, RM = 0.38 X 10-5.

1.0.

w

C',

z0

0.0

0.0~ 0.0 0.05 0.10 0.15 0.20 0.25

A (microns)

Fig. 7. Same as Fig. 6, q = 3 X 106 W/cm2, RM = 0.54 X 10-3.

1.0 -

w IC')z0

:0.5 /

0.0~0.0 0.05 0.10 0.15 0.20 0.25

A (microns)

Fig. 8. Same as Fig. 6, q 1 X 107 W/CM2 , RM = 0.69 X 10-2.


C')z0

C')

14i

IJ1r

Fig. 4. Sar

LLJC')z0

0.5-

w

0.5

0.0

,

wC')z0C')w

0.5 /w

W~~~~~~~~~

0.01 .1

0.0 0.05 0.10 0.15 0.20 0.25A ( microns)

Fig. 9. Relative response functions: q = 3 X 106 W/cm2 , Xex = 532nm, Xem = 600 nm, RM = 0.46 X 10-2.

the most sensitive temperature discrimination in thePlanck distribution which, nonetheless, allows a rea-sonable (5-10% of maximum) incandescence intensityat T = 3915 K.

A set of twenty-four simulated incandescence valueswas generated with q = 0.3 E6, 0.1 E7, 0.3 E7, 0.1 E8W/cm2 and t = 5(5)30 nsec. The value of q = 0.3 E6corresponds approximately to the lowest intensity atwhich laser-modulated incandescence can probably beobserved, and the value q = 0.1 E8 corresponds ap-proximately to the highest intensity at which the in-candescence from small particle is not swamped by theincandescence from large particles. As the laser in-tensity is varied over this range, the incandescencesignal varies over some 4 orders of magnitude. For thepurpose of the calculation, it was assumed that thesignal was not shot-noise limited, that nonpulsedbackground could be subtracted, and that an experi-mentalist would know the amplifier gain factors within1%, and hence the six data points for each value of thepower were normalized so that the maximum of each setwas unity. Computer-generated Gaussian noise witha standard deviation of -0, 1,2, and 5% of the maximumvalues was then added to the data. Any data pointswhich were negative were rejected; in no case was morethan one out of the twenty-four rejected.

The three parameter sets am = 0.02, o = 0.7; am =0.04, o = 0.5; and am = 0.04, o = 0.7 are particularlyappropriate for testing since they are approximately theZOLN parameters which Bockhorn et al. found tocharacterize the distribution of soot particles in aC3H8-0 2 premixed flame at 10, 20, and 40 mm, re-spectively, above the burner.24 The facile recovery ofthese distributions by the laser-modulated incandes-cence technique is evidence of the applicability of LMIto current combustion problems. At 5% added randomnoise, the parameters are recovered with 7%. However,for am 0.02,gm, very poor recovery of the size distri-bution parameters is obtained since the responsefunction falls rapidly below this value and has no

structure. Examination of the least-squares fits showsthat, neglecting for the moment the small variations ina0, it is clear that in these regions the parameter com-bination Na3 is reasonably well fixed, but N and a arenot individually constrained. Bockhorn et al. describeda similar unconstrained correlation involving am andco. Some additional linearly independent constraintwould have to be found to produce good recovery ofparameters.

The numerical experiments indicate that facile re-covery of the parameter of a soot size distribution(ZOLN) should be possible for parameters in the 0.025< am < 0.10 gim, 0.5 o 1.0 range. To test thesecalculations, we attempted to measure the time-de-pendent LMI excited in a sooting ethylene/air flamewith the fourth harmonic of Nd:YAG at 266 nm. Al-though strong incandescent signals could be obtainedfor em > 600 nm, the incandescence at X < 500 nm andt < 10 nsec was swamped by directly excited molecularfluorescence, whose spectrum closely matched that re-ported by Haynes and Wagner.25 Hence, the laser-modulated incandescence technique probably cannotbe used as a soot sizing diagnostic. To obtain good sizediscrimination, one must excite and observe in the ul-traviolet, and in doing so, inevitably the fluorescencefrom polynuclear aromatic hydrocarbons in the sootingflame will interfere.

The C2 vaporization technique should not suffer fromfluorescent interferences to the same degree since itssignal emerges from the flame as a coherent CARSbeam. The numerical experiments described for theLMI response function should be an adequate guide tothe size sensitivity of the C2 vaporization techniques,and hence RECLAS should have considerable potentialas a soot diagnostic.

IV. Conclusions

The equations governing the laser heating and va-porization of a spherical particle have been developedand within the uncertainties in the optical properties


of soot, have been integrated with only minimal ap-proximations. Through a choice of wavelengths atwhich the laser heating is applied, one may minimize 6and hence select the particle sizes which are heated.The particle temperatures may be sensed through theenhanced incandescence or through measurement of thevaporized C2. In both cases, the time and laser powerdependence of the signal may be inverted to obtain thesoot size distribution parameters provided the particlesare mostly >0.02 gm. The LMI method was subjectedto preliminary experimental tests, but attempts to de-tect the incandescence at Xem = 300 nm were unsuc-cessful. Greenhalgh's observation of reasonantly en-hanced CARS from C2 vaporized from soot (RECLAS)makes it likely that soot sizing could be achieved in aCARS experiment.

Either the LMI or RECLAS method should be ableto use visible or infrared wavelengths for laser heatingof soot and thereby measure the volume fraction of sootin the flame. Indeed, such techniques could provide anefficient method of surveying the relative soot volumefraction.

This work was performed while the author was at theUnited Technologies Research Center during 1981-82and their support and interest are gratefully acknowl-edged.

Appendix: Symbol and Value Table

Kabs(a) Mie absorption efficiency;a radius of soot particle, cm (typical <1 X 10-5

cm);q peak laser intensity, W/cM2 ;To ambient flame temperature, K (typical

1500-2000 K);T temperature of particle, K;Ka thermal conductivity of air, W cm-' K-1 =

5.83 X 10-5 (T/273) 0 -82 , N. V. Tsederberg,Thermal Conductivity of Gases and Liquids(MIT Press, Cambridge, 1965), p. 89; 8f

G geometry-dependent heat transfer factor = -

(Y + 1); af Euchen factor, see S. Chapman and T. G.

Cowlings, Mathematical Theory of Non-Uniform Gases (Cambridge U.P., London,1970);

a thermal accommodation coefficient -0.9;,y Cp/Cv (=1.40 for air);Kn Knudsen number = y/L = y/2a;X mean free path, cm = 2.355 X 10-8 T for air at

1 atm;L characteristic length; cm = 2a for sphere;AHv heat of vaporization of carbon, J/mol = 7.78

X 10-5;

Ws molecular weight of solid carbon = 12 g/mol;

M mass particle, grams;t time, sec;0-s density of solid carbon = 2.26 g cm- 3 , Ref.

8;

Cs specific heat of carbon = 1.90 J g-1 K-1,Handbook of Chemistry and Physics (CRCPress, Cleveland, 1962), p. 2266;

T* temperature K at which carbon vapor pres-sure p = p* (for p* = atm, T* = 3915), H. R.Leider, 0. H. Kuckovian, and D. A. Young,"Thermodynamic Properties of Carbon up tothe Critical Point," Carbon 11, 555 (1973);

Pv density of carbon vapor = PWv/RT;WV molecular wt. of vapor taken as 36 g/mol;P vapor pressure of carbon;Usl velocity of vapor;R gas constant = 8.31 J K-1 mol-.

References1. A. C. Eckbreth, "Effects of Laser-Modulated Particulate In-

candescence on Raman Scattering Diagnostics," J. Appl. Phys.48, 4473 (1977).

2. D. A. Greenhalgh, "RECLAS: Resonant-Enhanced CARS from

C2 Produced by Laser Ablation of Soot Particles," Appl. Opt. 22,

1128 (1983).3. C. Dasch, General Motors Research Center; private communi-

cation.4. R. W. Weeks and W. W. Duley, "Aerosol Particulate Sizes from

Light Emission during Excitation by TEA (Transversely ExcitedAtmospheric Pressure) Carbon Dioxide Laser Pulses," J. Appl.Phys. 45, 4661 (1974).

5. M. Kerker, The Scattering of Light and Other ElectromagneticRadiation (Academic, New York, 1969).

6. A. C. Eckbreth, in Experimental Diagnostics in Gas PhaseCombustion Systems, B. T. Zinn, Ed. (AIAA, New York, 1977),

pp. 517-547.7. A. C. Eckbreth, P. A. Bonczyk, and J. F. Verdieck, EPA Report

R79-954403-13 (1979).8. A. C. Eckbreth, P. A. Bonczyk, and J. F. Verdieck, "Combustion

Diagnostics by Laser Raman and Fluorescence Techniques,"

Prog. Energy Combust. Sci. 5, 253 (1979).9. B. J. McCoy and C. Y. Cha, "Transport Phenomena in the Rar-

efied Gas Transport Regime," Chem. Eng. Sci. 29, 381 (1974).

10. D. C. Lencioni and H. Kleiman, MIT LTP-27 (1974), unpub-

lished.11. A. J. Cantor, A Mie Scattering Computer Program, UTRC 77-28

(1977), unpublished.12. W. H. Dalzell and A. F. Sarofim, "Optical Constants of Soot and

their Application to Heat Flux Calculations," Trans. ASME, J.Heat Transfer 91, 100 (1969).

13. V. R. Stull and G. N. Plass, "Emissivity of Dispersed Carbon

Particles," J. Opt. Soc. Am. 50, 121 (1960).

14. S. Chippet and W. A. Gray, "The Size and Optical Properties of

Soot Particles," Combust. Flame 31, 149 (1978).15. J. J. Janzen, "The Refractive Index of Colloidal Carbon," J.

Colloid Interface Sci. 69, 436 (1979).16. S. C. Lee and C. L. Tien, in Proceedings, Eighteenth Interna-

tional Symposium on Combustion (The Combustion Institute,Pittsburgh, 1981), pp. 1159-1166.

17. E. A. Taft and H. R. Philipp, "Optical Properties of Graphite,"

Phys. Rev. A 138, 197 (1965).18. A. Voet, "The Absorption Spectrum of Carbon Black Disper-

sions," Rubber Age 82, 657 (1958).19. J. G. Carter, R. H. Huebner, R. N. Hamm, and R. D. Birkhoff,

"Optical Properties of Graphite in the Region 1100-3000 A,"Phys. Rev. A 137, 639 (1965).

20. J. Lahaye and G. Prado, in Chemistry and Physics of Carbon, Vol.

14, P. L. Walker, Jr., and P. A. Thrower, Eds. (Marcel Dekker,

New York, 1978), Chap. 3.


21. R. B. Bird, W. E. Stewart, and E. N. Lightfoot, Transport Phe-nomena (Wiley, New York, 1960), p. 431.

22. J. Berkowitz and W. A. Chupka, "Mass Spectrometric Study ofVapor Ejected from Graphite and Other Solids by Focussed LaserBeams," J. Chem. Phys. 40, 2735 (1964).

23. D. W. Marquardt, IBM SHARE Library, SDA 3094 (1966).24. H. Bockhorn, F. Felting, V. Meyer, R. Beck, and G. Wanne-

macher, in Proceedings, Eighteenth International Symposiumon Combustion (The Combustion Institute, Pittsburgh, 1981),pp. 1137-47.

25. B. S. Haynes and H. G. Wagner, "Soot Formation," Prog. EnergyCombust. Sci. 7, 229 (1981).

Meetings Calendar continued from page 2200

1985

1986January

19-24 Optical & Electro-Optical Engineering Los AngelesSymp., Los Angeles SPIE, P.O. Box 10, Bellingham,Wash. 98227

February

9-15 Astronomical Instrumentation Confs., Tucson SPIE,P.O. Box 10, Bellingham, Wash. 98227

13-14 Optical Fiber Sensors, OSA Top. Mtg., San DiegoOSA, Mtgs. Dept., 1816 Jefferson P., N. W., Wash.,D.C. 20036

March

9-14 Microlithography Santa Clara Confs., Santa Clara SPIE,P.O. Box 10, Bellingham, Wash. 98227

June

9-13 Quantum Electronics Int. Conf., Phoenix Mtgs. Dept.,OSA, 1816 Jefferson PI., N. W., Wash., D.C. 20036

September

Gradient-Index Optical Imaging Systems (Grin (VI), ItalyD. Moore, Inst. Optics, U. Rochester, Rochester, N. Y.14627

8-20 Optical & Electro-Optical Eng. Cambridge Symp.,Cambridge SPIE, P.O. Box 10, Bellingham, Wash.98227

17-19 Mathematics in Signal Processing Conf., Bath TheDeputy Secretary, Inst. of Mathematics & Its Appli-cations, Maitland House, Warrior Square, South-end-on-Sea, Essex SS1 2JY, England

22-25 Picture Archiving & Communications Systems forMedical Applications Mtg., Kansas City SPIE, P.O.Box 10, Bellingham, Wash. 98227

15-18 OSA, Ann. Mtg., Wash., D.C. OSA, Mtgs. Dept., 1816Jefferson P1., N. W., Wash., D.C. 20036

10-13 Conf. on Lasers & Electro-Optics (CLEO '86), SanFrancisco OSA, Mtgs. Dept., 1816 Jefferson P.,N. W., Wash., D.C. 20036

August

17-22 30th Ann. Inter. Symp. on Optical & Electro-Optical Eng.,San Diego SPIE, P.O. Box 10, Bellingham, Wash.98227

October

5-10 Optical & Electro-Optical Eng., Cambridge Symp.,Cambridge SPIE, P.O. Box 10, Bellingham, Wash.98227

21-24 OSA Ann. Mtg., Los Angeles OSA, Mtgs. Dept., 1816Jefferson P., N. W., Wash., D.C. 20036

0

11-14 4th Int. Congr. on Applications of Lasers & Electro-Optics, San Francisco Laser Inst. of Amer., 5151Monroe St., Suite 118W, Toledo, Ohio 43623

December

8-13 10th Ann. Int. Conf. on Infrared & Millimeter Waves,Lake Buena Vista, Fla. K. Button, MITNat. MagnetLab., Bldg. NW14, Cambridge, Mass. 02139


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October

November

Documents

Soot diagnostics based on laser heating