Chemical and Sooting Structures of Counterflow Diffusion Flames of Butanol Isomers: An Experimental and Modeling Study

ABSTRACT This work reports an experimental and numerical analysis on the sooting characteristics of butanol isomers. Light extinction and gas chromatography were used to measure soot and gas-phase species, respectively. Kinetic analysis of the tested flames was performed with detailed gas-phase mechanism and a sectional soot model. The present work aims to provide an understanding on the effects of butanol isomeric structures on sooting tendencies. For a comprehensive analysis, flames of both neat butanol fuels and butanol/hydrocarbon mixtures were studied. The results showed that the relative ranking of sooting tendencies among the butanol isomers were similar in neat butanol flames and in butanol-doped ethylene flames. In addition, we show that a small amount of butanol addition in ethylene flame enhanced soot formation. It was found that different isomeric structures mainly affected the formation of C3H3, which led to the different concentrations of important aromatic soot precursors. In the butanol-doped ethylene flames, the blending of the four butanol isomers increased the number of C3H3 formation pathways, which in turn significantly increased the production of benzene. Structural effects explaining for the differences in the sooting tendencies of the four butanol isomers in neat butanol flames and ethylene/butanol flames were found to be the same.


Introduction
Butanol is an alternative fuel with promising potentials for the emission reduction of greenhouse gases and soot particles (Vinod Babu, Madhu Murthy, Amba Prasad Rao 2017). As a second-generation biofuel, butanol can be produced from inedible crops including organic waste without posing threats to food security (Naik et al. 2010;Sarathy et al. 2014;). In addition, butanol has a higher energy density, higher cetane number, better miscibility with conventional hydrocarbons, and lower volatility as compared to the widely used ethanol fuel (Hua et al. 2020;Lipovsky et al. 2016). Due to the relatively high cost (Veza, Said, Latiff 2019), co-combustion of butanol with other conventional hydrocarbon fuels, avoiding the need of extensive modification of existing combustion devices, is believed to be a more economical option for its wide applications (Armas, García-Contreras, Ramos 2012). Therefore, it is of interests to investigate the effects of butanol addition on the combustion and emission characteristics of conventional petroleum-derived fuels.
The influence of butanol blending on soot emissions from practical combustion engines has attracted extensive research attention, due primarily to the well-perceived negative environmental implications of soot and the ever increasingly stringent soot emission regulations. For instance, (Şahin and Aksu 2015), as well as (Armas, García-Contreras, Ramos 2014) found that n-butanol doping can significantly reduce the smoke emissions from diesel engines. (Zheng et al. 2015) studied the influence of doping four butanol isomers in a single-cylinder diesel engine. Their results showed that while all the four butanol isomers can effectively reduce soot emissions, the quantitative level of the reduction depended on individual fuel structures. The soot emissions, from the highest to lowest, were in the order of tert-butanol/diesel, n-butanol/diesel, sec-butanol/diesel, and iso-butanol /diesel, indicating iso-butanol has the highest soot reducing potential.
Besides application potentials, butanol with its four isomers provides an interesting research platform on which the effects of molecular structures on soot formation can be investigated with controlled conditions. It is well known that engine soot emissions are dependent not only on fuel sooting propensities but various other fuel properties such as ignition delay and spray characteristics. The complex flow fields along with strong turbulence in the combustion chamber make it challenging to perform fundamental investigation of the sooting characteristics of butanol isomers under engine conditions. In consequence, it is necessary to carry out fundamental research in laboratory-scale flames that have wellcontrolled boundary conditions if the molecular structural effects on soot formation is to be resolved Wang and Chung 2019;Liu 2017, 2021). In this regard, (Russo et al. 2019) studied the effects of the addition of butanol in ethylene (C 2 H 4 ) on particulate matter formation in burner-stabilized premixed flames. Compared with the neat C 2 H 4 flames, the blending of four butanol isomers all reduced the total amount and the size of the soot particles with the most effective soot reducing fuel being tert-butanol, followed in order by iso-butanol, n-,and sec-butanol. (Camacho, Lieb, Wang 2013) found experimentally that the soot volume fraction in premixed flame of iso-butanol was higher than that in n-butanol flames with the same equivalence ratio. (Oßwald et al. 2011) showed that the mole fraction of benzene (which is an important molecular soot precursor) decreased in premixed flame in the order of tert-butanol > iso-butanol > sec-butanol ≈ n-butanol. (Chen et al. 2017) studied the soot reduction effects of the addition of four butanol isomers in partially premixed flames of diesel surrogates (80% n-heptane and 20% toluene in volume) with results showing that the soot formation tendency followed the order of tert-butanol > iso-butanol > sec-butanol > n-butanol. This result was different from Ref. (Russo et al. 2019) where reported tert-butanol was reported as the most effective in reducing the soot formation.
For non-premixed flames, (Singh, Hui, Sung 2016) showed in a counterflow flame configuration that tert-butanol have the highest sooting tendency and sec-butanol the lowest (tert-butanol > n-butanol > iso-butanol > sec-butanol). It is different from the conclusion of (Camacho, Lieb, Wang 2013) that the sooting propensity of iso-butanol is greater than that of n-butanol. With the same flame configuration,  also measured relative concentrations of polycyclic aromatic hydrocarbons (PAHs) using the technique of laser-induced fluorescence with results showing that when the detection wavelength was 334 or 400 nm, the signal intensity gradually decreased according to tertbutanol, iso-butanol, sec-butanol and n-butanol. Surprisingly, when the detection wavelength increased to 450 or 492 nm, the signal intensity of n-butanol was higher than that of iso-butanol and sec-butanol, and second only to tert-butanol. In addition to neat butanol flames, (McEnally and Pfefferle 2011) performed experiments dedicated to the effects of the addition of butanol on the chemical structures of CH 4 coflow diffusion flames. It was found that the concentration of PAHs increased with the addition of four butanol isomers in the order of tert-butanol > iso-butanol > sec-butanol > n-butanol, with the neat CH 4 flame having the lowest PAH. (Jin et al. 2016(Jin et al. , 2014(Jin et al. , 2017(Jin et al. , 2013(Jin et al. , 2015 performed further studies in jet flames of butanol/CH 4 mixtures using molecular beam mass spectrometry and obtained consistent conclusions as (McEnally and Pfefferle 2011). ) studied the effects of butanol addition in n-heptane flames and the results showed that as compared with the neat n-heptane flame, 50% addition of n-butanol, sec-butanol, and iso-butanol resulted in a reduction of peak soot volume fraction by 62%, 40%, and 33%, respectively; on the other hand, 50% addition of tert-butanol led to an increase by 57%.
A comparative analysis of the above studies revealed notable differences in literature results regarding the order of sooting propensity among the four butanol isomers. This order seemed to vary between flames with neat butanol fuel and those with butanol/ hydrocarbon as the fuel. Even for neat butanol cases, the conclusion seemed to depend on specific flame configurations. Therefore, additional studies with detailed comparative and quantitative analysis are required to shed more light on the underlying mechanisms that lead to the different sooting tendencies among the butanol isomers. In this regard, we set out to perform a combined experimental and numerical study on the soot formation process of butanol isomers, focusing on the molecular structural effects. Counterflow diffusion flames (CDFs) were established with neat butanol or butanol/C 2 H 4 mixtures as fuel. Soot volume fractions, major and intermediate combustion products were measured and used for validation of the numerical results based on which reaction pathway analysis was performed to provide kinetic insights. Our choice of the counterflow configuration and the C 2 H 4 baseline (in cases of mixture fuels) are briefly explained below.
CDFs established between two opposing streams of fuel and oxidizer have highly controllable boundary conditions and satisfactory flame stability that are beneficial for quantitative and systematic comparisons of sooting tendencies among different fuels. CDFs also exhibit a quasi-one-dimensional thermochemical structure along the normal direction of the flame, a feature greatly facilitating modeling, experimental measurement as well as kinetic analysis of the flame (Wang and Chung 2019). Furthermore, by adjusting the dilution ratio in the fuel and oxidizer streams, the reacting front can be adjusted to be on the oxidizer side of the stagnation plane resulting in soot formation (SF) type that are particularly useful to study the soot evolution process without much interference of soot oxidation (Singh, Hui, Sung 2016). Besides flames of neat butanol fuels, CDFs with butanol/C 2 H 4 mixtures were also studied in this work with an aim to clarify whether fuel mixing with conventional hydrocarbons would affect the relative ranking of the sooting tendencies among the four butanol isomers. C 2 H 4 was chosen as the base fuel because it has been long a classical target for soot studies, so many existing models were validated and optimized against experimental data in C 2 H 4 flames. Therefore, studying C 2 H 4 /butanol mixture flames can help us focus on the butanol part with minimal uncertainties from C 2 H 4 chemistry. Moreover, C 2 H 4 is one of the most important intermediate products in the combustion and decomposition of larger fossil fuels. Last but not least, previous studies (Salamanca, Sirignano, D'Anna 2012) have shown an interesting effect of fuel synergistic effects for C 2 H 4 /ethanol mixtures (meaning a non-monotonic variation of soot loading with ethanol addition ratio in C 2 H 4 flames), it would be interesting to see whether butanol isomers have similar effects. If so, it would be meaningful to compare and analyze such synergistic effects among the different isomers. Such investigations have never been performed.
This work investigates soot formation in CDFs of four butanol isomers and the influence of C 2 H 4 /butanol mixing. The objectives of the present study are: 1) to explore the order of sooting tendency of the four butanol isomers and the structural effects leading to the different sooting tendencies; 2) to investigate the effects of the addition of butanol isomers to C 2 H 4 on soot formation processes; 3) to analyze the similarities and differences of soot formation pathways between neat butanol flames and C 2 H 4 /butanol flames.

Experimental methods
The experimental apparatus shown in Figure 1 consists of a counterflow burner, a light extinction system and a gas chromatography (GC) system for soot and species mole fraction measurements, respectively. The same burner has been used in previous studies (Zhou et al. Zhou, et al., 2021). The burner assembly has two converging nozzles of 10 mm exit diameter arranged to oppose each other with a separation distance of L = 8 mm. Mixture of N 2 and O 2 was introduced from the top nozzle and fuel from the bottom one. The oxidizer and the fuel flows were shrouded by a coflow of N 2 through annular gaps concentric to the nozzle exits.
The gas flow rates were managed by thermal-based mass flow controllers (MFCs); the liquid fuels (butanol isomers) were metered and vaporized through a controlled evaporator and mixer (CEM) system ( Figure 1) which includes a nebulizing nozzle, an electric heating device, a liquid Coriolis MFC and a thermal-based MFC for the carrier gas (N 2 or C 2 H 4 ). Liquid fuels are stored in an argon gas pressurized tank. The heating temperature of the CEM was set at 20 K above the boiling point of the respective butanol fuels. All the fuel transfer lines and the bottom fuel nozzle were heated by strip heaters to avoid fuel condensation. The temperature of the fuel stream was heated to 393 K in all cases including the baseline neat C 2 H 4 flame for consistent comparisons.
CDFs can be categorized into soot formation (SF) flame and soot formation/oxidation (SFO) type based on the relative positions of the flame and the particle stagnation plane (Kang et al. 1997). In a SF flame, the flame is located on the oxidizer side from the stagnation plane. Since soot is formed on the fuel side of the flame, newly nucleated soot particles shall be transported toward the fuel side without much oxidation, and finally, they will leak through the stagnation plane. In a SFO flame, when the flame is located on the fuel side of the stagnation plane, nascent particles will migrate toward the flame and subsequently oxidized in the flame front (Wang and Chung 2019). In order to analyze the difference of sooting tendencies among butanol isomers in a more comprehensive manner, both SF and SFO flames of neat butanol fuels were investigated in this work. In the experiment of C 2 H 4 /butanol mixture fuels, SF flame was selected to better analyze the potential fuel synergistic effects on soot formation. Soot volume fraction (SVF/f V ) was quantitatively measured by the LE technique (Yan et al. 2019b). Detailed optical arrangement can be seen in Figure 1. It is noticed that the laser beam (λ = 632.8 nm) sequentially passed a mechanical chopper, two flat mirrors, a Galileo beam expander before being focused into the center axis of the flame. The diameter of laser beam at the focal point, which determines the spatial resolution of experiments, was measured to be around 120 μm through a knife-edge method. To perform extinction measurement at different locations of the flame, the whole burner assembly was moved relative to the fixed laser beam via a motorized translation stage. Assuming an axisymmetric soot distribution, the line-of-sight light attenuation data can be tomographically inverted to provide local extinction ratio K ext along the burner central axis (Dasch 1992). According to the Rayleigh-Debye-Gans-fractal aggregate (RDG-FA) theory, soot volume fraction f V can be related to K ext as follows: where E(m) is the soot absorption function which is dependent on the refractive index of soot, m. In the present work, a constant value of m = 1.57-0.56i was used (Santoro, Semerjian, Dobbins 1983;Singh, Hui, Sung 2016). Concentrations of major combustion products and C 1 -C 6 intermediate species were quantified by microprobe sampling and subsequent GC analysis. The gaseous samples were extracted through a fused silica probe whose nozzle was located at the central axis of the burner, and samples were then transferred through a heated sampling line to the GC system. The specific arrangement of microprobe sampling setup and the gas chromatography system can be seen in a previous work ).

Numerical simulation
One-dimensional numerical simulations were performed with the opposed-flow (OPPDIF) module in the Chemkin package (ANSYS Chemkin 17.0 (15151) 2014). The gas-phase chemistry used to describe the fuel pyrolysis, oxidation and PAH growth chemistry (up to coronene) was obtained from (Ranzi et al. 2012) and (Wang, Raj, Chung 2013), resulting in a gas phase kinetic mechanism with 8841 reactions and 345 species. The former detailed oxidation mechanism was developed using a hierarchical approach. Aromatic growth pathways from the latter (KM2) were incorporated so that the mechanism can describe the formation of PAHs up to coronene. Note, the above two sub mechanisms has been validated in a number of studies (Bystrov et al. 2020;Dalili et al. 2020;Hashimoto et al. 2015;Naseri, Veshkini, Thomson 2017;Ranzi et al. 2012;Veshkini et al. 2016;Yang, Lew, Mueller 2020). Based on the present experimental chemical speciation results (to be detailed later), the rates of three reactions in the mechanism were modified with details provided in the supplementary material along with a complete set of mechanism files in the Chemkin format.
Soot modeling were performed by coupling the present gas-phase reaction mechanism with a previously developed soot surface reaction model (Wang, Raj, Chung 2015). Details of the soot model can be found in (Wang, Raj, Chung 2015) along with a complete list of reactions. Briefly, the model includes 36 soot nucleation reactions from dimerization of 8 PAH molecules with sizes between (including) pyrene and coronene. After nucleation, nascent soot particle shall undergo soot mass growth reactions through surface chemistries and physical PAH condensation. In the meantime, particle-particle coagulations alter the size distributions of the particle ensemble and soot oxidation by OH and O 2 reduce the soot sizes. A discrete sectional method (Pejpichestakul et al. 2018;Sirignano, Kent, D'Anna 2013;Veshkini et al. 2016) was used to approximate the solution of the detailed particle number density transport equations. Soot surface mass growth was described by the surface hydrogen-abstraction-C 2 H 2 -addition (surface HACA) mechanism, originally proposed by (Appel et al., 2000) and modified to additional H-abstractions by CH 3 , C 2 H and C 3 H 3 radicals (Hwang and Chung 2001) (surface reaction mechanism provided in the supplementary material). PAH condensation process was modeled as a physical PAH-soot collision process. Different sized PAHs (ranging from pyrene to coronene) will have different condensation rate, which was obtained by multiplying the PAH-soot free-molecular collision rate with size-dependent PAH collision efficiency (details can be found in Ref. (Wang, Raj, Chung 2015)), and with the van der Waals enhancement factor of 2.2. The particle coagulation process (i.e. two soot particles collide with each other to form a larger spherical one) assumed to occur in a free-molecular regime, while the particle agglomeration or the formation of fractal-like soot aggregates were not considered at present (Kumar and Ramkrishna 1996). Note, the soot modeling was performed only for the ethylene baseline and butanol-doped flames to help explain the to-be-detailed fuel synergistic effects on soot formation.

Neat butanol isomers flames
We first discuss experimental results from soot measurements in neat butanol flames. The detailed experimental conditions are as follows: For SF flames, the fuel side was n-butanol/ iso-butanol/sec-butanol/tert-butanol diluted by N 2 (fuel mole fraction X F = 0.3), and the oxidizer was a mixture of O 2 and N 2 with oxygen mole fraction X O = 0.6. For SFO flames, the fuel mole fraction X F = 0.23, and the oxygen mole fraction X O = 1 (i.e., pure oxygen). The nozzle exit velocities of both the fuel and oxidizer streams were maintained at 15 cm/s for all cases, corresponding to a global strain rate of 75 s −1 . Figure 2 shows measured SVF profiles along the centerline of the flames of butanol isomers as a function of the distance from the fuel nozzle Z. Consistent with the soot evolution process in the respective cases (Xu et al. 2018), the skewed soot profile in the SF flames (a) and the nearly symmetric soot profile of the SFO flame (b) can both be clearly seen. Strong structural effects among the butanol isomers were observed in the present experiments. It can be noticed from Figure 2 that regardless of the flame type, sooting propensities of butanol isomers are consistently following the order of tert-butanol > isobutanol > sec-butanol > n-butanol. Quantitatively speaking, the difference of peak SVF between the iso-butanol and the sec-butanol flames is small, while tert-butanol flame is significantly more sooting than the others. The present result on sooting tendency ranking is consistent with previous study in premixed flames where iso-butanol was seen to soot more than n-butanol (Camacho, Lieb, Wang 2013); however, there is a notable difference from the observation by (Singh, Hui, Sung 2016) who showed n-butanol is more sooting than iso-butanol and sec-butanol in counterflow diffusion flames. At the moment, we are not certain about the origins of such discrepancies. Nevertheless, it may be worthwhile to mention that our results are consistent with those of (McEnally and Pfefferle 2011) and (Jin et al. 2016(Jin et al. , 2014(Jin et al. , 2017(Jin et al. , 2013(Jin et al. , 2015, both of which were performed in diffusion flames. Anyway, it is interesting to note that there is such an obvious difference in sooting tendencies among the butanol isomers, especially when noting the peak SVF of tertbutanol flame is an order of magnitude higher than those in flames of the other three butanol isomers, regardless of the flame type. This suggests that the position of hydroxyl group and the structure of carbon chain have strong influence on soot formation. This will be elaborated in depth in the next section, combining experimental chemical speciation data and numerical simulations with detailed chemistries.

Ethylene baseline and the effects of butanol addition
To investigate the interactions between butanol isomers and the hydrocarbons, SVF in neat C 2 H 4 baseline and butanol-doped counterflow diffusion flames of C 2 H 4 were measured. For the baseline C 2 H 4 flame, the fuel side was pure C 2 H 4 (i.e., fuel mole fraction X F = 1), and the oxidizer was 25% O 2 and 75% N 2 (oxygen mole fraction X O = 0.25). For the butanol-doped flames, part of the C 2 H 4 was replaced by the dopants. The doping ratio β, defined as the molar ratio of the dopant in the fuel mixture, was varied from 0 − 0.4. The nozzle exit velocities of both the fuel and oxidizer streams were maintained at the same as those for the neat butanol flames. Figure 3 shows the measured axial profiles of SVF along the centerline of the butanoldoped flames with various-doping ratios. It is interesting to note for all the four different butanol isomers, SVF varied non-monotonically with butanol doping ratio β. Peak SVF in the n-butanol-, iso-butanol -and sec-butanol-doped flames initially increased with β, reaching a maximum value at β = 0.1 and then decreased with further increase of β. The tert-butanol-doped flame showed a similar phenomenon, but the highest SVF appeared at β = 0.2. Note the fact that the addition of a small amount of low sooting tendency fuel may actually enhance soot formation in a flame of higher sooting tendency fuel were previously observed for diffusion flames of ethanol/C 2 H 4 (Litzinger et al. 2011;Salamanca, Sirignano, D'Anna 2012;Yang and Gülder 2021;Zhou et al. Zhou, et al., 2021), propane/C 2 H 4 (Hwang et al. 1998;Lee, Yoon, Chung 2004;Wang, Raj, Chung 2013), dimethyl ether/C 2 H 4 (Choi et al. 2015;Liu et al. 2012;Sirignano, Salamanca, D'Anna 2014), dimethoxymethane/ethylene (Tan et al. Tan, et al., 2021a), dimethyl carbonate/ethylene (Tan et al. Tan, et al., 2021a), iso-propanol/ethylene (Tan et al. Tan, et al., 2021a) and PODE 3 /ethylene (Tan et al. Tan, et al., 2021b) mixtures. This interesting phenomenon is termed as synergistic effects and the present study confirmed for the first time (as far as we are aware of) that it also occurs in diffusion flames of butanol/C 2 H 4 mixtures, and the quantitative extent of the synergistic effects strongly depend on the molecular structure of the butanol isomers. It is worthwhile to mention that our results are notably different from previous conclusion as derived from premixed combustion experiments (Russo et al. 2019) which showed the soot concentrations in burner-stabilized premixed C 2 H 4 flame were reduced consistently no matter that butanol isomer was added. This suggests the soot synergistic are highly dependent on flame configurations (i.e., premixed or non-premixed) which is actually not unexpected: similar phenomena have been elaborated in our previous work on ethanol/ ethylene mixtures with detailed kinetic explanations provided (Zhou et al. Zhou, et al., 2021). Note, however, further analysis in premixed system is not pursed in this work; our present focus was put on the structural effects of butanol isomers on soot formation in diffusion flames.
For better comparisons among the different butanol isomers and doping ratios, the peak SVF in each doped flame, after being normalized by that in the ethylene baseline flame, is shown in Figure 4. As can be noticed, at a fixed β, the sooting propensities of the butanol isomers doped-C 2 H 4 flames still follows the trend of tert-butanol being the highest, n-butanol the lowest, and iso-butanol and sec-butanol in between, which was consistent with the observation made in neat butanol flames. Moreover, Figure 4 shows that the peak SVF of the tert-butanol-doped flame (β = 0.2) is almost twice that in the C 2 H 4 baseline flame; it is much more sooting than the other three butanol isomer-doped flames. This is again consistent with the data shown in Figure 2 that the sooting tendency of tert-butanol flame is much higher than that of the other three butanol isomers. It is apparent that the present fuel synergetic effect on soot formation cannot be explained by the change in flame temperature, carbon flow or fuel oxygen content after butanol addition, because all of these vary monotonically with the increase of β. On the other hand, the chemical cross-linking between the butanol additives and the base fuel C 2 H 4 is believed to be the cause. It is also interesting to note that the peak SVFs of the four butanol isomer-doped flames are quite different, indicating the addition of the same amount of butanol isomers may result in quite opposite effects on soot formation. For instance, adding 40% of tert-butanol in ethylene CDF would enhance peak SVF by 70% while adding the same amount of n-butanol resulted in a reduction of peak SVF by 60%. Another point worthwhile to note is that the ranking of the sooting propensities among the four butanol isomers does not change with β: the sooting tendency of tert-butanol flame is always the highest, n-butanol the lowest, and iso-butanol and sec-butanol are comparable. These experimental observations will be analyzed in detail in subsequent sections where chemical speciation data and results of accompanying numerical simulations are presented.

Neat butanol flames
To help analyze the molecular structure effects on soot formation pathways, measurements of combustion intermediates, especially those directly related to aromatic formation, are of essential importance. In this regard, mole fraction profiles were quantified with microprobe sampling and GC analysis for CDFs of all the four butanol isomers. Note, however, under the flame conditions used in Section 4.1.1 for SVF measurements, the soot concentration in the flames were too high to allow microprobe sampling without frequently blocking of the probe. As a result, for the present sampling measurements both the fuel and oxidizer were further diluted by N 2 so that the fuel and oxygen mole fraction were reduced to 0.2 and 0.29, respectively (i.e., X F = 0.2 and X O = 0.29).
We present in Figure 5 measured mole fractions of major combustion products (i.e., CO, CO 2 , O 2 and H 2 ) along the central axis of the four butanol flames. Note that fuel butanol mole fractions were not available as the present GC column and detector setup were not suitable for measurements of oxygenated species. Numerical data was also included as lines. Due to the opposite flow direction of oxidant and fuel streams, there must be a plane with zero axial velocity between two opposite nozzles. This plane is termed as the gas stagnation plane which was marked as Z st,g in Figure 5. Under the current experimental conditions, the locations of the peak flame temperature (Z T , max ) were on the oxidizer side of Z st,g , confirming the fact that the current flames were of the SF type. Note, the experimental profiles were offset by 0.5 mm toward the oxidizer side to match with the computed mole fraction profile. The main reasons for the discrepancy in the profile locations between the experiment and prediction are as follows: First, the assumption of plug flow velocity boundary conditions (specified at the nozzle exit) may not fully represent the actual flow filed (Bouvet et al. 2014;Niemann, Seshadri, Williams 2015) due to radial non-uniformity and finite radial velocity gradient. Second, although the diameter of microprobe is rather small (inner diameter: 150 μm), the invasiveness of the microprobe still cannot be ignored; previous studies (Bhargava and Westmoreland 1998) have shown that the existence of sampling probe may lead to a shift in terms of the spatial profiles. Nevertheless, after the slight spatial shift, the numerical profiles were in reasonably good agreement with GC experimental data, which provided us with confidence in the predictability of the current kinetic mechanism for the overall flame thermochemical structures. A comparative analysis among the four butanol isomer cases revealed that the CO 2 and O 2 mole profile fraction profiles were almost independent on fuel type. On the other hand, the peak CO and H 2 mole fractions in the tert-butanol flame were notably lower than those in the flames of other three butanol isomers. This experimental observation was also well captured by the numerical model. Benzene (C 6 H 6 , abbreviated as A1 hereafter) is one of the first aromatic species to be formed in aliphatic flames. The formation of A1 has been shown to be a rate-limiting step for the overall PAH growth and soot formation process. Hence, it is important to investigate the kinetic pathways from fuel molecules to A1. As will become clear shortly, kinetic analysis in this work was based primarily on the predicted rates of production (ROP) of important combustion intermediates which included various reactive radical species. On the other hand, the present off-line GC technique could only detect stable species. Hence, for subsequent analysis that involve radical species only computed results shall be shown. Nevertheless, during the discussion we shall have the opportunity to show measured mole fraction profiles of various important stable intermediates to support the validity of the numerical models.
The measured and predicted mole fractions of A1 are depicted in Figure 6. The experimental data showed that the peak mole fraction of A1 was highest in the tert-butanol flame, followed in order by flames of iso-butanol, sec-butanol and n-butanol. This relative ranking was consistent with the ranking of SVF results as shown in Figure 2, suggesting the correlation between A1 mole fraction and SVF in butanol flames. Corresponding numerical simulation successfully reproduced the tendencies of A1 formation among the four butanol isomers although it quantitatively overpredicted A1 mole fraction in the tert-butanol and iso-butanol flames.
For a closer examination of A1 formation, detailed pathways analysis was performed, and the results are shown in Figure 7. Main reaction channels leading from fuel butanol molecules to A1 are indicated by arrows. The numbers near the arrows represented the quantitative contribution of this corresponding reaction channel, which was calculated as the ratio of the ROP from this individual reaction to the overall ROP of the species to which the arrow points to. For example, the number "31%" below "n-C 4 H 9 OH" represents the fact that the water elimination reaction of n-butanol accounted for 31% of all reactions to produce NC 4 H 8 in the n-butanol flame. An overall picture from Figure 7 is that the pyrolysis pathways of four butanol isomers to form A1 were notably different, for which we will analyze in detail. Figure 7. Main A1 formation pathways in four butanol isomers flames. Black, red, blue and green font colors represent the proportion of reactions in n-butanol, iso-butanol, sec-butanol and tert-butanol flames respectively (C 6 H 5 CH 3 : toluene, C 6 H 5 : phenyl radical, C 3 H 3 : propargyl radical, PC 3 H 4 : propyne, AC 3 H 4 : allene, C 3 H 5 -A: allyl radical, i-C 4 H 7 : iso-butenyl radical, NC 4 H 8 : 1-butene + 2-butene, C 3 H 6 : propylene, i-C 3 H 7 : iso-propyl radical, i-C 4 H 8 : iso-butene).
Firstly, it was identified that the reactions of ð Þ were the most important reactions contributing to A1 formation. For quantification of the relative importance of each reaction, their percentage contributions to the total A1 production rate were determined and the results were included in Figure 8. The ROP shown were all normalized by the total A1 ROP in the n-butanol flames so that the total ROP in n-butanol, iso-butanol, sec-butanol and tert-butanol are 100%, 317.2%, 113.8%, and 650.2%, respectively. To obtain the data shown, the net reaction rate profiles of each reaction were integrated over the entire flame region (Skeen, Yablonsky, Axelbaum 2010), after which the relative contribution of each reaction was determined by taking the ratio of individual integrated value to the total A1 production (i.e., the sum of these integrated values).
It can be seen in Figure 8 that the contribution to A1 formation from R1-R4 are significantly higher than that from R5-R7. Furthermore, the differences among the four butanol isomers are also seen to originate primarily from R1-R4. Therefore, the following discussions will be focused on how the four butanol isomers affect the formation of A1 through the reactions R1-R4.
Reactants involved in reactions R1-R4 include C 6 H 5 , C 6 H 5 CH 3 C 2 H 4 , and C 3 H 3 . It can be seen from Figure 7 that C 6 H 5 CH 3 was mainly formed through C 6 H 5 þ CH 3 , ð Þ while C 6 H 5 was in turn produced from 2C 3 H 3 ) C 6 H 5 þ H R9 ð Þ. Therefore, the propargyl radical C 3 H 3 played a decisive role in A1 formation in butanol flames. Figure 9a compares mole fraction profiles of C 3 H 3 among the four flames where the ranking of C 3 H 3 peak mole fractions was seen to be consistent with the ranking of Figure 8. Percentage contribution to A1 production from each reaction in four butanol isomers flames (C 2 H 3 : vinyl radical, CH 3 : methyl radical, C 9 H 8 : indene). A1 formation rate. We further investigated the ROP for C 3 H 3 and the results showed that the primary channels to form The data in Figure 9b and Figure 9c show that the peak values of PC 3 H 4 and AC 3 H 4 both followed the order of tert-butanol > isobutanol > sec-butanol > n-butanol, which largely explained the important role of reactions R10-R13 in the formation of C 3 H 3 and the reasons for the different concentration of C 3 H 3 in the four flames. Further analysis showed PC 3 H 4 was formed through isomerization reactions from AC 3 H 4 ðPC 3 H 4 þ H , AC 3 H 4 þ H; R14Þ, while AC 3 H 4 was mainly formed by the following five pathways: It was noticed that the reaction pathways to produce AC 3 H 4 are somewhat different in the four butanol isomer flames. In particular, AC 3 H 4 in tert-butanol flame was generated simultaneously through pathways P4 and P5. Note, the hydroxyl group in tert-butanol has nine identical adjacent hydrogen atoms available for H 2 O eliminate reaction to form i-C 4 H 8 (McEnally and Pfefferle 2005), which could then decompose first to create C 3 H 6 and then to AC 3 H 4 . In the meantime, i-C 4 H 8 could also dehydrogenate to i-C 4 H 7 and then to AC 3 H 4 by removal of a CH 3 radical. Quantitatively, P5 was the main pathway to form AC 3 H 4 in tertbutanol flame. The concentration of i-C 4 H 8 (Figure 10a) was significantly higher in tertbutanol flame than that in iso-butanol flame, while its concentration in n-butanol and secbutanol flames was almost negligible. The higher concentration of i-C 4 H 8 in the tertbutanol flame through pathway P4 results in a higher mole fraction of C 3 H 5 -A (Figure 10b) than that in n-butanol and sec-butanol. Note C 3 H 5 -A is the dominant source of AC 3 H 4 formation in the latter two flames; while tert-butanol has additional important pathway P5 to form AC 3 H 4 , explaining the higher concentration of AC 3 H 4 in tert-butanol flame.
The intermediate species involved in pathways P1 and P2 are the same. However, since the hydroxyl group in the chemical structure of sec-butanol is in the branched chain position with more adjacent H atoms (Viteri et al. 2017), H 2 O eliminate reaction in the secbutanol flame was more efficient, resulting in a higher concentration of NC 4 H 8 than in the n-butanol flame (Figure 10c). Subsequent decomposition of NC 4 H 8 through ð Þ led to the formation of C 3 H 5 -A, which ultimately resulted in a higher concentration of AC 3 H 4 ðAC 3 H 4 þ H , C 3 H 5 À A; R16 and C 3 H 5 À A þ H , AC 3 H 4 þ H 2 ; R17Þ in the sec-butanol flames as compared to the n-butanol flame.
Compared with n-butanol, the pyrolysis of iso-butanol tended to produce a large amount of i-C 3 H 7 , which were converted to C 3 H 6 ( Figure 10d) and C 3 H 5 -A through reactions Þ, respectively. Although the mole fraction of NC 4 H 8 in n-butanol flame was higher, its contribution to the formation of C 3 H 6 (13%) and C 3 H 5 -A (3%) were relatively low; while the higher concentration of i-C 3 H 7 in iso-butanol flame overwhelm the reaction channels toward C 3 H 4 species, which explained the higher AC 3 H 4 mole fraction in iso-butanol flame. In addition to the SF flames, the differences of the sooting tendencies among the four butanol isomers SFO flames (X F = 0.23 and X O = 1, Figure 2b) has also been analyzed. The mole fraction profiles of A1 and its main formation pathways are shown, respectively, in Fig. S1 and Fig. S2 of the Supplementary Material. It can be easily noticed from Figure 2 that the type of flames (either SF or SFO) did not affect the ranking of sooting tendencies among the butanol isomers. Further ROP analyses showed that the formation pathways of A1 in SFO flames were similar with that in SF flames, hence it can be reasoned that the causes for the different sooting tendencies of the four butanol isomers were similar, regardless of the flame types.
In summary, the different carbon-chain structures, and the positions of hydroxyl functional group in the four butanol isomers led to notable differences in the formation pathways of C 3 H 3 . In particular, C 3 H 3 in tert-butanol flame was formed through two efficient pathways at the same time, which made the C 3 H 3 concentration significantly higher. For all the studied neat butanol flames, C 3 H 3 was consistently the most important species that contribute to A1 formation, hence it made a significant difference in the mole fractions of A1, and ultimately led to different sooting tendencies in the four flames.

Ethylene baseline and butanol-doped flames
To explore the reasons why the concentration of soot increased when small amounts of butanol isomers was doped in the baseline C 2 H 4 flames and the different quantitative extent of the doping effects among the butanol isomers, the formation pathways of A1 were analyzed first. Similar with the neat butanol cases, the flame conditions were adjusted from those used in soot measurement to allow microprobe sample without blockage by soot particles. For the baseline C 2 H 4 flame, fuel and oxygen mole fractions were reduced to X F = 0.5 and X O = 0.2, respectively. For the butanol isomers doped flames, the doping ratios β were fixed at 0.2 so that the fuel stream was composed of 40% ethylene, 10% butanol isomers and 50% N 2 .
Experimental mole fraction profiles of major combustion species are shown in Figure 11 where the doping of butanol isomers was seen to have only minor effect on the concentrations of CO 2 and O 2 . On the other hand, the addition of tert-butanol led to a reduction of peak mole fractions of CO and H 2 -a similar fact as in neat butanol flames and again successfully captured by the numerical predictions. The measured and predicted mole fractions of A1 are compared in Figure 12. It can be noticed that the mole fraction of A1 increased after the doping of butanol isomers and the degree of the increase was different among the butanol isomers, following the trend of tert-butanol being the highest, n-butanol the lowest, and iso-butanol and sec-butanol in between. The above phenomena were reasonably well predicted by numerical simulation both qualitatively and quantitatively so that the performances of the present model were further corroborated.
The major production channels of A1 in the C 2 H 4 baseline and butanol-doped flames are shown in Figure 13. It can be found that the reactions rates relevant to A1 always increased no matter which dopant was added, although the degree of the increase depend on the individual dopant identity. As compared with the baseline case with β = 0, the total A1 ROP increased by 26.5%, 73.6%, 44.2%, and 123.2% with 20% addition of n-butanol, iso-butanol, sec-butanol, and tert-butanol, respectively. Similar to the neat butanol flames, the most important specie that affects the A1 formation in the butanol-doped C 2 H 4 flames was also C 3 H 3 . ROP analysis showed that C 3 H 3 (Figure 14a) was formed in the C 2 H 4 baseline flame mainly through the interaction between C 2 and C 1 species . On the other hand, doping of four butanol isomers would notably enhance the formation of C 3 H 3 through pathways P1-P5 (see Section 4.2.1): the water elimination or other decomposition reactions of butanol isomers led to the formation of C 3 species of AC 3 H 4 and PC 3 H 4 so that C 3 H 3 can be efficiently produced through the dehydrogenation reactions R10-R13. Indeed, data shown in Figure 14b and Figure 14c confirmed the addition of butanol isomers in the C 2 H 4 baseline flame would increase the concentrations of PC 3 H 4 and AC 3 H 4 , respectively.
Considering previous study on ethylene-ethanol mixtures (Yan et al. 2019a), we can notice that although the addition of small amounts of ethanol and butanol would both enhance soot formation in ethylene CDFs, the underlying mechanisms are different. For ethanol-doped flames, ethanol decomposed to form CH 3 , which enhanced the rates of the reactions between C 2 and C 1 to promote C 3 H 3 formation. On the other hand, for butanoldoped flames, butanol decomposition would provide a pool of C 3 species which could then dehydrogenate directly to form C 3 H 3 . The reasons for the different quantitative extent of the increase of C 3 H 3 after the addition of the with four different butanol isomers were found to be similar with what explained the different formation tendency of C 3 H 3 in neat butanol   isomer flames as described in Section 4.2.1: the different hydroxyl positions and carbonchain structures would lead to different decomposition pathways and thus different concentrations of C 3 H 4 species.
With the effects of butanol addition on A1 formation in C 2 H 4 flames explained, we next analyze the molecular growth process toward PAHs and soot particles. In this regard, we first validate the soot model with experimental predicted soot volume fraction profiles in the C 2 H 4 baseline and the butanol-doped (β = 0.1) flames in Figure 15. To avoid showing too many lines in a single figure, flames of the four butanol isomers were compared individually with the  baseline C 2 H 4 flame. Skewed profiles of SVFs can be observed in all cases, which are characteristics of typical counterflow diffusion flames of the SF type. As mentioned previously (Xu et al. 2018), in SF flames, soot particles nucleated on the fuel side of the flame sheet will be transported toward the stagnation plane Z ST,P in a direction that is away from the oxidizing flame front. Soot mass and particle size shall increase through surface reactions and/or particleparticle coagulations during this process while soot oxidation is largely absent. Therefore, SVF would continue to increase following the direction of the bulk flow until reaching the particle stagnation plane where the particles leaked out of the flame in the radial direction, leading to a sudden decrease of SVF across the stagnation plane. These phenomena are well reproduced by the numerical prediction; indeed, the agreement between the experimental and numerical data is satisfactory both qualitatively and quantitatively, indicating the fact that the current soot model can capture the basic characteristics of soot evolution processes.
To provide more insights into the data shown in Figure 15, numerical results on soot nucleation rates, mass growth rate (per unit volume) via surface the HACA mechanism and the surface area normalized HACA growth rate are presented in Figure 16(a-c), respectively. We first note that the soot nucleation rate increased after butanol addition, and the order of the degree of increase among the four butanol isomers was the same as that for PAH concentrations (Figure 16d,e). This is expected considering soot nucleation in the present work was modeled as dimerization of PAHs larger than pyrene (Wang, Raj, Chung 2015). The higher soot nucleation rate translated to higher number density of nascent soot particles and thus more reactive surface sites that are available for surface mass growth. Indeed, the volumetric surface reaction rate ω V,HACA shown in Figure 16b exhibited the same trend as the soot inception rate. On the other, the surface area normalized HACA growth rate (ω S,HACA ) was the highest in the C 2 H 4 baseline flames, which was explainable by Figure 16. Computed centerline axial profiles of soot inception rate (a), soot mass growth rate via surface HACA, ω V,HACA (b), the surface area normalized HACA growth rate, ω S,HACA (c), A4 (d), A7 (e) and C 2 H 2 (f) in C 2 H 4 baseline and butanol-doped flames. its highest C 2 H 2 mole fraction (Figure 16f). The present results indicated that the soot enhancing effects was rooted in the enhanced aromatic species formation and the soot nucleation rates after butanol addition.
In addition, as shown in Figures 3 and 4, when a large amount of butanol isomers was added in the C 2 H 4 baseline flame, the SVF will eventually decrease. The fact that the C 2 H 2 concentrations in butanol-doped flames are lower than that in C 2 H 4 baseline flame (Figure 16f) was observed. The lower C 2 H 2 concentration would have negative effect on surface HCAC mechanism. Eventually, this negative effect may overwhelm the increase of nucleation rates and thus lead to the decrease of SVF.
To sum up, the addition of butanol isomers to ethylene increased the concentration of C 3 H 3 , which in turn promoted the formation of benzene and other larger molecular soot precursors (i.e., PAHs). The difference among the four butanol isomers could be traced back to their decomposition products on which the rates of C 3 H 3 formation were dependent on. The higher mole fraction of PAHs led to higher soot inception rate which finally resulted in more soot being formed in the doped flames.

Concluding remarks
An experimental and computational study was performed to investigate the soot formation process in CDFs of butanol isomers. Major findings are summarized as follows: (1) In CDFs of neat butanol isomers flames, the sooting tendencies ranking followed the order tert-butanol > iso-butanol > sec-butanol > n-butanol for both the SF and SFO configurations. Experimental and simulation results showed that the order of benzene mole fractions in the four butanol isomers flames was consistent with the sooting propensities. Kinetic analyses revealed that different hydroxyl positions and carbon-chain structures of the butanol isomers mainly lead to different pathways of producing C 3 H 3 , which plays a decisive role in the formation of benzene, and then ultimately leads to different sooting tendencies.
(2) Soot concentrations in butanol-doped ethylene CDFs first increased and then decreased with the increase of butanol doping ratio, exhibiting a fuel synergistic effect. Small amounts of butanol addition extended the production channel of C 3 H 3 , leading to notable increases in C 3 H 3 concentration and subsequently a promotion of benzene and PAH formation. The enhanced PAHs concentrations resulted in higher soot nucleation rate, explaining the initial increase of SVF with butanol addition. Further addition of butanol would decrease the concentrations of C 2 H 2 , which is a key mass growth agent through the surface HCAC mechanism; such negative effects on surface reaction would ultimately overwhelm the increase in nucleation rates, leading finally to a decrease of SVF. (3) Relative ranking of sooting tendencies among the butanol isomers were the same, regardless of in neat butanol CDFs or in butanol-doped ethylene CDFs. The major decomposition pathways to C 3 H 3 from the butanol isomers were not affected by the presence of C 2 H 4 .