Flame propagation mechanism of nano-scale PMMA dust explosion

Flame propagation mechanism of nano-scale PMMA dust explosion

Journal Pre-proof Flame propagation mechanism of nano-scale PMMA dust explosion Xinyan Zhang, Wei Gao, Jianliang Yu, Yansong Zhang, Haiyan Chen, Xing...

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Journal Pre-proof Flame propagation mechanism of nano-scale PMMA dust explosion

Xinyan Zhang, Wei Gao, Jianliang Yu, Yansong Zhang, Haiyan Chen, Xingwang Huang PII:

S0032-5910(19)31161-1

DOI:

https://doi.org/10.1016/j.powtec.2019.12.056

Reference:

PTEC 15064

To appear in:

Powder Technology

Received date:

21 April 2019

Revised date:

22 December 2019

Accepted date:

27 December 2019

Please cite this article as: X. Zhang, W. Gao, J. Yu, et al., Flame propagation mechanism of nano-scale PMMA dust explosion, Powder Technology(2019), https://doi.org/10.1016/ j.powtec.2019.12.056

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© 2019 Published by Elsevier.

Journal Pre-proof

Flame propagation mechanism of nano-scale PMMA dust explosion Xinyan Zhang a,b,c,*, Wei Gao d, Jianliang Yu d, Yansong Zhang a, Haiyan Chen a, Xingwang Huang a a

School of Mining and Safety Engineering, Shandong University of Science and Technology, Qingdao 266590, PR China b

Mine Disaster Prevention and Control-Ministry of State Key Laboratory Breeding Base, Shandong University of Science and Technology, Qingdao 266590, PR China

c

National Demonstration Center for Experimental Mining Engineering Education, Shandong

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University of Science and Technology, Qingdao 266590, PR China d

School of Chemical Machinery and Safety Engineering, Dalian University of Technology, Dalian

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116024, PR China

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Abstract: Experiments of nano-scale polymethyl methacrylate dust explosions were conducted to reveal the flame propagation characteristics and evolution mechanism. The results showed that

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the flame preheat zone front was approximately smooth. The average pulsating flame propagation velocity and maximum temperature both increased with an increase in dust concentration. The

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thermal heat transfer rate and pyrolysis rate dominated the propagating flame. A transition from pyrolysis rate control to combustion reaction rate control occurred as the dust concentration

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increased during the combustion process. Speculating from the physical model of nano dust flame propagation including a post-flame zone, a luminous spot-flame reaction zone, a combustible

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premixed-gas reaction zone, a preheat zone, an unburnt particle stagnation zone, and an unburnt zone away from the flame front, the propagating flame was macroscopically analogous to the kinetic combustion of premixed gas. In addition, it was microscopically coupled with the localised diffusion combustion of luminous spot flames.

Keywords: Nano dust explosion, flame propagation mechanism, flame microstructure, flame temperature

1. Introduction Nanotechnology has become one of the fastest growing and most promising technologies. Nanomaterials have attracted much attention, and their use has grown tremendously in industrial applications such as batteries, cosmetics, pharmaceuticals, catalysts, clothing, plastics, tyres, and electronics. Nanomaterials exhibit special reactivity, strength, fluorescence, conduction, *

Corresponding author: School of Mining and Safety Engineering, Shandong University of Science and Technology, Qingdao, Shandong 266590, China. Tel.: +86 0532 86057037. Fax: +86 0532 86057050. E-mail address: [email protected] (Xinyan Zhang).

Journal Pre-proof absorption, reflection, and catalysis functions and have broad application prospects and significant economic benefits [1]. Nano dust is comprised of small particles with large specific surface areas and large numbers of surface atoms, which increase the risk of explosions. Therefore, preventing and mitigating nano dust explosion accidents to ensure the safe production has attracted intense attention. Current research has mostly focused on the sensitivity of nano dust explosions and the destructive power of shock waves. Studies have found that the sensitivity parameters of minimum ignition temperature, minimum ignition energy, minimum explosion concentration, and minimum oxygen content of nano dust explosions are much lower than those of micron dust [2–5],

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indicating the extremely high potential danger of nano dust. However, the agglomeration caused by the strong interaction between nano particles and the large specific surface area of particles

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prevent the maximum explosion pressure and maximum pressure rise rate from increasing

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significantly as the particle size decreases to a nano scale [5–10]. To date, no uniform conclusions on the severity of nano dust explosions exist because of their complex explosion mechanism.

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Therefore, it is necessary to investigate the mechanism of nano dust explosions in more depth. Current studies have been unable to effectively reveal the combustion characteristics and stable

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flame configuration of nano dust. A few studies that investigated the microscopic flame configuration and mechanism of flame evolution of nano dust explosions, which is crucial to

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explosion prevention and mitigation. Kylafis et al. [11] applied an optical technique of the Schlieren system to determine the flame speed in ignited nano powder-based hybrid mixtures and found that flame speed was strongly associated with the fraction of ultrafine particles. Bocanegra

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et. al. [12] found gas-phase flame propagation in a nano aluminium cloud and proposed a three-stage combustion model, which included oxidation in the condensed phase, in the gaseous phase, and in a homogeneous gaseous mixture. Sundaram et. al. [13] divided the oxidation process of nano aluminium particles into four stages based on phase transformations and chemical reactions. Huang et. al. [14] investigated the Bunsen type premixed flame microstructure of bimodal nano/micron-sized aluminium particles, which displayed either an overlapping or a separating flame depending on the combustion property of the aluminium particles at different scales. As for the agglomeration generally existing in nano dust, Tang et. al. [15] found that nano aluminium agglomerates had the same low ignition temperature and as fast an energy release rate as that of single particle combustion. They proposed a melt/vapour dispersion mechanism to cover the micro-explosion and subsequent accelerated oxidation reactions. However, the essential issues of nano dust explosions are still not fully understood. In this study, the dynamic flame evolution characteristics of nano dust explosions was investigated, the flame microstructure observed, and the flame propagation mechanism revealed to

Journal Pre-proof formulate safety strategies to prevent nano dust explosions and mitigate this hazard.

2. Experimental apparatus and material 2.1 Experimental apparatus The open-space dust explosion experimental apparatus illustrated in Fig. 1 was used to study the flame propagation characteristics of nano-scale dust explosions. The detailed configuration is described in our previous study [16]. The ignition unit was composed of a 15-kV voltage transformer and a pair of 1.0-mm diameter tungsten wire electrodes. The gap between the electrodes was approximately 4 mm. The discharge time for ignition was 10 ms, and the ignition

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energy estimated by the integral calculation of the current and voltage was approximately 4.5 J. A fine thermocouple comprised of 25-μm diameter Pt-Pt/Rh13% wires was used to detect the flame

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temperature. High-speed photography was adopted to track the dynamic flame evolutions. Micro photography and a Z-shaped parallel reflective Schlieren optical system were used to observe the

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flame microstructure.

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A pneumatic dispersion system was used to form the combustible dust clouds. During dispersion, the dust particles were partially lost and led to a lower initial concentration than that

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theoretically calculated. Therefore, the initial dust concentration was measured by the measurement apparatus [17] shown in Fig. 2. The dispersion conditions were the same as those of

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the combustion experiments. A dust-capture board driven by a cylinder was inserted into the gap of a moveable tube at the moment of ignition. After all the particles suspended in the moveable

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tube settled on the dust-capture board, the captured particles were weighed. The initial dust concentration was then determined by the ratio of the weighed particle mass and the volume of the moveable tube.

2.2 Experimental material

Series MP-300 (100 nm) and Series MX-80H3wT (800 nm) polymethyl methacrylate (PMMA) particles provided by Soken Chemical & Engineering Co., Ltd. of Japan were used as experimental materials. The thermo-physical parameters of PMMA are listed in our previous study [16]. The PMMA particles exhibited strong hygroscopicity because of the molecular structure of the polar-side methyl group. The moisture content can increase the liquid bridge forces between particles and lead to particle agglomeration. Therefore, the samples were dried in an air-dry oven for 24 h before conducting thermal property tests and explosion experiments to reduce the influence of moisture. 2.2.1 Particle morphology and size distribution

Journal Pre-proof The micrographs of PMMA particles were obtained using scanning electron microscopy (FEI Nova NanoSEM 450). As shown in Fig. 3, the spherical 100 nm particles were densely distributed, and amounts of large-sized agglomerates were observed with irregular shapes, whereas the 800 nm spherical particles were less densely distributed. The particle surfaces adhered to each other, and there were no obvious agglomerates. As for the particle-size distribution (PSD), a Malvern Mastersizer 2000 (AWM 2000) was first used to provide information of the dispersity and degree of agglomeration of the dust particles in their natural state. A phase doppler particle analyser system (TSI INCORPORATED) was then used to measure the PSD in suspension, reflecting the initial particle-size characteristics of a

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dust-cloud explosion. The results are shown in Fig. 4 and Table 1.

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The PSD of 100 nm particles was wider than that of the 800 nm particles and ranged from 0.448 μm to 89.337 μm before dispersion; most particles were in the range 25.179–28.251 μm.

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The average volume diameter D[4,3] and surface mean diameter D[3,2] were 24.877 and 10.486 μm, respectively. Obviously, the PSD in the sonicated suspension was much larger than that of the

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average particle size provided by the manufacturer, and the 100 nm particles easily adhered to each other and formed agglomerates because of the strong inter-particle cohesion forces. However,

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when the 100 nm particles uniformly placed in the dust chamber were continuously dispersed by a 0.5-MPa air flow for 0.5 s to form a uniform combustible dust cloud, the PSD of the dust particles

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suspended near the ignition electrodes had a D[4,3] of 24.896 μm and a D[3,2] of 22.893 μm. The PSD of the 800 nm particles ranged from 0.317 to 2.825 μm before dispersion, and most particles

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were in the range 0.796–1.002 μm. The D[4,3] and D[3,2] were 0.966 and 0.870 μm, respectively. Both were consistent with the average diameter provided by the manufacturer, indicating good dispersity in the sonicated suspension. However, the D[4,3] and D[3,2] of the suspension dust cloud were 27.433 and 22.680 μm, respectively. In addition, the dimensionless number ϕ was defined as the ratio of D[3,2] before and after dispersion to evaluate the degree of agglomeration. The ϕ for 100 nm and 800 nm particles were 2.18 and 26, respectively. The 800 nm particles formed agglomerates more easily than the 100 nm particles during dispersion because of the collisions and friction between the particles in a high-speed air flow. The results indicated that the PSD of a combustible dust cloud is affected by many factors. The ultra-fine particles were more prone to agglomerate, which reduced their suspension ability because of large inner-particle van der Waals, electrostatic, and fluid forces. In addition, during dispersion, the frequent collisions and friction between dust particles in the high-speed air flow generated a large electrostatic force to drive agglomeration. At the same time, if the dispersion flow strength was strong, the shear force could break the agglomerates to ease agglomeration.

Journal Pre-proof 2.2.2 Thermal pyrolysis and oxidation characteristics The thermal pyrolysis and oxidation characteristics of 100 nm and 800 nm PMMA were analysed using a synchronous thermal analyser (SDT-Q600). The data of thermogravimetry (TG), differential thermogravimetry (DTG), and differential scanning calorimetry (DSC) profiles were recorded simultaneously. Non-isothermal thermogravimetric analysis was adopted. PMMA dust samples of approximately 10 mg were placed in ceramic crucibles. The samples were heated at a heating rate of 10 °C/min from room temperature to 800 °C. Compressed air was used as a protective gas with a flow rate of 100 mL/min. The results are shown in Figs. 5 and 6. The weight loss of both the 100 nm and 800 nm particles mainly contained two stages: rapid weight-loss

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dominated by thermal pyrolysis reaction and slow weight-loss mainly preceding the thermal

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oxidation reaction of the pyrolysis products.

Under thermal heat affection, the 100 nm particles started to lose weight at approximately

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228 °C. The weight loss was caused by pyrolysis rather than evaporation. The reasons are that first, the PMMA has no obvious melting point. A glass transition occurs as the temperature increases.

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The pyrolysis probably occurs in a molten-phase or a condensed-phase [18, 19]. Second, there was no obvious endothermic peak on the DSC curve at around 220–230 °C, inferring that no

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evaporation phase change occurred. Third, the evaporation temperature of PMMA particles is 375 °C [18, 20]. Obviously, the pyrolysis temperature is lower than the evaporation temperature.

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Therefore the weight loss at around 220–230 °C was caused by pyrolysis rather than evaporation. Then the TG curve started to decline as the weight loss rate quickly increased. At approximately

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350 °C, the maximum weight-loss rate was reached at the DTG peak. Subsequently, the weight-loss rate quickly decreased as the temperature continuously increased. When the temperature exceeded 400 °C, the pyrolysis entered the slow weight-loss stage. In this stage, the DSC reading reached an exothermic peak at approximately 403 °C. At this point, the gaseous volatiles violently reacted with oxygen and released a large amount of heat, and an obvious small DSC endothermic peak occurred which was most likely caused by the instantaneous endothermic phase change of the large agglomerates. Heat was gathered inside the agglomerates. The inner particles led and vaporised rapidly and led to an instantaneous thermal expansion and increase in inner thermal stress, and thus the agglomerates fragmented. Then, the oxidation reaction of the remaining pyrolysis products occurred at approximately 443 °C with a small exothermic peak, and the weight loss reached approximately 100%, indicating the termination of pyrolysis and oxidation. The thermal pyrolysis of 800 nm particles started to lose weight at approximately 228 °C corresponding to the decline of TG and increase in the weight-loss rate under the effect of

Journal Pre-proof pyrolysis. At approximately 274 °C, the DTG reading reached a peak corresponding to the maximum weight-loss rate, and the weight-loss rate decreased quickly. When the temperature reached 365 °C, the pyrolysis entered the slow weight-loss stage, and the weight gradually decreased. At approximately 471 °C, a sharp DSC exothermic peak occurred manifested by a vigorous oxidation reaction of gaseous volatiles. Then the weight loss approached 100% and pyrolysis terminated. Therefore, it can be deduced that the nano PMMA particles were pyrolysed in the temperature range 228–400 °C. The particles mainly depolymerized in two ways, which were the breakage of the double bond at the end of the chain, and the breakage of the random C-C bond in

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the main chain corresponding to the peak of pyrolysis rate on the DTG curve during rapid weight-loss. The pyrolysis products mainly contained the gas-phase MMA, CO2 and CH3OH [21].

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In the temperature range 400–500 °C, the pyrolysis product MMA proceeded a vigorous oxidation

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reaction, which consumed O2 and released a large amount of heat corresponding to the exothermic peak on the DSC curve during slow weight-loss. In addition, the large agglomerates in nano dust

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could lead to an instantaneous endothermic phase change and influence the pyrolysis oxidation

3. Result and discussion

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3.1 Propagating flame structure

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procedure.

The flame evolutions of 100 nm and 800 nm PMMA dust clouds with an initial dust

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concentration of 364 g/m3 are displayed in Figs. 7 and 8. The direct flame images clearly demonstrate the substantial differences in flame shape and self-sustainable propagation. As shown in Fig. 7, the 100 nm dust flame propagated approximately into a spherical shape. The flame front was smooth and continuous with slight deformation, and luminous spot flames were distributed in the flame luminous zone. However, the 800 nm dust flame shown in Fig. 8 was comparatively feeble and could not self-sustain propagated after ignition. The flame was significantly influenced by the ignition energy and the agglomeration. The influence of ignition energy on the 800 nm dust flame lasted more than 18 ms after ignition. The corresponding flame was strong, emitted a white dazzling light, and then quickly quenched. As discussed above, the 100 nm dust flame exhibited self-sustaining propagation as the flame size gradually increased. The dust cloud quickly and fully absorbed the ignition energy during ignition and supported the rapid development of the flame because of the large energy absorption surface area and quick pyrolysis of small particles. However, the 800 nm dust cloud had severe large-sized agglomerates, and the flame could not fully absorb and consume the energy during ignition. The large agglomerates combusted strongly under the affection of the ignition energy with a white dazzling light; however, without a

Journal Pre-proof continuous ignition energy supply, the flame could not support self-sustaining propagation. To track the quenching evolution of the 800 nm dust flame, the flame edge was extracted using an image edge detection algorithm based on MATLAB. The Roberts operator was used to calculate the difference between two adjacent pixels of the flame image f(x,y) in the diagonal direction. The Roberts gradient GRf(x,y) was calculated as equation (1), and then an appropriate threshold GR was selected. If the calculated Roberts gradient was greater than or equal to GR, the pixel (x,y) was then determined to be a step edge point.



GR f  x, y   max  f  x, y   f  x  1, y  1   f  x  1, y   f  x, y  1



1 2 2

(1)

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2

To precisely identify and extract the flame edge, the flame image was first superimposed to

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enhance the edge topography, and then threshold segmentation was performed. Usually, the grey-level threshold segmentation method is used in flame image segmentation. To reduce the

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influence of the flame background radiation on the extraction of the flame edge, threshold

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segmentation of the red channel was first processed to accurately extract the characteristic values of the flame image. Then, the grey-level threshold segmentation was used to obtain the flame grey

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image. Finally, the flame grey image was converted to a binary image, and the Roberts operator was used to detect and extract the flame edge.

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The highest point of extracted flame edge was defined as the flame front. Thus, the distance from the flame front to the ignition point of the 800 nm dust flame was tracked as shown in Fig. 9.

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The moment that the ignition electrodes stopped charging was defined as 0 ms of flame propagation. The propagation of the 800 nm dust flame can be divided into two stages. In stage 1, from 1 to 18 ms after ignition, the flame experienced a strong affection of ignition energy. In this stage, the influence of ignition energy on the dust flame gradually became weaker. The distance from the flame front to the ignition point decreased as the flame size decreased. As shown in Fig. 4, the 800 nm dust cloud was in severe agglomeration. Under a continuous supply of energy, the agglomerates absorbed and stored energy. The thermal expansion and fragmentation of agglomerates and the pyrolysis and oxidation of the small particles occurred gradually under the excitation of energy. Thus, the particles were ignited and a spherical flame formed. The energy stored in the particles was gradually consumed until it was unable to support more particles to participate in the combustion reaction. The particles that had already started reacting gradually consumed the stored energy to burn until the combustion was complete, and the flame size gradually decreased. In stage 2, from 18 to 60 ms, the dust flame was unable to retain self-sustaining propagation and finally quenched. This occurred because the depletion of ignition energy led to a lack of supporting energy, and the serious self-sedimentation of particles led to a

Journal Pre-proof significant reduction of concentration in the combustion flow field. From 18 to 41 ms, the flame front was elevated upwards. The thermal buoyancy effect on the dust flame was more intense than the decrease in the flame size. From 42 to 60 ms, the flame was rapidly quenching. The flame became unstable and the flame front position fluctuated. The effect of thermal buoyancy was negligible until the flame was extinguished. It can be deduced that the effect of ignition energy and ignition duration time on a nano dust flame with severe agglomeration is complex, and in-depth research is needed to further clarify the mechanism of ignition energy on a nano dust flame. 3.2 Flame microstructure

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The flame evolution of a 100 nm PMMA dust cloud with an initial dust concentration of

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193 g/m3 recorded by the high-speed Schlieren system is shown in Fig. 10. The thickness of the flame preheat zone δp was defined as the distance from the luminous reaction zone front to the

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Schlieren front, as illustrated in Fig. 11. The actual flame front (flame preheat zone front) of the 100 nm dust cloud was smooth and propagated upwards continuously. The flame surface rarely

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had apparent wrinkles. The thickness of the flame preheat zone in the front of the flame light-emitting zone was approximately 3–4 mm. Speculating from the smooth flame surface and

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relatively thin flame preheat zone, the nano dust flame was similar to that of a premixed gas combustion flame because of the rapid pyrolysis, which is quite different from the diffusion flame

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of micron dust [22–24]. It can be inferred that the mass diffusion process might not be the dominant factor that controls nano dust flame propagation. In addition, luminous spot flames were

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observed in the flame zone as shown in Fig. 12. By analysing the 100 nm dust flame microstructure shown in Fig. 13 as discussed in our previous study [25], an improved physical model was established for describing the nano dust flame microstructure. As shown in Fig. 14, the 100 nm dust flame mainly includes three zones: the flame preheat zone, the combustion reaction zone, and the post-flame zone. In the flame preheat zone, small particles first pyrolysed, and volatiles thoroughly mixed with air to form a combustible premixed gas. Only pyrolysis and mixing occurred, and there was no combustion reaction in the preheat zone. The premixed gas determined the preheat zone thickness and flame propagation velocity. The combustion reaction zone was divided into two zones. One was a thin zone, R1, behind the preheat zone, where the premixed gas combustion occurred. The other was a thick zone, R2, behind the thin zone, where premixed gas-phase combustion and diffusion combustion occurred. Many scattered luminous spot diffusion flames existed because of the combustion of the agglomerated particles. The thickness of R1 was considered equal to that of the preheat zone. The thickness of R2 was much thicker because of the slower combustion of the large

Journal Pre-proof particles and agglomerates. The post-flame zone corresponding to the intense luminous region mainly contained combustion products with high temperatures; virtually no combustion reaction occurred. In addition, because of the initial residual turbulence and the turbulence induced by the dust flame self-instability, the flame surface was disturbed with a slight deformation [25]. 3.3 Flame propagation velocity and flame temperature The flame-front positions and upward propagation velocities of the 100 nm dust clouds with initial dust concentrations of 193, 285, and 377 g/m3 were comparatively analysed as shown in Fig. 15. Under the excitation energy of ignition, the flame formed and rapidly propagated upwards. The distance from the ignition point to the flame front was basically linear with the propagation

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time [17]. The flame propagated in a pulsating manner because of the turbulence effect and energy

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balance mechanism in the preheat zone. Figure 15 (d) clearly shows that both the average pulsating propagation velocity and the degree of pulsation increased with an increase in the dust

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concentration. With more nano particles participating per unit time and volume, the mass and heat

and a combustion with a faster velocity.

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transfer in the preheat zone and the reaction zone intensified, resulting in a more violent pyrolysis

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The flame temperature distributions shown in Fig. 16 show that the temperature of the nano PMMA dust flame roughly went through four stages. In stage 1, the flame temperature increased

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quickly after ignition because of the rapid pyrolysis and combustion of the small particles in the flame preheat and thin reaction zones. The temperature reached an initial maximum value at the end of this stage and then entered the stage 2 slow fluctuating temperature rise. In stage 2, the

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large particles and agglomerates that had not completely pyrolysed or combusted participated in the oxidation reaction and released large amounts of heat. The combustion reaction fully occurred and the flame fully developed. The flame temperature sustainment increased and reached the maximum value at the end of this stage. The heat balance between pyrolysis and combustion caused a slight fluctuation in the temperature rise. In stage 3, the flame temperature fluctuation decreased as a result of the interaction between the heat loss and the supplementary heat from the complex combustion of the large agglomerates. The thermal heat loss dominated the flame development as the reaction intensity gradually decayed. In stage 4, the combustion reaction was complete, no more heat was released, and the flame temperature decreased rapidly with the obvious heat loss. The maximum temperature of 100 nm dust flames with initial concentrations of 193, 285, and 377 g/m3 were 1,100, 1,227, and 1,580 °C, respectively. The flame maximum temperature increased notably with an initial increase in the concentration. The higher the initial concentration, the more particles were initially involved in pyrolysis and combustion, and the earlier flame

Journal Pre-proof temperature began to rise. Moreover, the particle agglomeration became more severe with an increase in the initial concentration [11], resulting in a shorter duration of the rapid temperature-increase stage, and a lower initial maximum temperature. In the flame fluctuating temperature rise stage, more large particles and agglomerates were continuously involved in the oxidation reaction in the combustion zone, leading to a higher maximum temperature. 3.4 Flame propagation mechanism 3.4.1 Time-scale analysis of pyrolysis and combustion processes Dimensionless numbers of the Thiel number (Th) and Damköhler number (Da) were

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calculated to evaluate the dominant regime of nano dust explosions [26–31]. Th is defined as the ratio of heat transfer characteristic time (theat) to pyrolysis characteristic time (tpyro); if Th > 1, the

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heat transfer rate controls the particle pyrolysis process; otherwise, the pyrolysis rate controls it. Da is defined as the ratio of pyrolysis characteristic time (tpyro) to combustion characteristic time

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(tcomb); Da > 1 denotes that the pyrolysis rate controls the particle combustion process; otherwise,

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the combustion reaction rate controls it.

The theat is determined by the slower process of external and internal heat transfer and is

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calculated as

s Cps Lc . hc  T 3

(2)

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theat 

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where ρs and Cps are the density and specific heat of the solid particle at atmospheric pressure, Lc is the characteristic length, hc is the heat transfer coefficient, ΔT is the temperature difference between the particle-self and the surrounding gas, ε is the emissivity, σ is the Stephen-Boltzmann constant.

The tpyro is calculated as

tpyro 

C33  s D322

8C1  g / Cpg  ln 1  B 

.

(3)

where λg and Cpg are the thermal conductivity and specific heat of the gas phase PMMA at constant pressure, B is the mass transfer number, D32 is the particle Sauter diameter, C1 and C3 are the ratio of the particle surface diameter and volume diameter to the Sauter diameter, respectively. The tcomb of the pyrolysis products is calculated as

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tcomb 

gTi 2 Tf  Ti  . Cpg u vf2Tu2 Ti  Tu 

(4)

where vf is the propagation velocity, ρu is the air density, Tu, Ti and Tf are the ambient air temperature, ignition temperature and flame maximum temperature, respectively. The Th and Da of the 100 nm dust flames were calculated with initial concentrations of 193, 285, and 377 g/m3 as listed in Table 2. The theat and tpyro both decreased as the initial concentration increased. This means that both the particle heat transfer rate and the pyrolysis rate increased. With more particles participating in the combustion, the heat-release rate quickly increased, and

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the thermal heat transfer source correspondingly intensified, leading to a decrease in theat. As the initial density of small particles increased, a quick pyrolysis and oxidation in the initial period was

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achieved and amounts of heat were released in a short time. This contributed to a quick pyrolysis of the large particles and accelerated the evolution of pyrolysis to form combustible gas, leading to

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a decrease in tpyro and an increase in the pyrolysis rate. The tcomb reflecting the burning rate of

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combustible volatiles did not substantially change with an increase in the initial concentration. The tcomb was constant because of the combustion regime of the 100 nm dust flame. The flame

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propagation of the nano dust cloud was dominated by the premixed gas combustion in the R1 zone, and the sufficient premixing of combustible pyrolysis products with air was achieved in the

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preheat zone. The combustion process was not dependent on the mass transfer rate, and the combustion rate of the fully mixed flammable mixtures was not affected by the dust cloud

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concentration.

The Th and Da were both larger than 1 with various initial dust concentrations. This indicates that the particle heat transfer rate was the major controlling factor during the particle pyrolysis and that the pyrolysis rate controlled the overall combustion process. In addition, the Th increased slightly with an increase in the initial concentration, revealing that the effect of heat transfer on pyrolysis was more significant. However, the Da decreased as the concentration increased, revealing the attenuation of predominant effect that the pyrolysis rate played on flame propagation. In addition, a transition from the pyrolysis rate control regime to the combustion reaction rate control occurred as the dust concentration increased during flame propagation. Owing to the complex pyrolysis and combustion of agglomerates existing in the 100 nm dust flame [16], the pyrolysis characteristic time of the 100 nm dust particles was prolonged, resulting in a large Da value. 3.4.2 Flame propagation mechanism The temperature distribution of a propagating flame, the particle trajectory characteristic, the

Journal Pre-proof turbulence disturbance effect, and the dynamic process of the thermal heating, pyrolysis, ignition, and combustion of particles were thoroughly considered. A physical model, which properly described the nano dust flame propagation mechanism, was established as shown in Fig. 17. The nano dust flame propagation was divided into six zones: zone I, the post-flame zone; zone II, the luminous spot-flame reaction zone; zone III, the combustible premixed gas-phase flame reaction zone; zone IV, the preheat zone; zone V, the unburnt particle stagnation zone; and zone VI, the unburnt zone away from the flame front. During flame propagation, the particles near the flame zone are subjected to multiple forces, and the resultant force determine the direction of movement and the velocity of the unburnt

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particles. It was assumed that the gas away from the flame front was stationary and that the direction of gas expansion movement above the flame front was upward because of the flame

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thermal expansion. The non-vertical component force can be ignored in this case. The motion

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equation of unburnt particles can be expressed as

(5)

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dv 1  D3 s p  Fd  Ft  Fg  Fa  3 D g  vg  vp  6 dt 2 g  g  T 1 1 4.5D   D 3 s g   D 3  g g   Tg g  2g  s  x 6 6

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where Fd is the viscous resistance owing to the velocity difference between the particles and the surrounding gas, Ft is the thermophoretic force owing to the temperature difference in the flow field, Fg is the particle gravity, and Fa is the buoyancy, D is the particle diameter, vp and vg are the

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velocities of the particles and the surrounding airflow, μg is the gas dynamic viscosity, Tg is the gas temperature, g is the gravitational acceleration, ρs and ρg, are the density of the particle and the gas, λs and λg are the thermal conductivity of the particle and the gas. When the unburnt particles were far removed from the flame front corresponding to zone VI, the unburnt particles were mainly affected by particle gravity and not thermal flame expansion. The cold particles moved downwards at a self-sedimentation velocity. The particle temperature was approximately that of ambient temperature. When the cold particles slowly approached the flame front, the downward movement speed of the particles gradually decreased under the affection of the thermal expansion gases of the propagating flame. When the cold particles entered zone V just ahead of the flame front, the speed of most particles reduced to zero [32]. However, the agglomerated particles in the nano dust cloud continued moving downward because of the large self-gravity, but their speed reduced. When the cold particles further approached the propagating flame and entered zone IV, the preheat zone, the particle temperature rapidly increased from the ambient temperature Tu to the particle pyrolysis temperature Tp under the heat

Journal Pre-proof radiation of the flame combustion zone and the thermal convection between the surrounding high-temperature gases and particles. At this time, because of the small ratio of heat capacity to surface area, the small particles were first rapidly heated to Tp, started to pyrolyse to produce combustible volatiles, and then fully mixed with the surrounding air to form premixed combustible gases. As the temperature continued to increase to the ignition temperature Ti, the premixed combustible gases were ignited in zone III, the combustible premixed gas-phase flame reaction zone corresponding to zone R1 as shown in Fig. 14. A luminous flame formed and developed analogous to that of a premixed gas-phase combustion flame. At this moment, the downward

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speed of the large agglomerates in zone IV decreased to a minimum, whereas the large particles that had not yet completely pyrolysed moved upward in the same direction of flame propagation

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because of the large thermophoretic force. Zone III was mainly dominated by the premixed

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gas-phase combustion of pyrolysis volatiles. The thickness of zone III δr,1 was considered equal to that of the preheat zone δp,r as the flame propagated, and the combustion velocity of zone III

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determined the upward propagation velocity of the luminous flame zone. At the rear edge of zone III, the flame temperature increased to an initial maximum value Tf,ini.

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While the premixed gas was burning in zone III, because of the relative opposite movement of the downward settling agglomerates and upward propagating flame, the agglomerates at

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positions a1, b1, c1, d1, and e1 in zone IV at time t1 were moved to the corresponding positions a2, b2, c2, d2, and e2 in zone II at time t2. Under intensive heat transfer, pyrolysis occurred first on

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the surface of the agglomerates. In this case, the local high concentration of the premixed pyrolysis products and the gas around the agglomerates were formed and combusted to form the white-yellow light typical of diffusion spot flames. As combustion progressed, the external surface of the agglomerates and their inner particles continued pyrolysis by absorbing heat inside the spot flame. The agglomerates expanded, and the inner thermal stress increased continuously. When the inner thermal stress reached a critical value, the agglomerates fragmented and formed smaller-sized agglomerated clusters. These fragmental smaller-sized agglomerates pyrolysed and formed a flammable mixture surrounding the entire surface of the agglomerates and filled in between the fragmental agglomerated clusters and their inner particles. Then, local premixed gas-phase oxidation occurred and a spot flame developed [16]. By then the agglomerates had begun to move upward in the same direction as the flame propagation because of the gasification and combustion consumption of the particles and the thermal expansion of the propagating flame. If an agglomerate was considerably large, it would pyrolyse and locally burn while moving upward, forming the upward-moving tail-like spot flame illustrated as A2. The spot flames developed and finally disappeared until the burning agglomerates marked B1, C1, and D1 in zone

Journal Pre-proof II at time t1 completely pyrolysed and combusted corresponding to the development of the local gas-phase flames marked B2, C2, and D2, respectively, in zone II at time t2. As the spot flames developed, the single large-sized particles in zone II instantaneously pyrolysed, generated combustible volatiles, and combusted. In zone II, the flame temperature fluctuation increased because of the flame heat feedback mechanism, reflecting the competition among the heat absorption of the agglomerate pyrolysis, the heat release of the oxidation combustion, and the heat loss to the surrounding atmosphere. Zone II corresponding to zone R2 apparently contained the diffusion combustion of the agglomerates and the premixed gas combustion of the large particles within a thick reaction region. The thickness of zone II depended on the degree of agglomeration.

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In the post-flame zone I, the combustion reaction had already completed resulting mainly in high-temperature combustion products. The heat radiation of the solid combustion products played

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an important contributing role in the increase in the flame heat flux of the complex feedback heat

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transfer of the flame front. The flame temperature in zone I continued to increase. After reaching the maximum value Tf, max, the temperature started to decrease because of the energy and heat

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losses corresponding to the flame temperature decrease stage illustrated in Fig. 16. In addition, the combustion intensity, flame structure, and flame evolution behaviours were

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highly sensitive to the flame flow-field characteristics. Both the initial turbulent intensity and the flame propagation instability contributed to the slight wrinkle deformation of the flame front and

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unstable propagation of the nano dust flame. The propagation instability was rooted in the Kelvin-Helmholtz instability caused by the velocity difference between the flame front and the

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unburned gas, the Rayleigh-Taylor instability caused by the flame combustion expansion, and the thermal-diffusion instability. The deformation of the flame shape can strongly affect both the heat loss through convection and the heat feedback to the flame zone through heat radiation [20]. In addition, with greater turbulent intensity, the mass and heat transfer during particle turbulent motion can be greater than the macroscopic transfer produced by molecular thermal motion, resulting in a greater mass and heat diffusion in a flow field than that of laminar diffusion. Thus, the combustion intensity and flame propagation velocity can be more intense in a nano dust explosion. In this study, the experimental results of the nano dust flame propagation characteristics, including the flame microstructure, propagation velocity and temperature distribution all verified the proposed flame propagation mechanism. At the same time, the time-scale analysis persuasively proved the pyrolysis rate controlled regime for combustion and the effect of agglomerates on the particle combustion and flame propagation mechanism. However, the proposed mechanism has not been validated by simulation yet. Further in-depth researches need to establish an appropriate

Journal Pre-proof mathematical model for simulation validation, which is the focus of our further research.

Conclusions The nano-scale dust flame evolution characteristics during the initial stage of explosion were experimentally studied to clarify the flame propagation mechanism. The conclusions obtained are as follows: (1) Besides the inner-particle cohesion forces, the friction electrostatic and shear forces caused by the friction and frequent collisions between dust particles in a high-speed air flow seriously influence the PSD and degree of agglomeration of nano PMMA dust clouds. The

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agglomeration significantly affects the dispersion propensity, thermal pyrolysis, oxidation

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characteristics, and flame propagation mechanism of a nano dust explosion. (2) The formation of a nano PMMA dust flame includes a preheat zone, a thin combustion

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reaction zone, a thick combustion reaction zone, and a post-flame zone. The flame preheat zone front is smooth and continuously propagated. The flame surface rarely has apparent wrinkles, and

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the flame zone contains distributed luminous spot flames. The thickness of the flame preheat zone

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is approximately 3–4 mm.

(3) Nano PMMA dust flames propagate upward in a pulsating fashion because of the turbulence and energy balance in the preheat zone. Both the average flame propagation velocity

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and degree of pulsation increase with an increase in dust concentration. (4) The temperature of a nano PMMA dust flame roughly passes through the following four

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stages: rapid increase, fluctuating increase, fluctuating decrease, and rapid decrease. With an increase in the initial dust concentration, particle agglomeration becomes more severe and results in a shorter rapid temperature increase stage, a lower maximum initial flame temperature, and a higher maximum flame temperature.

(5) The flame evolution of a nano PMMA dust explosion is macroscopically analogous to the kinetic combustion of premixed gas and microscopically coupled with the localised diffusion combustion of luminous spot flames. Flame propagation is mainly controlled by the heat transfer and pyrolysis rates of dust particles, and a transition from the pyrolysis rate control regime to the combustion reaction rate control occurs as the dust concentration increases during flame propagation. (6) A physical model of nano dust flame propagation which included a post-flame zone, a luminous spot-flame reaction zone, a combustible premixed-gas reaction zone, a preheat zone, an unburnt particle stagnation zone, and an unburnt zone away from the flame front, was established,

Journal Pre-proof and a nano dust flame propagation mechanism was proposed.

Acknowledgements The authors gratefully acknowledge the financial support from the National Natural Science Foundation of China (51904170), Natural Science Foundation of Shandong Province (ZR2018BEE006), and Scientific Research Foundation of Shandong University of Science and Technology for Recruited Talents (2017RCJJ007). The authors also thank Soken Chemical & Engineering Co., Ltd. of Japan for providing the experimental PMMA particles.

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Table 1 Characteristic diameters of 100 nm and 800 nm PMMA particles MP-300 (100 nm) Before dispersion

After dispersion

D[4,3] (μm) D[3,2] (μm)

24.877 10.486

24.896 22.893

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MX-80H3wT (800 nm)

Before dispersion

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Characteristic diameters

0.966 0.870

After dispersion 27.433 22.680

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theat (ms)

tpyro (ms)

193 285 377

11.03 10.95 10.60

3.03 2.93 2.69

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tcomb (ms)

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Dust concentration (g/m3)

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Table 2 Calculated theat, tpyro, tcomb, Th and Da of the 100 nm PMMA dust flames with various initial concentrations

0.27 0.27 0.27

Th

Da

3.64 3.73 3.94

11.22 10.94 9.96

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Fig. 1 The open-space dust explosion experimental apparatus

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Fig. 2 The dust concentration measurement apparatus

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Fig. 3 SEM micrographs of 100 nm and 800 nm PMMA particles

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Fig. 4 PSDs of 100 nm and 800 nm PMMA dust particles

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Fig. 5 Thermal analysis result of 100 nm PMMA dust particles

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Fig. 6 Thermal analysis result of 800 nm PMMA dust particles

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Fig. 7 Flame evolution of a 100 nm PMMA dust cloud with an initial dust concentration of 364 g/m3

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Fig. 8 Flame evolution of a 800 nm PMMA dust cloud with an initial dust concentration of 364 g/m3

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Fig. 9 Flame-front position of a 800 nm PMMA dust cloud with an initial dust concentration of 364 g/m3

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Fig. 10 Flame evolution of a 100 nm PMMA dust cloud with an initial dust concentration of 193 g/m3 recorded by the high-speed Schlieren system

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Fig. 11 Thickness of the flame preheat zone

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Fig. 12 Luminous spot flames in the flame zone

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Fig. 13 100 nm PMMA dust flame microstructure with an initial dust concentration of 285 g/m3 [21]

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Fig. 14 Physical model for the nano PMMA dust flame structure

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Fig. 15 Flame-front positions and propagation velocities with various initial concentrations (a)-(c), and the comparison of velocities (d) for 100 nm PMMA dust clouds

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Fig. 16 Flame temperatures with various initial concentrations for 100 nm PMMA dust clouds

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Fig. 17 Physical model for the nano dust flame propagation

Journal Pre-proof Declaration of interests ☒ The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

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☐The authors declare the following financial interests/personal relationships which may be considered as potential competing interests:

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Highlights A physical model of the nano PMMA dust flame propagation is established.

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A nano PMMA dust flame propagation mechanism is proposed.

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A time-scale analysis reveals the controlling regime during the flame propagation.

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The agglomeration significantly affects the nano dust flame propagation mechanism.

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