The effect of particle size polydispersity on the explosibility characteristics of aluminum dust

Powder Technology 254 (2014) 331–337

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The effect of particle size polydispersity on the explosibility characteristics of aluminum dust Diana Castellanos a, Victor H. Carreto-Vazquez a, Chad V. Mashuga b, Remi Trottier b, Andres F. Mejia a, M. Sam Mannan a,⁎ a b

Artie McFerrin Department of Chemical Engineering, Mary Kay O'Connor Process Safety Center, Texas A&M University, College Station, TX 77843-3122, USA The Dow Chemical Company, Freeport, TX 77541, USA

a r t i c l e

i n f o

Article history: Received 6 March 2013 Received in revised form 21 October 2013 Accepted 17 November 2013 Available online 10 January 2014 Keywords: Aluminum Deflagration index Particle size distribution Polydispersity

a b s t r a c t This paper reports experimental results elucidating the effect of particle size polydispersity (σD) on the explosion severity of aluminum dust. Five mixtures with a median diameter (D50) of 15 μm and σD values of 0.95, 1.17, 1.48, 1.87, and 2.51, were systematically prepared by mixing original aluminum samples having narrow size distributions. The explosion severity of each sample was determined in a 36 L dust explosion vessel by measuring the maximum pressure (Pmax), the maximum rate of pressure rise ((dP/dt)max), and the deflagration index (KSt). Interestingly, we found that values of Pmax and KSt revealed an increase in explosion severity as σD increases, where the latter presented a more dramatic effect due to the contribution of fine particles on the combustion kinetics. The effect of dust concentration on the explosion propagation was analyzed comparing the time span to reach (dP/dt)max, (τ), during a dust explosion. τ was obtained from the experimental pressure traces of the original samples and their mixtures. The values of Pmax and KSt were plotted as a function of the median diameter (D50) and the volume- (D4,3) and surface- (D3,2) weighted mean diameter. We observed that D3,2 provided a better description of the average sample size and D50 is inadequately related to the real hazard potential of aluminum dust. Therefore, we suggest that the explosion hazard characterization of these types of materials should be reported in terms of D3,2 and σD. © 2013 Elsevier B.V. All rights reserved.

1. Introduction Dust explosions represent a serious industrial problem. They can occur if dust particles are well dispersed within a confined space in the presence of an ignition source. The severity of these explosions can be characterized from experimental parameters such as the maximum explosion pressure (Pmax) and the deflagration index (KSt). KSt is calculated from the maximum rate of pressure rise ((dP/dt)max) and the vessel volume (KSt = (dP/dt)max · V1/3) [1]. These parameters are utilized to predict the consequences of a dust explosion for a given scenario and usually reported along with the median diameter (D50). A dust explosion is a surface-area dependent process, where the dust explosibility increases as the particle diameter decreases (i.e., surface area increments) [1,2]. Here, we demonstrate that dust explosion hazards can be affected not only by the mean diameter but also by the size polydispersity (σD). σD is a measure of the width of the particle size distribution (PSD) and is not frequently reported along with the mean diameter [3,4]. σD can affect KSt values [5], and significant uncertainties can be found during the extrapolation of KSt values for a given dust with varying σD. ⁎ Corresponding author. E-mail address: [email protected] (M.S. Mannan). 0032-5910/$ – see front matter © 2013 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.powtec.2013.11.028

Many natural and industrial dusts present a wide particle size distribution (high σD). However, most of the experimental and theoretical combustion studies are carried out with samples of low σD. In addition, it is difficult to compare experimental data from different researchers when the results are reported in relation to different definitions of average particle size. In order to understand the effect of σD on dust explosion hazards, we restricted our analysis to aluminum dust samples. Aluminum dust has several important production methods and applications [6]. For instance, aluminum dust can be used to improve the optical properties of pigments [7,8], increase the fire rates of chromium (Cr) production [6], and enhance the combustion and reactivity in propellants [9,10]. Aluminum dust undergoes an exothermic reaction in the presence of air (4Al + 3 (O2 + (79/21) N2) → 2Al2O3 + (79/7) N2). This material, having a low σD, has been used to study several combustion parameters, such as burning velocity [11,12], ignition temperature [12], combustion [9,13], and ignition time [14]. Given that aluminum dust has been involved in devastating explosion accidents [1,15–17], several investigations have been conducted to analyze the effect of particle size on explosion hazard parameters such as Pmax and KSt [17–19]. These combustion parameters are very sensitive to the variation of particle size [20–24]. Huang et al. [25] reported that the aluminum dust laminar flame speed is affected by the fine particle

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concentration within the mixture. Therefore, for a dust at a given particle diameter, the values of Pmax and KSt will be affected by a systematic variation of the small and large particle size fraction contained in the mixture (i.e., different σD). Our work here explores the effect of aluminum dust size polydispersity on the dust hazard parameters such as P max and KSt . Aluminum samples of similar D50 but varying σD were prepared by mixing commercially available samples of different D50 and narrow size distributions. The original samples and their mixtures were tested in a 36 L dust explosion vessel. The time span to reach the maximum rate of pressure rise (τ) was calculated from the pressure time curves obtained in the 36 L vessel. τ values give insights of the effect of D50, σD and dust concentration on the velocity of the flame propagation of the tested samples. The results obtained in this research demonstrate the importance of σD on aluminum dust explosion hazard characterization. 2. Methodology 2.1. Determination of Pmax, KSt, and τ of aluminum dust samples The dust explosion equipment used in this work utilizes a 36 L semispherical stainless steel vessel, which was designed based on the ASTM standard E-1226-05 [26]. This equipment has been carefully calibrated to produce comparable results to the ones obtained with the 20 L and 1 m3 standard equipment [27]. In a typical experiment, a dust sample is loaded into a dust container. Later, the 36 L vessel is sealed, evacuated, and the air reservoir is pressurized. A fast acting valve is opened for 50 ms to release air from the reservoir and disperse the sample inside the vessel through a rebound nozzle. The dispersion process increases the vessel pressure to one bar absolute. After a delay time of 25 ms, two 5 kJ igniters are activated and the resulting explosion pressure trace is recorded. A customized LabView™ program controls the equipment and processes the experimental data. Fig. 1 shows a typical pressure (barg) profile as a function of time (ms) during a dust explosion test, where (dP/dt)ex, Pex, and τ are obtained for a specific dust concentration. Pex is corrected into Pm to account the cooling effects of the vessel walls and the pressure effects caused by the igniters [26]. (dP/dt)ex is multiplied by the cubic root of the vessel volume to obtain (dP/dt) exV1/3. Pmax and KSt are the maximum values of Pm and (dP/dt)exV1/3 at varying dust concentrations. The optimum concentration corresponds to the concentration where Pmax and KSt values are found. 2.2. Aluminum sample preparation and size characterization In order to understand the effect of σD at a fixed D50 during a dust explosion, we systematically combined aluminum samples with the following mean diameters: 2, 5, 9, 15, 20, 25, and 30 μm. The combined samples were prepared by adding each component in a jar filled to about 2/3 capacity and manually blending each sample for 30 min

Fig. 1. Typical pressure profile during a dust explosion test.

using a Figure 8-track to ensure self-mixed samples. The blending process was conducted under inert conditions in a glove box. Original samples and the resulting mixtures were stored under nitrogen atmosphere to prevent aluminum oxidation. The qualitative characterization of the alumina (Al2O3) content in the samples was conducted using X- ray diffraction (XRD) before and after the blending process (see ESI Fig. S11 and text). A quantitative estimation of the alumina content was obtained using the density of aluminum (1500–1700 kg/m3) and the amorphous alumina (3050 kg/m3 [28,29]). According to Trunov et al., [30], the natural oxidation in nano and microsized aluminum dust is around 2.5 nm. Thus, the Al2O3 content of the original samples is expected to vary from 1.5 to 0.1 wt.% for particles between 2 and 30 μm, respectively. The particle size distribution of the original samples was determined using a Mastersizer 3000 analyzer (Malvern Inc, Worcestershire, UK) and an LS 13 320 Coulter multi-wavelength laser diffraction particle size analyzer (Beckman Coulter, Inc. Brea, CA). The laser diffraction measurement was performed in wet-mode using water as the suspension medium. Micro 90® manufactured by International Products Corporation was used as a surfactant. Aluminum PSD results from both instruments were in very good agreement. The measurements provide the size distribution on a volume (or mass) basis and the statistical diameters, D10, D50, and D90. Dxx refer to the particle size for which xx% of the particles by weight are finer. Table 1 summarizes the particle size characterization of these samples. Table 2 shows the corresponding mass fractions of the original aluminum samples used to prepare each of the five blends having similar D50 and varying σD. The particle size polydispersity (σD) characterized by the span of the size distribution is calculated using the following expression: σ D ¼ ðD90 –D10 Þ=D50

ð1Þ

The PSD of the resulting mixtures was calculated by adding the initial size distributions in accordance to their contributions or mass fractions. The aluminum dust density is the same in all samples. The calculated size distributions shown in Fig. 2 were also verified experimentally with the Beckman Coulter analyzer described above. The calculated and experimentally measured PSD presented excellent agreement. Micrographs of aluminum mixtures were obtained using scanning electron microscopy (SEM-JEOL JSM-7500 F). Fig. 3 shows the SEM images of the resulting mixtures. As observed from the micrographs, polydispersity increases from Blend 1 to Blend 5. Blend 1 (σD = 0.95) presents the highest homogeneity in particle size, while Blend 5 (σD = 2.51) is the most heterogeneous in particle size. 3. Results and discussion 3.1. Effect of D50 on Pmax and KSt values of aluminum dust samples at low σD In order to analyze the effect of D50 on Pm and (dP/dt)exV1/3 at a relatively low polydispersity, the original samples listed in Table 1 were tested using the 36 L dust explosion vessel. Fig. 4 shows the experimental explosion hazard parameters of the original samples as a function of aluminum dust concentration. The experiments conducted using nominal dust concentrations of 125, 250, 500, 750, 1000, and 1500 g/m3 were repeated and the standard deviation is shown by the error bars. The maximum values at Pm and (dP/dt)exV1/3 curves were conducted three times. The Pmax and KSt values obtained at the optimum concentrations can be found in Table 3. In general, finer particles (D50 = 2 μm) produced a higher Pm and (dP/dt)exV1/3. In agreement with Dufaud et al., [24,31], Pmax and KSt values monotonically increase as D50 reduces. Interestingly, the optimum concentrations, where Pmax and KSt values are found, decreased as D50 decreases. A rapid rupture of the oxide layer in small particles might contribute to such a high explosion 1

Electronic supplementary information (ESI).

D. Castellanos et al. / Powder Technology 254 (2014) 331–337 Table 1 Particle size characterization of the original aluminum samples using a Malvern laser diffractometer. Original sample mean diameter (μm)

D10 (μm)

D50 (μm)

D90 (μm)

σD

Specific surface area (m2/g)

2 5 9 15 20 25 30

0.98 2.66 6.03 9.41 12.70 15.46 18.15

2.32 4.57 8.84 14.90 19.98 24.67 30.42

4.62 7.49 12.96 23.55 31.31 39.08 52.77

1.57 1.06 0.78 0.95 0.93 0.95 1.14

4.39 2.01 0.71 0.43 0.32 0.26 0.21

severity at lower optimum concentrations. As particle size decreases, the oxide layer has a higher curvature and experiences higher internal pressures which increase the propensity to rupture [32]. Furthermore, aluminum dust particles of reduced size are characterized by a large surface area that increases volatilization and combustion rate. These results confirm that the combustion reaction is directly related to the total surface-area available. 3.2. Effect of σD on Pmax and KSt values of aluminum dust at a fixed D50 To study the effect of σD on P m and (dP/dt)ex V1/3 at a fixed D50 (~ 15 μm), the blended samples previously described in Table 2 were tested following the exact same procedure used with original samples. The experiments conducted using nominal dust concentrations of 125, 250, 500, 1000, and 1500 g/m3 were repeated and the standard deviation is shown by the error bars. Fig. 5 shows experimental results of Pm and (dP/dt)exV1/3, for dust explosion tests performed at different dust concentrations. Interestingly, although the samples are characterized by a similar D50, the aluminum explosibility increases along with σD. We observed significant variations on (dP/dt)exV1/3 values, which reveal that the effect of σD on the combustion reaction kinetics cannot be neglected (Fig. 5b). This gradual increase in Pm and (dP/dt)exV1/3 values is attributed to the higher fraction of fine particles suspended in the cloud. The fine aluminum particles presented in the dust cloud increase the total surface area available for combustion to occur, thus increasing the combustion reaction rate [33]. Table 4 contains Pmax and KSt values obtained for the different blends at varying σD. Experimentally, the sample with the lowest polydispersity (Blend 1, σD ~ 0.95), resulted in a KSt of 231 ± 9 bar-m/s, whereas the sample with the highest polydispersity (Blend 5, σD ~ 2.51) presented a KSt value of 403 ± 14 bar-m/s. Interestingly, Pmax and KSt values (local maximums in Fig. 5) are achieved at lower concentrations as polydispersity increases. The results obtained using Blend 5 exhibited a similar trend to the original samples having 2 and 5 μm (Fig. 4.) As the fraction of fine particles increases, the total surface area and volatilization rate increase, enhancing the explosion propagation. These results confirm the dominant effect of the particles having a reduced size on the combustion process of polydisperse samples. Thus, risk assessment evaluations based on hazards associated to samples with low σD, can lead to significant underestimations.

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In comparison to large-sized particles, it is well known that small ones exhibit lower ignition temperature [12,34], lower heat diffusion time [35], and faster burning rate [12,25]. Hence, particles of reduced diameters possess more efficient flame propagation. It is generally assumed that micro-sized aluminum particles are covered by an alumina (Al2O3) shell. This alumina layer can break by melting at 2350 K or via core-thermal expansion [11]. During shell-breaking, the aluminum particles can easily ignite. The smaller particles present a lower ignition temperature due to their large specific surface area that improves the heat transfer to the aluminum core [36]. Once the ignition temperature is reached, the combustion process initiates and the produced heat is transferred to the neighbouring-unburned particles [35]. The efficiency of this heat transference can be favoured by a shorter inter-particle spacing (i.e., high nominal dust concentration) [35]. Flame propagation continues until the heat released from the combustion process is not able to maintain the ignition temperature of the unburned particles [35]. Thus, in our experiments we are expecting that the fraction of smaller particles added into the dust samples will ignite at lower temperatures and facilitate the heat transfer to the larger particles. To quantitatively relate the explosibility parameters with size polydispersity, Pm and (dP/dt)ex · V1/3 values were plotted as a function of σD for each dust concentration, as shown in Fig. 6a and b, respectively. From Fig. 6 we selected the highest values, which correspond to Pmax and Kst (Table 4). From data interpolation, we obtained a linear relationship of Pmax and Kst as a function of σD: K St ¼ ð114  17Þ þ ð117  10Þ  σ D

ð2Þ

P max ¼ ð8:0  0:4Þ þ ð0:8  0:2Þ  σ D

ð3Þ

Eqs. (2) and (3) are valid for aluminum dust of D50 = 15 μm in a range of polydispersity between 0.95 and 2.5. In general, we observed a monotonic growth of the explosion severity parameters, Pmax and KSt, along with σD. The values of KSt during the dust explosion tests presented a stronger effect from σD compared to Pmax. The slope of these correlations is given by the effective concentration of the fine particles in the cloud, which might be affected by the particle dispersion inside the dust explosion vessel. Liu et al., [37] reported a strong powder flowability dependency on particle size and PSD. The y-intercept of these correlations might be influenced by the particle median mean diameter, surface chemistry, and chemical composition. It is worth to mention that these correlations should not be extrapolated for mixtures outside the stated polydispersity range (0.95 ≤ σD ≤ 2.5). Additional factors such as particle agglomeration can reduce their effective surface area within the dust cloud, leading to unexpected reductions on the explosion severity. For instance, Bouillard et al. [38] reported that 200 and 100 nm aluminum particles presented Kst values of 673 and 362 bar-m/s, respectively. This surprising reduction on Kst was attributed to a higher tendency of the 100 nm particles to aggregate. Interestingly, Fig. 6b shows that at low aluminum dust concentrations (b250 g/m3), (dP/dt)max · V1/3 was not significantly affected by

Table 2 Mass fractions of initial aluminum samples used to generate five blends at similar particle median mean diameter (D50) and varying size polydispersity (σD). Blend

1 2 3 4 5

Mass fraction ¼

Original sample mass Total blend mass

2 (μm)

5 (μm)

9 (μm)

15 (μm)

20 (μm)

25 (μm)

30 (μm)

– – – 0.100 0.333

– – 0.125 0.100 –

– 0.200 0.125 0.100 –

1 0.600 0.500 0.400 0.333

– 0.200 0.125 0.100 –

– – 0.125 0.100 –

– – – 0.100 0.333

D10 (μm)

D50 (μm)

D90 (μm)

σD

9.41 8.07 5.79 3.44 1.68

14.90 14.32 14.26 14.21 14.55

23.55 24.83 26.85 30.00 38.23

0.95 1.17 1.48 1.87 2.51

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particles concentration increases). Another potential explanation to the effect of polydispersity at higher concentrations is the increased impact frequency between the aluminum particles that facilitate the breakup of their aluminum oxide layer. As mentioned in Section 3.1, due to the higher curvature of the small particles, the mechanical stress experienced by the aluminum oxide layer increases its propensity to rupture [32]. Therefore, the role played by the fine particles facilitating flame propagation within the dust cloud is more appreciable at higher nominal dust concentrations. 3.3. Analysis of the explosibility characteristics versus D50, D4,3, and D3,2

Fig. 2. Summary of particle size distributions for mixtures having D50 of 15 μm and varying σD. Blends 1, 2, 3, 4, and 5 correspond to polydispersities of 0.95, 1.17, 1.48, 1.87, and 2.51, respectively.

σD. This effect might be explained by the large inter-particle spacing found at low dust concentration. Although reduced diameter aluminum particles burn at lower temperatures, the heat is dissipated into the air instead of being transferred to the neighbour particles. On the other hand, as dust concentration approaches an optimum value (~ 1000 g/m3), the inter-particle spacing is reduced and the effect of size polydispersity becomes more significant (i.e., the fine

KSt and Pmax values were also analyzed in terms of different definitions of particle size. Fig. 7 shows KSt and Pmax values plotted as a function of median mean diameter (D50), and volume- (D4,3) and surface(D3,2) weighted mean diameters, respectively. These average particle sizes were obtained from the experimental particle size distributions obtained from the Beckman Coulter analyzer. D50 corresponds to the particle size for which 50% of the particles by weight are finer. D4,3 was calculated using the following expression [39]:         4 3 3 3 D4;3 ¼ Σy dN = Σy dN ¼ Σy  y dN = Σy dN ¼ ðΣydϕÞ=ð100Þ

ð4Þ

Fig. 3. SEM micrographs of aluminum samples having D50 of 15 μm and varying σD. Blends 1, 2, 3, 4, and 5 correspond to σD of 0.95, 1.17, 1.48, 1.87, and 2.51, respectively. Right bottom micrograph corresponds to a typical aluminum particle having a diameter of around 15 μm.

Fig. 4. Experimental results of the original aluminum dust samples having D50 of 2, 5, 9, 15, 20, 25, and 30 μm and σD of 1.57, 1.06, 0.78, 0.95, 0.93, 0.95, and 1.14, respectively. (a) Pm and (b) (dP/dt)exV1/3 versus nominal dust concentration.

D. Castellanos et al. / Powder Technology 254 (2014) 331–337 Table 3 Summary of Pmax and KSt values of original aluminum dust samples.

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Table 4 Summary of Pmax and KSt values of blended aluminum dust samples.

Original sample D50 (μm)

Pmax (barg)

KSt (bar-m/s)

Blend

Pmax (barg)

KSt (bar-m/s)

2 5 9 15 20 25 30

11.7 ± 1.1 10.3 ± 0.4 9.2 ± 0.2 9.02 ± 0.1 7.4 ± 0.3 7.5 ± 0.2 8.3 ± 0.3

451 ± 27 413 ± 15 299 ± 5 231 ± 9 116 ± 6 105 ± 8 119 ± 12

1 2 3 4 5

9.02 ± 0.1 8.50 ± 0.5 9.23 ± 0.1 9.33 ± 0.3 10.02 ± 0.2

231 ± 9 236 ± 19 293 ± 6 345 ± 2 403 ± 14

The surface mean diameter, D3,2, also called the Sauter mean diameter, corresponds to the diameter of an sphere with equal surface area, and it was obtained using the following equation [39]:       3 2 3 D3;2 ¼ Σy dN = Σy dN ¼ ðΣdϕÞ= Σy dN=y ¼ 100=ðΣdϕ=yÞ

ð5Þ

In the case of the original samples (low σD), Pmax and KSt values presented a strong influence with D50, D4,3, and D3,2. However, the blended samples did not present a coherent relationship with Pmax and KSt along with D50 and D4,3. This observation was specially noticed in samples having σD values larger than 1.5 (Fig. 7a, b, d, and e). On the other hand, Fig. 7c and f shows that regardless of the σD value, D3,2 is more adequately related to the hazard potential of the material. Hence, the surface-weighted average diameter (D3,2) provides the best description of the particle size distribution. This confirms that the combustion process is essentially a surface-area-related process. Given that D50 does not properly describe the PSD of a combustible dust, we recommend that the explosion hazard characterization of these types of materials should be reported in terms of D3,2 and σD. 3.4. The effect of D50 and σD on the flame propagation velocity In this study, the time span to reach the maximum rate of pressure rise (τ, Fig. 1) was used to obtain insights of the effects of D50, σD, and dust concentration on the velocity of the flame propagation of the tested samples. τ values were measured during each dust explosion test conducted with original and blend samples. Fig. 8a and b shows the measured τ values as a function of nominal dust concentration of original and blend samples, respectively. For the original samples, Fig. 8a shows a monotonic reduction of τ as D50 decreased and as dust concentration increased. In the case of blended samples, τ reduced as σD and concentration incremented as shown in Fig. 8b. Interestingly, τ presents a stronger dependence on concentration at relatively high σD. For instance, a dramatic reduction on τ was

observed on blend 5, where τ dropped from 40.6 to 10.7 ms as the dust concentration incremented from 125 to 1500 g/m3. This effect is explained from the role played by the fine particles on the combustion process, which is enhanced by the reduction of the inter-particle spacing. 4. Conclusions In conclusion, we elucidated the effect of particle size polydispersity (σD) on the propagation of aluminum dust explosions. A series of dust samples of varying σD at a fixed median mean diameter (D50 ~ 15 μm) were prepared by mixing original samples having narrow size distributions. We found that at constant D50, the explosion hazards dramatically increased with σD. The sample with the lowest σD (0.95) resulted in a lower explosion hazard, with a Pmax of 9.15 barg and a KSt value of 179 bar-m/s. While the sample with the highest σD (2.51) showed the greatest explosion hazard with a Pmax of 10.25 barg and a KSt value of 413 bar-m/s. This effect was attributed to the concentration of aluminum particles of reduced diameter suspended in the dust cloud. In comparison with large-sized aluminum dust, fine particles not only ignite at lower temperatures but also combust more rapidly due to their extensive specific surface area. We also observed that D3,2 exhibited the best correlation between particle size and the explosion parameters, Pmax and KSt. Thus, the explosion hazard characterization of combustible dust should be reported in terms of D3,2 and σD. We believe that the methodology used here can be extended to other combustible metals such as titanium, magnesium, tungsten, boron, etc. Similar correlations can be applied to design proper explosion protection systems to prevent undesirable catastrophic events in dust-handling industry. Acknowledgments We acknowledge The Dow Chemical Company for supporting this study by providing the measurements of particle size distribution. We also like to thank to Henan Yuan Yang Aluminum Industry Co. Ltd, People's Republic of China, for providing the aluminum samples.

Fig. 5. Experimental results of aluminum blends having D50 of 15 μm at varying σD, using a 36 L dust explosion vessel. Blends 1, 2, 3, 4, and 5 correspond to σD of 0.95, 1.17, 1.48, 1.87, and 2.51, respectively. (a) Pm and (b) (dP/dt)ex · V1/3 values.

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Fig. 6. Experimental results plotted as a function of aluminum dust polydispersity. (a) Pm values. The solid line is the linear fit of Pmax values, Pmax = (8.0 ± 0.4) + (0.76 ± 0.2) × σD. (b) (dP/dt)ex · V1/3 values. The solid line represents the linear fit of KSt values, KSt = (114 ± 17) + (117 ± 10) × σD.

Fig. 7. Explosion characteristics of aluminum dust in relation to different definitions of average particle size. (a), (b), and (c) for KSt values as a function of D50, D4,3, and D3,2, respectively. (d), (e) and (f) for Pmax as a function of D50, D4,3, and D3,2, respectively. Solid circle data points represent results reported by Dufaud et al., [24,31]. Squared data points represent results from the original samples. Blends 1, 2, 3, 4, and 5 correspond to σD of 0.95, 1.17, 1.48, 1.87, and 2.51, respectively.

Fig. 8. Calculated τ values as a function of nominal dust concentration. (a) Original dust samples having D50 of 2, 5, 10, 15, 20, 25, and 30 μm and σD of 1.57, 1.06, 0.78, 0.95, 0.93, 0.95, and 1.14, respectively. (b) Dust blends having D50 of 15 μm at varying σD. Blends 1, 2, 3, 4, and 5 correspond to σD of 0.95, 1.17, 1.48, 1.87, and 2.51, respectively.

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