Soot maturity and absorption cross sections

Author's Accepted Manuscript

Soot Maturity and Absorption Cross Sections Xerxes López-Yglesias, Paul E. Schrader, Hope A. Michelsen

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PII: DOI: Reference:

S0021-8502(14)00067-6 http://dx.doi.org/10.1016/j.jaerosci.2014.04.011 AS4781

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Journal of Aerosol Science

Received date: 25 December 2013 Revised date: 17 April 2014 Accepted date: 17 April 2014 Cite this article as: Xerxes López-Yglesias, Paul E. Schrader, Hope A. Michelsen, Soot Maturity and Absorption Cross Sections, Journal of Aerosol Science, http://dx. doi.org/10.1016/j.jaerosci.2014.04.011 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting galley proof before it is published in its final citable form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.

Soot Maturity and Absorption Cross Sections Xerxes López-Yglesias*, Paul E. Schrader, and Hope A. Michelsen Combustion Research Facility, Sandia National Laboratories, Livermore, CA, USA *Present address Brechtel Manufacturing Inc., Hayward, CA Address correspondence to Hope A. Michelsen, P. O. Box 969, MS 9055, Sandia National Labs, Livermore, CA 94551, E-mail: [email protected], Phone: 925-294-2335; FAX: 925-294-2276

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Running title: Soot Thermal-Accommodation Coefficient and Absorption Cross Section

We used time-resolved laser-induced incandescence (LII) to compare optical and physical properties of soot at the edge and in the center of two co-flow diffusion flames in common use for soot optical-diagnostics development. We made these measurements over a wide range of laser fluences using a laser wavelength of either 532 or 1064 nm. Our results, combined with previous results, suggest that the 532:1064 nm absorption cross-section ratio is 1.8 for mature soot and increases with increasing hydrogen content and decreasing soot maturity. The absolute absorption cross sections at 532 and 1064 nm, on the other hand, increase with soot maturity. Differences in the signal decay rates between center and edge regions further suggest that the thermal-accommodation coefficient decreases with increasing soot maturity. These results were analysed using an energy- and mass-balance model that accounts for the effects of soot maturity on the absorption cross section, thermal-accommodation coefficient, and particle density. Given the sensitivity of LII to these parameters, it may be possible to use a combination of in situ measurements of pulsed LII fluence curves and temporal profiles to gain information about soot maturity. Keywords: soot; thermal accommodation; absorption; cross section; flame; LII

1. Introduction The optical properties of soot are plagued by large uncertainties, which limit the accuracy of soot optical measurement techniques for combustion and atmospheric applications. The wavelength dependence of the absorption cross section, for instance, has been measured to deviate from an inverse wavelength dependence expected for a particle in the Rayleigh regime (Chang and Charalampopoulos, 1990; Köylü, 1996; Köylü and Faeth, 1996; Krishnan et al., 2001; Snelling et al., 2004). The measurements give widely varying results, however, leaving large uncertainties that encompass even the sign of the deviation (Michelsen et al., 2010). These uncertainties are largely attributable to the non-spherical morphology of soot, the variability of its fine structure

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and composition as it evolves in the combustor, the variability in its morphology and composition as it ages in the atmosphere, the range of conditions under which its optical properties have been measured, and the variety of techniques used to make these measurements. Clean, mature soot is composed of small “primary” particles of polycrystalline graphite 10-50 nm in diameter covalently bound into dendritic aggregates of varying size. Mature soot absorbs strongly and broadly across optical wavelength regions and appears black. Less mature soot maintains some of its original hydrocarbon characteristics and thus includes significant hydrogen content. Previous studies have suggested that the wavelength dependence of the absorption cross section tends to shift to shorter wavelengths and decreases in magnitude with increasing hydrogen-to-carbon ratio (H/C) and decreasing percentage of sp2 hybridization, i.e., decreasing soot maturity (Bond and Bergstrom, 2006; D'Alessio et al., 1972; Dalzell and Sarofim, 1969; Habib and Vervisch, 1988; Hopkins et al., 2007; Minutolo et al., 1996; Siddall and McGrath, 1963). Very hydrogen-rich soot particles with little sp2 character often appear brown, rather than black (Andreae and Gelencsér, 2006). These effects are observable over a range of combustion conditions, including laboratory flame conditions (D'Alessio et al., 1972; Habib and Vervisch, 1988; Migliorini et al., 2011; Minutolo et al., 1996; Olofsson et al., 2013; Russo et al., 2013; Siddall and McGrath, 1963), biomass burning conditions (Hopkins et al., 2007; Liu et al., 2013), and engine conditions (Adler et al., 2010; Manin et al., 2013; Strawa et al., 2010), but the effects are not well quantified. In addition, mature soot can be coated with a layer or multiple layers of organic and/or inorganic species, which can also lead to changes in absorption and scattering cross sections (Ackerman and Toon, 1981; Bond et al., 2006; Cappa et al., 2012; Fenn and Oser, 1965; Fuller et al., 1999; Jacobson, 2000; Lack and Cappa, 2010; Liou et al.,

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2011; Stout et al., 2003; Witze et al., 2005). Understanding these effects is critically important for interpreting optical measurements of soot in combustors, exhaust streams, and the atmosphere and for understanding the impact of soot, i.e., black carbon, on climate. Because these effects rely on the underlying particle structure, information gathered from fundamental controlled studies should be transferable to more complex conditions. Laser-induced incandescence (LII) has recently been employed to measure relative absorption cross sections at selected wavelengths (Bejaoui et al., 2013; Cléon et al., 2011; Michelsen et al., 2010; Therssen et al., 2007; Yon et al., 2011). LII measurements entail heating particles with a high-power laser and recording the resulting radiative emission. The particle temperature increases when the laser beam irradiates the particle and reaches a maximum when the conductive-cooling rate balances the absorptive-heating rate. When the laser source is pulsed, this balance usually occurs at the end of the laser pulse at atmospheric pressure. The particle temperature tends not to exceed the sublimation point of ~4000 K, however, and the peak temperature can occur early in the laser pulse at high laser fluences when the particle temperature approaches the sublimation point. For conditions under which conductive cooling, sublimation, and other heating, cooling, and mass-loss mechanisms are negligible compared to absorptive heating, the particle temperature is approximately proportional to the absorption cross section. The LII signal depends on the particle temperature, and the temporal maximum of the LII signal can be used as a proxy for the maximum temperature attained by the particles. Because of the relationship between the LII signal and the particle temperature and the relationship between the particle temperature and the absorption cross section, the LII signal recorded with different laser wavelengths can be used to directly infer the

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relative absorption cross section at different wavelengths. This technique has the advantage over extinction measurements because it is directly related to the absorption cross section and does not require any assumptions about, or measurements of, the scattering cross section whereas extinction is a measure of attenuation by the combination of absorption and scattering. Therssen et al. (2007) were the first to demonstrate the use of LII to infer the relative absorption cross section of soot at 532 and 1064 nm. The Rayleigh approximation yields a predicted cross-section ratio Vabs(532)/Vabs(1064) of 2. The results of Therssen et al. (2007) are consistent with this value for soot from a methane diffusion flame and with similar measurements by Yon et al. (2011) for Diesel and diester fuels ignited with a premixed methane flame and with measurements by Bejaoui et al. (2013) in a methane premixed flat flame and in a Diesel spray ignited with a premixed methane flame. The results of Therssen et al. (2007) yielded a lower value of 1.8±0.1 for an acetylene/air premixed flame, which is consistent with the measurements of this ratio by Michelsen et al. (2010) of 1.78±0.03 and with the wavelength dependence reported previously by Köylü and Faeth (Köylü, 1996; Köylü and Faeth, 1996) for mature soot in ethylene diffusion flames. Cléon et al. (2011) applied the technique in a methane/oxygen/nitrogen low-pressure premixed flame; they derived a value of 2.70±0.14 for soot at large distances from the burner and even higher values closer to the burner. These results suggest that this wavelength dependence is influenced by soot characteristics, such that mature graphitic soot gives much lower values of

Vabs(532)/Vabs(1064) than less mature soot with higher hydrocarbon content. In addition to optical properties, soot maturity and composition can influence other physical properties. Some of these properties, in turn, can influence LII signals. Particle coatings, for instance, can lead to aggregate restructuring and collapse, which

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can reduce the effective surface area and conductive cooling rate after pulsed-laser heating (Bambha et al., 2013). Previous work has also indicated that the conductivecooling rate decreases with increasing soot maturity (Bladh et al., 2009). This observation is consistent with a decrease in surface roughness and associated decrease in the thermal-accommodation coefficient as hydrogen is removed from the surface and the surface becomes more graphitic and ordered (Rettner et al., 1996; Saxena and Joshi, 1981; Thomas et al., 1974). In addition, theoretical and experimental studies have shown that graphite surfaces pucker when hydrogen is bound to the surface (Güttler et al., 2004; Miura et al., 2003; Sha and Jackson, 2002; Sha et al., 2005; Zecho et al., 2002). Because LII is sensitive to these non-optical physical properties of soot particles, understanding the LII signal response to these properties is required for the correct interpretation of these measurements. In particular, pulsed LII is often used to infer soot primary-particle sizes. Temporally resolved measurements are recorded at laser fluences where maximum particle temperatures are below the sublimation point and conductive cooling is the major heat-loss mechanism. The conductive-cooling rate depends on the surface-to-volume ratio of the primary particles. In order to infer primary-particle sizes, the measured LII temporal profiles are fit with a model that calculates cooling rates, particle temperatures, and LII signals, and the particle diameter is used as an adjustable parameter. The conductive-cooling rate calculations rely on the effective thermalaccommodation coefficient used in the model. Uncertainties in this parameter lead to large uncertainties in the inferred particle sizes. In this study we recorded LII temporal profiles from soot in ethylene laminar diffusive flames over two orders of magnitude in laser fluence at laser wavelengths of 532 and 1064 nm and detection wavelengths of 681.8 and 747 nm. The results shown

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here were measured at 681.8 nm. The flames were generated by two similar co-flow diffusion burners, the Gülder burner (Crosland et al., 2011; Migliorini et al., 2011; Snelling et al., 1999; Snelling et al., 2011; Snelling et al., 2004) and the Santoro burner (Dansson et al., 2007; Dobbins and Megaridis, 1987; Goulay et al., 2013; Goulay et al., 2009a, 2010; Goulay et al., 2009b; Kliewer et al., 2011; Köylü et al., 1997; Megaridis and Dobbins, 1989; Puri et al., 1993; Santoro and Miller, 1987; Smyth et al., 1997; Vander Wal, 1998; Vander Wal et al., 1997; Vander Wal et al., 1999). Both burners are widely used in soot studies. We selected these burners because the LII community has chosen these burners as target flames for measurement comparisons (Schulz et al., 2006). In principle these flames should give similar results, and there is a general interest in comparing these flames to determine consistency in LII measurements under similar combustion conditions. These measurements allowed us to infer the absorption cross-section ratios for the two laser wavelengths, i.e., Vabs(532)/Vabs(1064). The cross-section ratios measured here depend on the burner used and the measurement radial position in the flame. We observed differences in the LII temporal profiles and fluence dependence for both flames that suggested compositional differences between the particles at the center and edge of the flame. The magnitude of these differences in the Santoro burner was much greater than in the Gülder burner. We also observed differences in signal decay rates that appear to be attributable to differences in conductive-cooling rates associated with particle

composition.

The

results

suggest

that

the

cross-section

ratio

Vabs(532)/Vabs(1064) and the thermal-accommodation coefficient increase with decreasing soot maturity, whereas the absolute absorption cross sections at 532 and 1064 nm decrease with decreasing soot maturity.

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2. Experimental Approach 2.1 Flames The experimental setup is shown in Fig. 1. Measurements of soot were made in flames generated by one of two nonsmoking laminar co-flow diffusion burners at atmospheric pressure. Both burners were constructed with a central fuel tube surrounded by a larger region for the co-flow of air. The Santoro burner included a brass fuel tube with an 11-mm inner diameter surrounded by ceramic honeycomb with a 102-mm outer diameter, and the flame from this burner was stabilized with a 195-mm tall chimney, 102-mm in diameter (Santoro and Miller, 1987). The visible flame height was 98 mm for an ethylene fuel flow rate of 0.23 standard liters per minute (SLM) and air co-flow flow rate of 43 SLM. Flow rates were measured with mass flow controllers (MKS Type 1479A for ethylene and MKS Type 1589A for air) relative to 0°C and 760 Torr (Santoro et al., 1983). The Gülder burner included a mild steel fuel tube with an 11-mm inner diameter and an outer coflow diameter of 89 mm (Snelling et al., 1999). The visible flame height was 65 mm for an ethylene fuel flow of 0.180 SLM and air co-flow of 264 SLM (Gülder et al., 1996). The flame was stabilized with a tall mesh screen chimney of ~10.2-mm diameter, 255 mm in height from the burner body. Measurements were made at atmospheric pressure. 2.2 Laser set-up We used either the fundamental (1064 nm) or second harmonic (532 nm) output of an injection-seeded Nd:YAG laser (SpectraPhysics Pro 230-10) to irradiate the soot. The pulse duration was 9.0 ns full width at half max (FWHM) at 1064 nm and 7.9 ns FWHM at 532 nm with a repetition rate of 10 Hz. The 1064-nm beam initially passed through a half-wave plate and thin-film polarizer to discriminate against the off-

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polarization introduced by the strain birefringence from the YAG rods. Each beam passed through a motorized half-wave plate and two thin-film polarizers for controllable beam attenuation. The beams were relay-imaged to the detection region in the flame using two telescopes. The near-field output of each beam was imaged onto a 2-mm ceramic aperture using a 1:1 telescope comprised of two 1000-mm focal-length (fl) plano-convex lenses. The role of the aperture was to pass the central portion of the beam to optimize the final spatial and spatio-temporal profiles. This section of the beams was then relay-imaged to the detection region in the flame using a 2:1 telescope comprised of a 1000-mm fl lens and a 500-mm fl lens. This telescope reduced the size of each beam by a factor of 2 and produced a collimated beam at the detection region. Spatial profiles produced at the flame were monitored using a beam profiling camera system with a 6.7 X 6.7 μm pixel size (DataRay WinCamD-UCM); typical spatial profiles are shown in Fig. 2. Fast photodiodes (Electro-Optics Technology ET3500 for 1064 nm, ET4000 for 532 nm) were scanned vertically and horizontally across the beam at the detection region to establish the temporal spread across the beam. The spatial and spatio-temporal profiles were monitored daily, and the spatio-temporal profile was optimized for each dataset. The percent standard deviation of the beam at the detection region was ~11% at 1064 nm and ~12% at 532 nm. The time spread of the spatiotemporal profile was <1.3 ns at 1064 nm and <1.5 ns at 532 nm across all experiments. Throughout the course of these experiments the laser fluence was varied between 0.01 and 2.50 J/cm2. The fluences were calculated by using the average beam diameter at the detection region, which was either 1.078±0.007 mm or 0.964±0.001 mm, depending on the aperture in use. The average pulse energy was measured with a surface absorbing thermopile detector (Coherent PS19Q). The colinearity of the 532-nm and 1064-nm

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beams was established by ensuring that they were aligned to the same target before and beyond the burner. 2.3 Signal detection The LII signal was imaged onto a gated photomultiplier tube (PMT) (Hamamatsu R7400-20) using an achromatic 1:1 telescope (Optosigma 027-3015-MNTD) positioned at a 90° angle relative to the laser beam. The signal was (1) attenuated by a neutral density filter with an optical density of 0.7 if the fluences were >0.040 J/cm2 at 532 nm and >0.078 J/cm2 at 1064 nm, (2) polarization filtered to discriminate against fluorescence interferences and laser scatter using a polarizing cube positioned to reject vertically polarized laser light followed by a polarization scrambler, (3) wavelength filtered to exclude C2 Swan-band emission and laser scatter using a 10-nm bandpass filter centered on 681.8 nm (10-nm bandpass) or 747 nm (33-nm bandpass) and a 532/1064-nm notch filter (Semrock NF03-532/1064E-25), and (4) spatially filtered using a 100-m aperture at the front face of the PMT. Measurements were made at 50 mm height above the burner (HAB) for the Santoro burner and at 42 mm HAB for the Gülder burner. The edge data were recorded at a radial position of 2.60 mm from the centerline for the Santoro burner and at 2.25 mm from the centerline for the Gülder burner. These positions correspond to the maximum in the soot density in the radial direction for each flame. The burners were mounted on a translation stage to move the flame relative to the detection region in order to switch between the center and edge regions. The translation stage was also used to make measurements of the soot radial profiles using the peak LII signal at high fluence (0.30 J/cm2 at 532 nm). Signals were recorded on a 3-GHz bandwidth oscilloscope (Tektronics, TDS694C), triggered by a fast InGaAs photodiode (Electro-Optics Technology, ET-3500) viewing 1064 nm scattered light from the laser oscillator. LII temporal profiles were averaged for 500

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laser shots with a sampling rate of 10 gigasamples/s. We measured a laser timing profile by placing an optical fiber in the detection region with the flame turned off and recording the laser temporal profile scattered from the fiber using the same PMT as was used in the LII experiments with the notch filter removed from the optical path. 3. Analysis Approach 3.1 Peak LII signal and fluence curves The LII signal S from a single primary particle over a range of emission wavelengths

O0-O' can be estimated from the Planck function according to S

:S D

O' 2

³ HO

O0

2Shc 2 6 dO , ª § hc · º O e 5 Oe «exp¨ ¸1» ¬ ©Oe k B T ¹ ¼

(1)

where the emissivity HO accounts for deviations from a perfect blackbody, 6O accounts for the wavelength dependence of the detection system, : accounts for the solid angle detected and detection efficiency, h is the Planck constant, c is the speed of light, kB is the Boltzmann constant, D is the primary-particle diameter, and T is the particle temperature. In the absence of particle size changes and at any particular wavelength or wavelength range and detector efficiencies, the maximum signal will be achieved when the particle temperature reaches a maximum. Measurements that give the same peak LII signal indicate that the particles have reached the same maximum temperature if the measurements are made with the same detection system, detection volume, and particle sizes, morphologies, composition (by the time it reaches the maximum value), and volume fractions, given no optical interferences. At temperatures well below the sublimation temperature and under conditions where absorptive heating dominates the energy balance of the particle, the energy-balance equation can be simplified to yield the expression (Michelsen et al., 2010)

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Tmax

M

³ c Tc dTc| V s

F,

abs L

(2)

T0

where M is the particle mass, cs is the specific heat, Tmax is the maximum particle temperature, T0 is the initial/ambient temperature, FL is the laser fluence, and Vabs is the absorption cross section. Tmax is assumed to occur at the end of the laser pulse at low laser fluences for which the maximum temperature is well below the sublimation temperature. This approximation neglects the effects of conductive cooling and the temperature dependence of the absorption cross section. Assuming that the particle specific heat is constant over this temperature range, performing the integration and rearranging gives

Tmax |

VabsFL Mc s

 T0 .

(3)

Under some conditions, the refractory mature soot particle may be coated with a semi-volatile hydrocarbon coating adsorbed to the surface. If the particles include such a coating, the energy imparted by the laser may also heat and vaporize this coating. Equation (2) can be modified to account for coating vaporization (Bambha et al., 2013), i.e., Tmax

M

³ c Tc dTc M s

vap

T0

ª 'H coat º «c coat Tboil  T0  »| V F , W coat ¼ abs L ¬

(4)

where Mvap is the mass of coating vaporized during the laser pulse, ccoat is the specific heat of the coating, Tboil is its boiling point, Hcoat is its enthalpy of vaporization, and Wcoat is its molecular weight. Assuming that the specific heat of the core particle is constant over this temperature range, performing the integration, and rearranging gives

Tmax |

VabsFL Mc s



M vap Mc s

ª'H coat º  c coat Tboil  T0 » T0 , « ¬ W coat ¼

12

(5)

which indicates that the maximum particle temperature is reduced by an amount that depends on how much energy is devoted to coating vaporization. Under conditions for which the coating is fully vaporized, Mvap is the total mass of the coating and is constant, and Tmax is approximately linearly dependent on the absorption cross section and laser fluence at low laser fluences. 3.2 Absorption cross-section ratio inferred from peak LII signal Whether the particles are coated or not, for any particular detection wavelength, the peak LII signal will occur at Tmax (see Eq. (1)). If the peak LII signal is the same for two laser wavelengths (O1 and O2), and the particle sizes and composition are the same, Eq. (1) implies that the maximum temperature should also be the same, and Eqs. (3) and (5) give

>V O F O @ abs

1

L

1

Tmax

>V O F O @ abs

2

L

2

Tmax

(6)

for particles of the same composition and size measured under the same ambient conditions. Equation (6) yields a cross section ratio of

Vabs O1 Vabs O2

FL O2 FL O1

,

(7)

where the right-hand side of the equation is the ratio of fluences for the two laser wavelengths at which the LII signals reach the same peak value. The absorption cross section for a particle in the Rayleigh regime (O>>SD|m|) can be expressed as (Bohren and Huffman, 1983; Kerker, 1969)

Vabs

S 2 D 3 E ( m) , O

(8)

where E(m) is the dimensionless refractive-index function for absorption for a complex refractive index of m, and O is the absorption wavelength. According to the Rayleigh approximation, the absorption cross-section ratio is given by

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Vabs O1 Vabs O2

E m, O1 O2

E m, O2 O1

.

(9)

If E(m) is independent of wavelength, the cross-section ratio is predicted to be equal to the inverse of the ratio of the wavelengths when the absorptive heating rate is much larger than that of all other heating and cooling mechanisms, mass loss by sublimation is minimal, and interferences from fluorescing species is negligible. 3.3 Absorption cross-section ratio inferred from delayed LII signal Cléon et al. (2011) recently proposed an alternative analysis to circumvent the problems introduced by interferences under conditions perturbed by laser-induced fluorescence (LIF) interferences. They noted that LIF generally has a much shorter lifetime than LII at low fluences. They argued that, if the particles reach the same maximum temperature, under the same ambient conditions, the conductive-cooling rates and LII signal-decay rates should also be the same. Delayed detection that samples LII after the decay of LIF from interfering species could thus be used as a proxy for the maximum particle temperature. For comparison, we have implemented this approach by comparing the fluences at which the LII signals are the same for the two laser wavelengths 50 ns after the onset of the laser pulse, as suggested by Cléon et al. (2011). One third of the peak value of the laser temporal profile on the rising edge of the waveform is defined as a reference for laser onset used in this analysis. The results using this approach are referred to here as delayed LII signals. 3.4 Absorption cross-section differences inferred from fluence curves In order to gain insight into the differences between absorption cross-section ratios in different parts of the flame and for different soot maturity, we made comparisons between the center and edge regions of each flame at the same laser wavelength. For coated and uncoated particles that have the same core particle and reach the same maximum temperature under the same ambient conditions, Eq. (5) implies that 14

Vcoat Fcoat Mc s



º V M vap ª'H coat F  c coat Tboil  T0 » uncoat uncoat , « Mc s ¬ W coat Mc s ¼

(10)

where Fcoat is the fluence for the hydrocarbon-coated particle that brings the core particle to the same maximum temperature as does Funcoat for uncoated particles, Vuncoat is the absorption cross section for uncoated particles, and Vcoat is the corresponding absorption cross section for coated particles. Simplifying and rearranging Eq. (10) yields Fcoat

M vap Vuncoat Funcoat  Vcoat Vcoat

ª'H coat º  c coat Tboil  T0 ». « ¬ W coat ¼

(11)

The peak temperature determines the peak LII signal, and plotting the fluences for coated particles against the fluences for uncoated particles that give the same normalized peak LII signal yields a linear plot from which the coating enhancement to the absorption cross section can be derived from the slope, and the mass of vaporized coating can be derived from the intercept. Bambha et al. (2013) demonstrated this type of analysis for oleic-acid coatings on mature soot particles. This analysis can be extended to particles with different core particles and ambient temperatures. Previous work has demonstrated that higher fluences are required to bring less mature soot particles to the same peak LII signal as mature soot particles (Cléon et al., 2011; Maffi et al., 2011; Olofsson et al., 2013). Results presented here show that particles in the center of these diffusion flames require higher fluences than those at the edge to reach the same normalized peak LII signal. Generalizing Eq. (11) to include differences in core particle composition and ambient temperature yields

Fctr

M vap Vedge M ctrc ctr Fedge  Vctr M edgec edge Vctr





ª'H coat º M ctrc ctr Tedge  Tctr , (12)  c coat Tboil  Tctr » « Vctr ¬ W coat ¼

where Mctr is the particle mass in the flame center, Medge is the particle mass on the flame edge, cctr is the specific heat for the core particles in the center (without any

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coating), cedge is the specific heat for particles on the edge, Vctr is the absorption cross section of particles in the center, Vedge is the absorption cross section of particles on the edge, Fctr is the laser fluence that matches the normalized peak LII of the edge particles at a laser fluence of Fedge, Tctr is the ambient temperature at the center, and Tedge is the ambient temperature at the edge. According to Eq. (12), plotting Fctr relative to Fedge should yield a line with a slope of one if the physical characteristics (absorption cross section, mass, and specific heat) of the uncoated or core particles in the center and on the edge are the same. Because the absorption cross section depends linearly on particle mass, Eq. (12) can be written to emphasize that this relationship does not depend strongly on particle size, i.e., Fctr





º OU ctrc ctr Tedge  Tctr M vap E m,edge U ctrc ctr U ctr O ª'H coat , Fedge   c coat Tboil  Tctr » « E m,ctr U edge c edge M ctr 6SE m,ctr ¬ W coat 6SE m,ctr ¼

(13) where E(m, edge) is the refractive-index function for uncoated mature soot particles at the edge of the flame, E(m, ctr) is the refractive-index function for less mature particles in the center of the flame, Uedge is the density of the particles at the edge, and Uctr is the density of the core particles in the center of the flame. If there is a hydrocarbon coating on the particles in the center, the intercept, given by Intercept

½ ª'H º 1 ­ ®M vap « coat  c coat Tboil  Tctr » M ctrc ctr Tedge  Tctr ¾, Vctr ¯ ¬ W coat ¼ ¿





(14)

depends on the coating mass and physical characteristics in addition to the difference between the ambient temperatures in the two flame regions. Otherwise, the intercept is determined only by the ambient temperature difference and physical characteristics of the particles at the center.

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3.5 Absorption cross-section ratio inferred from combined center and edge data

Because all of the parameters in the curly brackets in Eq. (14) are independent of the laser wavelength, the ratio of the intercepts from fits to the 532- and 1064-nm data should give another measure of the cross-section ratio for the particles in the center, i.e., I1064 I532

Vctr 532 , Vctr 1064

(15)

where I1064 is the intercept of the linear fit to the plot of Fctr relative to Fedge for the 1064-nm data, and I532 is the corresponding intercept to the fit for the 532-nm data. Likewise, the slopes from these plots is given by Slope

Vedge M ctrc ctr Vctr M edgec edge

E m, edge U ctrc ctr . E m, ctr Uedgec edge

(16)

If the density and specific heat of the core particles in the center are the same as those of the uncoated mature particles at the edge (which may not be a bad assumption for graphitic core particles), the slope yields the E(m) ratio for the particles in the two regions. The product of the ratios of the slopes with the ratios of the intercepts yields the absorption cross-section ratios for the two wavelengths at the edge, i.e., S532 I1064 S1064 I532

Vedge 532 , Vedge 1064

(17)

where S1064 is the slope of the linear fit to the plot of Fctr relative to Fedge for the 1064nm data, and S532 is the corresponding slope to the fit for the 532-nm data. 3.6 Corrections and uncertainties

For the analyses presented here, we collected the peak and delayed LII signals and averaged over 12 scans of fluence per burner, flame position, and laser wavelength at a collection wavelength of 681.8 nm. No normalization was applied to the individual runs. Normalizations of peak and delayed LII signals were applied after averaging of

17

the fluence scans, and the same normalization was applied to both wavelengths at each flame location; i.e., 1064 and 532 nm data were not normalized independently. We corrected the fluences for the center and edge of the flames for attenuation by soot in the flame using fluence-dependent transmittance measurements W made through the flame at the appropriate HAB for each flame and laser wavelength. The fluencedependent transmittance for the Santoro burner was described by Michelsen et al. (2010), and a description of the corresponding values for the Gülder burner is in preparation. The fluence at a radial position x along the beam path in the flame is given by FL O, x FL O,0 W O N ,

(18)

where FL(O,0) is the initial laser fluence, and the exponent N represents the integrated soot concentration over the path length traversed in the flame, i.e., x

N

³f C(r)dr f . ³f C(r)dr

(19)

The normalized radial soot concentration C(r) was inferred from measurements of the peak LII signal at a 532-nm laser fluence of 0.30 J/cm2 as a function of radial position r in the flame, as shown in Fig. 3. The radial distributions are asymmetric about the centerline because of the fluence dependence of the peak LII signal and attenuation of the beam in the flame. To partially account for these asymmetries, we numerically reflected the peak signal from one side of the flame across the centerline and used this mirrored image to calculate the integral for the edge attenuation. Assuming perfect cylindrical symmetry in the radial distribution yields a value of 0.5 for N at the flame center. Equation (19) gives a value for N of 0.062 at the front edge of the Gülder flame and 0.093 at the front edge of the Santoro flame.

18

We matched the peak or delayed average LII signals for 532 and 1064 nm measured as a function of fluence and took the ratio of these fluences to derive the cross-section ratio. Uncertainties for this ratio include the uncertainties in the peak (or delayed-signal) values and the fluence, and were calculated using ªF O º L 1 » ' « F O « ¬ L  2 » ¼S1

S2

ªF O º « L 1 » « ¬FL O2 » ¼S1

S2

ªdF O 'S 'FL O1 dFL O2 'S2 'FL O2 º L 1 1 » u «    dS2 FL O2 FL O2 » « ¬ dS1 FL O1 FL O1 ¼

(20) where S1 is the peak (or delayed) LII signal at O1, and S2 is the peak (or delayed) LII signal at O2. These uncertainties in the cross section, calculated using either peak or delayed LII values, rise as the scaled peak LII values approach 0 or 1. At low fluences, uncertainties are significant because the signal levels approach the measurement noise floor. At high fluences where values of the normalized peak LII signal approach 1, the analysis is not valid because sublimation can no longer be ignored. A weighted mean of the cross-section ratio was calculated over an appropriate range of fluences. The upper end of the fluence range was determined by finding the fluence where sublimation appeared to have a measurable effect on the LII temporal profiles. This fluence was identified as the point at which the signal-decay rate increased enough to move the LII temporal maximum to earlier times. At fluences where sublimation occurs, the signal-decay rate increases, and the peak occurs earlier in the laser pulse. Figure 4 shows the timing of the leading edge of the peak at half height as a function of fluence at 1064 nm for the Santoro burner. The peak starts shifting to earlier times above a fluence of 0.10 J/cm2 in the flame’s center region and above a fluence of 0.08 J/cm2 in the flame’s edge region, suggesting a measureable influence of sublimation at these fluences. The peak shifts to later times with increasing fluence at low fluences. This effect may represent a competition between absorptive heating and conductive cooling at low fluences. At these fluences the peak occurs when

19

absorptive heating balances conductive cooling, and this point will occur later in the laser pulse at higher fluences. No statistically significant differences were observed in this fluence value between the two burners. Thus, the weighted mean cross-section ratios were calculated for 1064-nm fluences of 0.10 J/cm2 at the center of the flame and 0.08 J/cm2 at the edge of the flame. These fluences correspond to normalized peak LII values of 0.32 at the Gülder center, 0.21 at the Santoro center, 0.22 at the edge of the Gülder flame, and 0.24 at the edge of the Santoro flame. 3.7 Analysis of absorption rates and signal-decay rates using an LII model

We used an energy- and mass-balance model to assess the impact of soot maturity on conductive cooling rates and absorption cross sections. We used a model that includes heating by laser absorption, oxidation, pyrolysis, and annealing, and cooling by radiative emission, sublimation, thermionic emission, and conduction to the surrounding atmosphere (Michelsen, 2003, 2014; Michelsen et al., 2007a), but we focused on data taken at laser fluences below the point at which the particles reach the sublimation temperature. We compared LII temporal profiles and peak signals recorded in the edge and center regions of the Santoro flame. We used measured primary-particle sizes, fractal dimensions, and ambient temperatures as input into the model and reproduced the signal-decay rates and normalized peak LII signals in these regions. The model allowed us to compare the absorption cross sections and effective thermalaccommodation coefficients for the particles in these two regions. The model incorporates an absorption cross section given by Eq. (8) with E(m) expressed as (Michelsen, 2003) E m

O1[ E . 6S

(21)

The dispersion exponent [ accounts for deviations from a 1/O dependence observed in the visible and near-IR regions, and E is an empirical scaling factor (Köylü, 1996;

20

Köylü and Faeth, 1996; Selamet and Arpaci, 1991). The absorption-cross-section ratio at two wavelengths O1 and O2 is related to the value of [ according to [ Vabs O1 §O2 · ¨ ¸ . Vabs O2 ©O1 ¹

(22)

Previous studies have shown the dispersion exponent to be correlated with the hydrogen-to-carbon ratio (H/C) of the soot (D'Alessio et al., 1972; Dalzell and Sarofim, 1969; Habib and Vervisch, 1988; Minutolo et al., 1996; Siddall and McGrath, 1963), such that particles with higher H/C absorb more strongly at shorter wavelengths. To account for this dependence on soot maturity, the dispersion exponent in the model is expressed as

[ 0.756X ann 1.34 1  X ann ,

(23)

where Xann is the fraction of the particle that has undergone annealing and represents the fine structure order and maturity of the particle; Xann increases as H/C decreases. When Xann reaches one, H/C is zero. Soot primary particles have been demonstrated to undergo annealing to more ordered forms of graphite, such as carbon onions, at temperatures above 2500 K (Bacsa et al., 1993; de Heer and Ugarte, 1993; Ugarte, 1994). Laser heating of soot particles causes similar ordering to occur (Bambha et al., 2013; Michelsen et al., 2007b; Vander Wal and Choi, 1999; Vander Wal et al., 1998). In our model annealing occurs following laser heating, and thus Xann increases on time scales of tens to hundreds of nanoseconds, depending on laser fluence and particle temperature. Previous work has also demonstrated that the magnitude of the absorption cross section, i.e., the value of E, increases with decreasing H/C, increasing soot maturity, and increasing graphitic structure in the visible and near-IR regions (Batten, 1985; Foster and Howarth, 1968; Habib and Vervisch, 1988; Hopkins et al., 2007; Minutolo et al.,

21

1996; Russo et al., 2013). The LII model accounts for this dependence on soot maturity by expressing E according to

§ X ann 1 · [-1 3 u 10 5 T  298.15 @ cm , ¸1 > ©0.17238 ¹

E 90.265exp¨

(24)

where T is given in Kelvin. This expression also accounts for an observed temperature dependence to the absorption cross section, part or all of which is attributable to a decrease in the particle density and thermal expansion with increasing temperature (Michelsen, 2014; Michelsen et al., 2010). Both [ and E were determined empirically by comparison with a wide range of LII data (Michelsen, 2014). The primary particle density Us depends on soot maturity and annealing and is estimated according to

Us

2.28X ann 1.631  X ann

3 3 º ª 6 8 2 1 2.17 u 10 T  298.15  4.98 u 10 T  298.15   » « ¼ ¬

g/cm3,

(25)

where the denominator accounts for thermal expansion of the particle (Michelsen et al., 2010); the value for the thermal-expansion coefficient used here was derived from polycrystalline graphite (Rasor and McClelland, 1960). The density of the particle at room temperature ranges from a value consistent with highly ordered graphite when the particle is fully annealed (Xann=1) (Fried and Howard, 2000) to values consistent with polycrystalline graphite when less mature (Xann<1) (Engle et al., 1970; Rasor and McClelland, 1960). The influence of soot maturity on conductive-heat transfer between the particle surface and the gas phase is not well established. Results published by Bladh et al. (Bladh et al., 2009), however, indicate that the thermal-accommodation coefficient decreases with increasing soot maturity. These observations are supported by experimental and theoretical studies of surface roughening of graphite and enhanced

22

energy transfer between gases and the graphite surface when hydrogen is bound to the surface. (Güttler et al., 2004; Miura et al., 2003; Rettner et al., 1996; Saxena and Joshi, 1981; Sha and Jackson, 2002; Sha et al., 2005; Thomas et al., 1974; Zecho et al., 2002). In order to account for these effects, we have used a model that includes a sootmaturity-dependent thermal-accommodation coefficient given by (Michelsen, 2014)

DT

DTGraphite  DTS 0 1  X annS ,

(26)

where DTS0 is the thermal-accommodation coefficient for a particle with significant surface hydrogen. As the particle is pyrolized or oxidized, and hydrogen is removed from the particle surface, the surface undergoes an annealing process. The surface order is represented by XannS, which is zero at the surface hydrogen saturation coverage of 0.4 (Zecho et al., 2002) and one when the surface is devoid of hydrogen. In our model, surface annealing occurs after the particle is laser heated and takes place on time scales in the range of tens to hundreds of nanoseconds, depending on laser fluence, particle temperature, and partial pressure of oxygen. When the surface is fully annealed, the thermal-accommodation coefficient is reduced to the value inferred from gas-surface scattering experiments on graphite DTGraphite, which is given by (Michelsen, 2009) D TGraphite

>0.28  3.23 u 10

5

@

T  0.8exp1.53 u 10 3 T ,

(27)

where temperature is given in K. 4. Results and Discussion

4.1 Fluence curves: Effects of wavelength, ambient temperature, and particle composition LII temporal profiles were measured at 681.8 nm using laser wavelengths of 532 and 1064 nm and fluences ranging from 0.01 to 2.50 J/cm2 for both the Gülder and Santoro flames. Figure 5 shows the peaks of these temporal profiles plotted as a function of laser fluence for the edge and center regions for the Santoro and Gülder flames. Figure 5 also

23

shows the corresponding delayed LII signals derived according to the approach used by Cléon et al. (2011). The peak and delayed signals increase non-linearly with fluence at low fluences. The peak signal saturates at fluences for which the particle temperature reaches the sublimation point (Goulay et al., 2009b). The delayed LII signal decreases with fluence at these fluences because, once the particles reach the sublimation temperature, the LII signal-decay rate increases, the LII peak occurs earlier in time, and the signal quickly drops as the particles are vaporized. Figure 5a presents the peak and delayed LII data for both 532 nm and 1064 nm in the Santoro flame, and Fig. 5b shows the corresponding results for the Gülder flame. As expected based on Eq. (7), the fluence curve for 1064 nm is shifted to higher fluences (by approx. a factor of 2) relative to the 532-nm fluence curve. One might expect the best agreement in the fluence curves for regions of the flame with the most consistent composition. The edge regions should have more mature soot than the center regions and therefore should demonstrate the most similar behavior between the two flames. The comparison of the edge regions for both flames shown in Fig. 5c demonstrates the same fluence dependence of the peak LII signals within the error bars for fluences >0.04 J/cm2 at 1064 nm and >0.06 J/cm2 at 532 nm for soot in this flame region. The delayed LII signal demonstrates the same differences as the peak LII at low fluence. At higher fluences there are differences in the delayed signal that are attributable to the differences in the signal decay rates in different regions, which are described in detail below. Figure 5d shows a comparison for the LII peak values at the center of the two flames. The distinct shift of the peak LII values towards higher fluences in the Santoro center data relative to the Gülder center data (particularly at 1064 nm) demonstrates more significant differences between the two flames in the center region than in the edge region.

24

Figures 5a and 5b compare the center region with the edge region for the two flames. The fluence curves for both peak and delayed values recorded in the center of the flame show a significant shift to higher fluences relative to those recorded at the edge. This behavior is demonstrated in both flames, but the effect is more pronounced for the Santoro flame. One possible explanation for this fluence shift is related to the influence of surface adsorbates or coatings on LII signals. Bambha et al. (2013) demonstrated a similar shift of peak LII values to higher fluence for particles coated with a volatile coating of oleic acid. When volatile coatings are present, an additional amount of energy is required to remove the coating before the particles reach their peak temperature. Such heavy coatings, however, are not expected for these combustion conditions. Alternatively this fluence shift could be attributable to changes in the physical and optical characteristics of the particles, such as a lower absorption cross section for less mature soot, as would be expected in the flame center. A higher specific heat and/or particle density for the particles in the center of the flame might also explain this shift. Maffi et al. (2011) and Olofsson et al. (2013) measured similar fluence shifts, which increased with a decrease in particle maturity. Olofsson et al. (2013) suggested that this shift was attributable to a decrease in the absorption cross section with decreasing particle maturity, as suggested by the first term on the right-hand side of Eq. (12). This conclusion is consistent with the results of Bladh et al. (Bladh et al., 2011a), which suggested that the absorption cross section at 1064 nm decreased with decreasing soot maturity. Maffi et al. (2011) speculated that the shift in the fluence curves was attributable to a graphitization process. Equation (12) also suggests that the difference in ambient temperature will contribute to this shift.

25

In an attempt to understand the contributions from some of these factors, we have plotted Fctr relative to Fedge (the fluences that give the same normalized peak LII on the center and edge) for each laser wavelength and burner. Figure 6 shows the results and linear fits to the data. The fit range for these values is limited to values of Fedge of 0.0120.154 J/cm2 at 1064 nm and 0.015-0.079 J/cm2 at 532 nm. The fit results are given in Table 2. The Santoro flame yields slopes larger than one for both wavelengths, suggesting that the particles in the edge region have a higher absorption cross section and/or lower density or specific heat than those in the center region (see Eq. (16)). The slopes for the Gülder flame are closer to one, indicating more similar particles in the two regions. All intercept values derived from the linear fits to the data in Fig. 6 are statistically greater than zero, and the values for 1064 nm are greater than those for 532 nm, as would be expected based on the higher absorption cross section for the shorter wavelength (see Eq. (14)). The intercept values are approximately a factor of two higher than would be expected based solely on the temperature differences between the center and edge regions (the second term on the right-hand-side of Eq. (14)). The differences in the fluence curves between the center and edge regions thus appear to be consistent with a combination of effects, including differences in ambient temperature, particle composition, and absorption cross section between the two regions within each flame. Accounting for effects of particle maturity on the absorption cross sections and particle density yields good agreement between the LII model predictions for the peak LII and the corresponding measured values. Figure 7 shows the model results for the peak LII as a function of laser fluence compared to the measurements from the center and edge of the Santoro flame. In Fig. 7a the measurements were reproduced by a model using the soot-maturity-dependent absorption cross section and particle density

26

given in Section 3.7. Figure 7b shows a comparison of the measurements with a modified version of the model that accounts for differences in particle density and ambient temperature between the edge and center regions but uses an absorption cross section with values of [=0.80 and E=48.556 cm-0.2 instead of the soot-maturitydependent values from Eqs. (23) and (24). This absorption cross section reproduces the edge fluence curves but does not reproduce the center fluence curves. In fact, there is very little difference between the center and edge curves calculated with this modified model, suggesting that only a small fraction of the fluence shift between center and edge curves is attributable to the differences in the ambient temperature and estimated particle density between the center and edge regions. The better agreement demonstrated in Fig. 7a indicates that differences in the peak LII signals between the two flame regions can be explained by changes in the wavelength dependence and magnitude of the absorption cross section with soot maturity. 4.2 Absorption cross-section ratios: Effect of particle composition The relative absorption cross sections for the Santoro and Gülder burners at both the center and the edge, shown in Figs. 8-11, were calculated from the data shown in Fig. 5 using Eq. (7). The averages of these values for both peak and delayed LII signals are listed in Table 3. In general the ratios are independent of fluence except at low fluences, where the peak and delayed LII signals are close to zero, and at high fluences, where sublimation invalidates the analysis. Michelsen et al. (Michelsen et al., 2010) demonstrated that the absorption cross section increases with increasing fluence and noted that this increase is consistent with a swelling of the particles with increasing particle temperature. Because the cross-section ratio analysis is based on matching the peak particle temperatures for the two wavelengths for each ratio calculated, the absorption cross sections for the two wavelengths should scale in the same way, and the

27

absorption cross-section ratio should be independent of the temperature-induced change in the absorption cross sections. The Santoro edge data collected at 681.8 nm agrees with the previously measured value in Michelsen et al. (Michelsen et al., 2010) collected under the same conditions. The agreement of the peak and delayed ratio values supports the conclusion that there are no interferences perturbing the results for the Santoro edge data because LIF should be too short-lived to appear in data collected after 50 ns (Cléon et al., 2011; Therssen et al., 2007). In addition, we repeated these measurements with a detection wavelength of 747 nm, and the results were the same as those at 681.8 nm. If LIF were important, we would expect a larger cross-section ratio at detection wavelengths perturbed by LIF (in this case, more likely at 681.8 nm than at 747 nm). The Gülder flame also yields good agreement between peak and delayed ratio values, indicating negligible LIF interferences under these flame conditions. The absorption cross-section ratios calculated using Eq. (7) are statistically consistent with the absorption cross-section ratios derived using Eqs. (15) and (17) and the fits in Fig. 6; these values are also summarized in Table 3. The Santoro edge values collected at 681.8 nm are in agreement within 1 error limits with results obtained by Therssen et al. (Therssen et al., 2007) in acetylene/air premixed flames. The Gülder edge and center values are consistent with those observed by Therssen et al. (Therssen et al., 2007) in a methane diffusion flame, with the results of Yon et al. (Yon et al., 2011) for a premixed Diesel/diester flame, and with the results of Bejaoui et al. (Bejaoui et al., 2013) for premixed methane and Diesel/methane flames. Our results indicate that the absorption cross-section ratio is 1.8 for mature soot and increases as the hydrocarbon content of the particles increases. This conclusion is consistent with the results of Cléon et al. (Cléon et al., 2011) who demonstrated that

28

the ratio increased with decreasing HAB (i.e., increasing hydrocarbon content) in a low pressure, laminar premixed flame. The LII model provides an estimate based on the calculated absorptive heating rates that reproduce the measurements. For a fully mature, graphitic soot particle, the model predicts the absorption cross-section ratio to be 1.69. For particles in the edge of the Santoro flame, the model reproduces the data with a value for Xann of 0.9, which yields a cross section ratio of 1.76, and, for particles in the center of the Santoro flame, the model reproduces the data when Xann is 0.5, yielding a cross-section ratio of 2.07. 4.3 Temporal profiles: Effects of ambient temperature and particle size, morphology, and composition Figure 12 shows LII temporal profiles at selected laser fluences for 532 and 1064 nm. Fluences were matched for profiles that reached the same normalized peak LII, allowing for comparison of decay rates from the same peak temperature. In the edge region, the temporal profiles recorded in the Gülder flame demonstrate faster signal decay rates after the laser pulse than those recorded in the Santoro flame. The reverse is true in the center region, but the decay rates for the two flames are closer in this region. In addition, the center profiles consistently demonstrate faster decay rates than the edge profiles for both flames. Faster LII decay rates may indicate smaller primary-particle sizes because smaller particles have higher surface-to-volume ratios and hence higher conductive-cooling rates (Melton, 1984; Roth and Filippov, 1996; Weeks and Duley, 1974; Will et al., 1998; Will et al., 1995). The mean primary-particle sizes d p inferred from transmission electron microscopy (TEM) images collected for the Santoro flame (summarized in Table 4) are smaller in the center than at the edge, but the difference is small and statistically insignificant (Dobbins and Megaridis, 1987; Köylü and Faeth, 1995; Megaridis and Dobbins, 1989). The TEM data also indicate that particles are

29

smaller in the center of the Gülder burner (Tian et al., 2006) than in the center of the Santoro burner (Köylü et al., 1997; Vander Wal et al., 1999), which would lead to a faster signal decay rate in the Gülder flame than in the Santoro flame rather than the slower decay rate observed. Particle-aggregate sizes and morphologies can also have an effect on LII signaldecay rates. Shielding caused by primary-particle overlap or bridging between primary particles is expected to reduce conductive-cooling rates; thus smaller aggregates with less bridging or overlap will have faster signal decay rates (Bladh et al., 2011b; Johnsson et al., 2013; Kuhlmann et al., 2006; Liu et al., 2005; Liu et al., 2006). Recent work has also demonstrated that less compact aggregates, which have smaller fractal dimensions, have significantly faster signal-decay rates (Bambha et al., 2013). The TEM results again do not support this explanation for the decay-rate differences. The reported fractal dimensions Df are all in the range of 1.7-1.8. The reported values summarized in Table 4 show no clear evidence of a systematic difference in N , Df, and

kf between the center and edge positions for the Santoro burner, and the values for the center of the Gülder flame are the same as those from the Santoro flame within the error bars. In addition, different ambient temperatures for the two flames may give rise to different signal decay rates. The measured temperatures for these flames (see Table 5) suggest that temperatures in the Gülder flame on the edge and in the center are higher than in the Santoro flame at the relevant HABs. This difference would lead to a slightly slower (rather than faster) conductive-cooling rate in the Gülder edge region than in the Santoro edge region, which suggests that temperature differences between the two flames are not responsible for differences in the observed signal decay rates in the edge regions. The observed temperature differences between the center and edge regions in

30

both flames, however, would lead to faster decay rates in the center than at the edge, as observed, but our model indicates that the temperature differences would not be sufficient to explain the trend in signal decay rates (shown below). The observed differences could be attributable to higher thermal-accommodation coefficients and higher conductive-cooling rates for less mature soot. This explanation is plausible because higher hydrogen content will lead to rougher particle surfaces on a molecular scale, which, in turn, leads to higher accommodation coefficients (Honig and Ducker, 2010; Rettner, 1998; Saxena and Joshi, 1981; Thomas et al., 1974). This trend of increasing thermal-accommodation coefficient with decreasing soot maturity is consistent with the results of Bladh et al. (Bladh et al., 2009). Figure 13 shows a comparison of the full LII model (solid black lines) with data from the Santoro burner in the edge (solid gray lines) and center (dotted gray lines) regions at the fluences shown in Figs. 12a and 12b. These fluences are below the fluence at which the particles reach the sublimation point; they were selected to bring the particles to a temperature corresponding to a peak LII approximately a third of the value at which the LII saturates. According to the model, the average Tmax is 3465±13 K. The full model uses measured primary-particle size, fractal dimension, and ambient temperature for the center and edge regions as input and includes the soot-maturity dependent DT given in Eq. (26). This model provides excellent agreement with the measured temporal profiles. Figure 13 also shows a comparison between the measurements and a modified version of the model (dashed black lines). This version of the model accounts for differences in primary-particle size, aggregate morphology, and ambient temperature between the edge and center regions but uses an effective thermal-accommodation coefficient that does not depend on soot maturity (DTS0=0). When this version of the model is constrained to reproduce the edge profiles, it does not give good agreement with the

31

center profiles. Under these conditions, the differences between the measured temporal profiles for the center region and the modified model (the dashed black line in between the measured temporal profiles in each panel) is attributable to an enhancement in the conductive-cooling rate that can be reproduced by using the thermal accommodation coefficient given by Eq. (26). The modified model can almost reproduce the center profiles if the primary-particle size in the center is reduced by 35%, but this modification is not supported by the TEM data. 5. Summary and Conclusions

We have used LII fluence curves to derive relative absorption cross sections of soot at 532 and 1064 nm at the center and edge of flames produced by Gülder and Santoro co-flow diffusion burners, target flames for measurement comparisons in the LII community. We used ratios of fluences at which LII signals for the two wavelengths matched and performed the analysis both at the peak of the LII signal and at a 50-ns delay time (to circumvent potential LIF interferences). The results of the two approaches gave good agreement for each flame condition. The results indicate that the absorption cross-section ratio increases with decreasing soot maturity. Both flames yielded higher absorption cross-section ratios in the center region than on the edge, which is consistent with the results of Cléon et al. (2011) who demonstrated that this ratio increases with decreasing soot maturity. The absorption cross-section ratio in the edge of the Gülder flame was slightly higher than in the edge region of the Santoro flame, suggesting that the soot in the edge region of the Gülder flame at this HAB is less mature than at the corresponding location in the Santoro flame. In contrast, the ratio in the center of the Gülder flame was lower than in the center of the Santoro flame, and soot in the center of the Gülder flame is probably more mature than that in the center of the Santoro flame.

32

Our cross-section ratio values are consistent with previously reported results (Cléon et al., 2011; Michelsen et al., 2010; Therssen et al., 2007; Yon et al., 2011) and suggest that the absorption cross-section ratio

Vabs (532) is 1.8 for mature soot and increases Vabs (1064)

with increasing hydrogen content, i.e., decreasing soot maturity. An LII model that includes a soot-maturity-dependent absorption cross section and reproduces measurements in the edge and center regions of the flame yields a value for this ratio of 1.69 for fully mature, graphitic soot. Measurements of this ratio may provide a means to determine soot maturity or characterize composition. The fluence curves are shifted to higher fluences in the center relative to the edge region in both flames and at both laser wavelengths, suggesting that the absolute absorption cross sections increase with soot maturity. This result is supported by comparisons with an LII model that includes a soot-maturity dependent absorption cross section. The center region fluence curves for the Santoro flame are shifted to higher fluences than those for the center region of the Gülder flame, and the edge region Gülder curves are shifted to slightly higher fluences than the Santoro edge curves. Given a soot-maturity dependent absorption cross section, these observations are consistent with less mature soot in the edge region of the Gülder flame and more mature soot in the center of the Gülder flame than in the Santoro flame, which is consistent with the trends in the absorption cross-section ratio in these regions. Analysis of LII temporal profiles in the center and edge regions of these flames indicates that the thermal-accommodation coefficient decreases with soot maturity after accounting for differences in primary particle size, aggregate morphology, and ambient temperature. This observation is consistent with results presented by Bladh et al. (2009). The observed trends in the absorption cross-section ratios and absolute absorption cross sections are correlated with trends in the signal-decay rates. The LII signal-decay rates

33

decrease with soot maturity and are slower in the edge region than at the center for both flames, in the edge of the Santoro flame than in the edge of the Gülder flame, and in the center of the Gülder flame than in the center of the Santoro flame. Given the internal consistency in these results and sensitivity of these measurements to soot maturity, it may be possible to use a combination of in situ measurements of LII fluence curves and temporal profiles to gain information about soot composition.

Acknowledgements. We thank Daniel Strong for the rendition of the experimental setup shown in Fig. 1 and Pascale Desgroux and Salma Bejaoui for helpful suggestions. This work was funded by the Division of Chemical Sciences, Geosciences, and Biosciences, the Office of Basic Energy Sciences, the U. S. Department of Energy. Sandia is a multi-program laboratory operated by Sandia Corporation, a Lockheed Martin Company, for the National Nuclear Security Administration under contract DE-AC04-94-AL85000.

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47

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Figures

Figure 1. Illustration of the experimental set-up. Soot was generated in a co-flow diffusion ethylene-air flame at atmospheric pressure and irradiated with the 1064-nm or 532-nm output from an injection-seeded Nd:YAG laser. The beam was attenuated with a half-wave plate and thin-film polarizers. The near-field laser output was relay imaged to a ceramic aperture, which selected the center of the beam, and the ceramic aperture was relay imaged with a reduction in size to the detection region in the flame. The beam was monitored with an imaging beam profiler. There were separate optical lines for the different wavelengths (not shown in the illustration). The LII signal was imaged onto a photomultiplier tube through a polarizer crossed with the laser polarization to minimize fluorescence interferences and laser scatter, notch filters (for the laser wavelength), and a bandpass filter centered at 681.8 nm. The signal was collected on a 3-GHz oscilloscope. Figure 2. Spatial beam proles of the laser beam at (a) 532 nm and (b) 1064 nm. Cross sections through the center of each profile are shown to the left and on the top for the

48

532-nm beam and on the bottom for the 1064-nm beam. The 1Vstandard deviation of the intensity from the mean was ~12% for the 532-nm beam and ~11% for the 1064 nm beam. Figure 3. Peak LII signal as a function of radial position in the flame. Profiles are shown for (a) the Santoro at an HAB of 50 mm and (b) the Gülder burner with the laser at an HAB of 42 mm. The laser direction is from the left. The peak LII signal can be used as a proxy for particle concentration in the flame. For both burners, the peak LII is mirrored across the centerline of the flame to account for the decreasing peak LII as a function of increasing fluence at high laser fluences. Figure 4. Timing of the rising edge of the LII temporal profile. The curves represent the time when the rising edge of the LII temporal profile reaches half of the peak value as a function of fluence for 1064-nm excitation. The time was measured relative to the peak of the laser pulse. Results are shown for the center and edge of the Santoro flame. The shift in the peak value to later times at low fluences may be due to changes in the balance between absorptive heating and conductive cooling as the wings of the laser pulse increase in amplitude. The shift in the peak value to earlier times at high fluences is associated with the onset of sublimation. Figure 5. Delayed and peak LII signal as a function of fluence. Peak values shown here represent the average of 12 scans in fluence for each combination of burner, flame position, and laser wavelength. The peak (symbols) and delayed (lines) LII values for the (a) Santoro and (b) Gülder burner flames are shown from the edge and center of the respective flames using 532 and 1064 nm laser wavelengths. The burners are crosscompared along the (c) edge and (d) center of the flame using the delayed (lines) and peak (symbols) LII signal at 532 and 1064 nm. For this figure the maximum of the 532nm peak LII signal is scaled to unity at a fluence of ~0.175 J/cm2 in the center and

49

~0.195 J/cm2 at the edge for both burners, and the 1064-nm peak LII signal and 532-nm and 1064-nm delayed signals are appropriately scaled relative to the 532-nm peak values. Figure 6. Fctr plotted as a function of Fedge for both flames for analysis using Eq. (11). Results are shown separately for laser wavelengths of (a) 532 nm and (b) 1064 nm. Error bars represent 1 standard deviation about the mean. Linear fits to the data were performed over the fluence ranges of 0.012-0.154 J/cm2 at 1064 nm and 0.015-0.079 J/cm2 at 532 nm. The results are summarized in Table 2. Figure 7. Measured and modeled peak LII signal as a function of fluence. Symbols represent measured values for the Santoro flame and are the same as the symbols in Fig. 5a. The lines present model predictions using (a) a soot-maturity dependent absorption cross section and (b) an absorption cross section that is independent of soot maturity. Figure 8. Ratio of the absorption cross section as a function of normalized peak LII signal from data collected at the edge of the Santoro flame. Points are calculated from the peak LII signal and delayed values shown in Fig. 5 with the delayed ratios plotted at the corresponding normalized peak LII. The 1064-nm fluence corresponding to each ratio point is shown for reference. Error bars representing 1 standard deviation about the mean are shown as half error bars to avoid congestion on the graph. The peak LII signal was normalized to the maximum of the 532 nm peak LII signal across all fluences. Figure 9. Ratio of the absorption cross section as a function of peak LII signal from data collected at the center of the Santoro flame. Points are calculated from the peak LII signal and delayed values shown in Fig. 5 with the delayed ratios plotted at the corresponding peak LII. The 1064-nm fluence corresponding to each ratio point is shown for reference. Error bars representing 1 standard deviation about the mean are

50

shown as half error bars to avoid congestion on the graph. The peak LII signal was normalized to the maximum of the 532 nm peak LII signal across all fluences. The measured value derived from digitized data from Yon et al. (Yon et al., 2011) is also shown; error bars for Yon et al. (Yon et al., 2011) represent a ±5% uncertainty in the accuracy of the data.

Figure 10. Ratio of the absorption cross section as a function of peak LII signal from data collected at the edge of the Gülder flame. Points are calculated from the peak LII signal and delayed values shown in Fig. 5 with the delayed ratios plotted at the corresponding peak LII. The 1064-nm fluence corresponding to each ratio point is shown for reference. Error bars representing 1 standard deviation about the mean are shown as half error bars to avoid congestion on the graph. The peak LII signal was normalized to the maximum of the 532 nm peak LII signal across all fluences. Figure 11. Ratio of the absorption cross section as a function of peak LII signal from data collected at the center of the Gülder flame. Points were calculated from the peak LII signal and delayed values shown in Fig. 5 with the delayed ratios plotted at the corresponding peak LII. The 1064-nm fluence corresponding to each ratio point is shown for reference. Error bars representing 1 standard deviation about the mean are shown as half error bars to avoid congestion on the graph. Data from Yon et al. (Yon et al., 2011) is also shown with error bars representing a ±5% uncertainty in accuracy. Figure 12. LII temporal profiles recorded at different laser fluences and laser wavelengths of (a) 532 nm and (b) 1064 nm. LII signal was collected on the edge (solid lines) and center (dashed lines) of co-flow diffusion flames produced by the Santoro and Gülder burners. Measurements were made at 50 mm height above the burner (HAB) for the Santoro burner (black) and at 42 mm HAB for the Gülder burner (gray). See Table 6 for the fluences at which the LII temporal profiles were recorded. Curves were scaled to each other at the temporal maximum.

51

Figure 13. Measured and modeled LII temporal profiles. The data (gray lines) are the same as those shown in Figs. 12a and 12b for the Santoro burner and are described in the legend. The solid black curves represent the model predictions with a soot-maturity dependent

thermal-accommodation

coefficient.

The

dashed

black

curves

(indistinguishable from solid black lines) show the model predictions for the edge, and the dotted blacks show model results for the center where soot maturity was neglected in the calculation. Measurements and model results are shown for laser wavelengths of (a) 532 nm and (b) 1064 nm. Fluences are listed in Table 6. Model and measurement curves were scaled to each other.

Tables

Table 1. Ratios of absorption cross sections (532:1064-nm) reported previously Table 2. Linear fits to Fctr versus Fedge shown in Fig. 6* Table 3. Absorption cross-section ratios in the center and on the edge of the Santoro and Gülder flamesa Table 4. Particle physical characteristics determined by TEM image analysis Table 5. Temperatures in the edge and center regions of the Santoro and Gülder flames Table 6. Fluences associated with data shown in Figs. 12 and 13

52

Table 1. Ratios of absorption cross sections (532:1064-nm) reported previously __________________________________________________________________

V abs (532) V abs (1064)

Source

__________________________________________________________________ Therssen et al. (2007)

1.82±0.09, 2.00±0.10a

Michelsen et al. (2010)

1.78±0.03b

Yon et al. (2011)

2.00±0.10a

Cléon et al. (2011)

2.70±0.14c to ~3.9 1.95±0.10a

Bejaoui et al. (2013)

__________________________________________________________________ a

Error bars represent ±5% uncertainty in the accuracy of the measurement.

b

Error bars represent 1 standard deviation about the mean.

c

The formulation of the error bars is unknown.

53

Table 2. Linear fits to Fctr versus Fedge shown in Fig. 6* __________________________________________________________________ Burner

Wavelength (nm)

Slope

Intercept (J/cm2)

__________________________________________________________________ Gülder

532

0.991±0.028

0.00266±0.00063

Gülder

1064

1.058±0.017

0.00524±0.00076

Santoro

532

1.059±0.031

0.00332±0.00098

Santoro

1064

1.220±0.014

0.00694±0.00083

__________________________________________________________________ *Error bars represent 1 standard deviation about the mean. Ratios are calculated using Eqs. (15) and (17).

54

Table 3. Absorption cross-section ratios in the center and on the edge of the Santoro and Gülder flamesa __________________________________________________________________ Location

Peak LII

Delayed LII

Eq. (18)b or (20)c

__________________________________________________________________ Santoro edge

1.82±0.06

1.82±0.06

1.81±0.75

Gülder edge

1.92±0.06

1.91±0.07

1.85±0.52

Santoro center

2.17±0.07

2.12±0.08

2.09±0.84

Gülder center

2.04±0.05

2.03±0.07

1.97±0.54

__________________________________________________________________ a

Error bars represent 1 standard deviation about the mean.

b

Equation (18) used for centreline values.

c

Equation (20) used for edge values.

55

Table 4. Particle physical characteristics determined by TEM image analysis __________________________________________________________________ Burner Position d p nm

Source

N

Df

kf*

Rg nm

__________________________________________________________________ Köylü, Faeth (1995) laminar Köylü et al. (1997)

all

1.78±0.01 1.76±0.30

Santoro center 31±3.1

65±13 1.72±0.1

2.8±0.6 96±19

Dobbins, Megaridis (1987) Megaridis, Dobbins Santoro edge

33±7

(1989) Puri et al. (1993)

Santoro edge

32±3.2

Vander Wal et al.

Santoro center 33.3±3.2

75±37 1.74±0.10

0.4 146±22 1.60.3

(1999) Tian et al. (2006)

Gülder center

29±7

79.5 1.77±0.01 2.48±0.02 103±25

__________________________________________________________________ *Values inferred from the square root of the mean square radius of gyration Rg and values for N , Df, and d p given here using the equation (Brasil et al., 1999)

§ d · f N ¨¨ p ¸¸ . © 2Rg ¹ D

kf

56

Table 5. Temperatures in the edge and centerline regions of the Santoro and Gülder flames __________________________________________________________________ Source

Burner

HAB (mm)

r (mm)

Temperature (K)

__________________________________________________________________ Santoro et al. (1987) Santoro

50

0

1578±100

Santoro et al. (1987) Santoro

50

2.3

1713±100

Santoro et al. (1987) Santoro

50

2.6

1750±100

Goulay et al. (2013) Santoro

50

2.3

1676±40

Kliewer et al. (2011) Santoro

50

0

1511±55

Kliewer et al. (2011) Santoro

50

2.3

1770±55

Kliewer et al. (2011) Santoro

50

2.6

1790±55

Gülder et al. (1996)

Gülder

42

0

1656

Liu et al. (2002)

Gülder

42

0

1650

Liu et al. (2002)

Gülder

42

2.25

1830

Hadef et al. (2013)

Gülder

42

0

1650±100

Hadef et al. (2013)

Gülder

42

2.25

1850±100

__________________________________________________________________

57

Table 6. Fluences associated with data shown in Figs. 12 and 13 __________________________________________________________________ Figure panel Santoro edge Santoro center J/cm2

J/cm2

Gülder edge

Gülder center

J/cm2

J/cm2

__________________________________________________________________ Panel a

0.048

0.052

0.050

0.052

Panel b

0.086

0.110

0.088

0.093

Panel c

0.070

0.077

0.070

0.071

Panel d

0.133

0.165

0.137

0.146

Panel e

0.117

0.120

0.120

0.121

0.227 Panel f 0.234 0.248 0.244 __________________________________________________________________

58

Highlights

1. We used laser-induced incandescence to study optical and physical properties of soot. 2. The 532:1064-nm absorption cross-section ratio appears to be 1.8 for mature soot. 3. The absorption cross-section ratio appears to decrease with soot maturity. 4. The thermal accommodation coefficient appears to decrease with soot maturity. 5. The 532- and 1064-nm absorption cross sections appear to increase with soot maturity.

59

Figure1color

Figure3

Figure4

Figure5

Figure6

Figure2

Figure7

Figure8

Figure9

Figure10

Figure12

Figure13

Figure11