Relative importance of the lift force on heavy particles due to turbulence driven secondary flows

Saffman lift forces on dense particles due to gradients in both streamwise and cross-stream velocities in a downward, fully developed turbulent square duct flow at Re_τ = 360 are studied using large eddy simulations. Volume fraction of the dispersed phase is low enough (≤ 10^− 5) that the one-way coupling approach is reasonable, i.e., two-way coupling and particle-particle collisions are not considered. Eulerian and Lagrangian approaches are used to treat the continuous and dispersed phases, respectively. Subgrid stresses are modeled with the dynamic subgrid kinetic energy model of Kim and Menon [W.W. Kim and S. Menon. Application of the localized dynamic subgrid-scale model to turbulent wall-bounded flows, AIAA 97-0210, 1997.]. The particle equation of motion includes drag, lift forces due to both the streamwise and cross-stream velocity gradients, gravity, and is integrated using the fourth-order accurate Runge-Kutta scheme. Dependence of particle drag and lift forces on duct cross-sectional location and particle response time is demonstrated using the mean value contours and probability density functions (PDFs) of particle forces. It is shown that the streamwise component of the mean drag force experienced by particles of all response times is a deceleration force, i.e. on average, fluid streamwise velocity lags the particle streamwise velocity. Secondly, the two wall-normal (or lateral) components of the mean drag force are oriented such that the particles experience a net mean force toward the duct corners. PDFs of particle drag force components show that smaller response time particles experience a wider range of drag force about the mean value, as compared to the more inertial particles. Contours of mean wall-normal lift forces due to streamwise velocity gradients show that this force predominantly acts toward the duct walls and that the maximum lift force occurs close to the walls. PDFs of lift force due to streamwise velocity gradients show that the range of fluctuations increases with particle response time, but the dependence on particle response time is weaker compared to drag force. Lift forces due to cross-stream velocity gradients are at least an order of magnitude smaller than lift forces due to streamwise velocity gradients and are found to decrease in their range of fluctuations with particle response time. It is demonstrated that lift forces due to secondary flow velocity gradients are not as important as those due to streamwise velocity gradients in a square duct flow.     

Coupled CFD–DEM of particle-laden flows in a turning flow with a moving wall

The nature of the particle–solid interactions and particle–fluid interactions in rectangular duct bend geometry with/without a moving wall is studied, taking into account particle collision, colloidal, and hydrodynamic forces, and four way coupling between the fluid flow and particles. The focus is on systems where particles and fluid phase have similar length scales, fluid Reynolds number (Re_f) ∼ 1, and particle's Stokes number (St) ∼ 1. Particles move toward the walls of the channel near the bend, and have long residence times in these regions. Buoyancy force has negligible effect on particle motion, where adhesion and drag forces lead to particle motion and agglomeration patterns. The effect of a free surface on agglomeration sites in the turning flow is elucidated.     

Numerical study of particle dispersion in the wake of gas-particle flows past a circular cylinder using discrete vortex method

A numerical investigation on the particle dispersion in the wake of particle-laden gas flows past a circular cylinder at Reynolds number of 10⁵ is presented. In the numerical method, the Discrete Vortex Method with the diffusion velocity model is employed to calculate the unsteady gas flow fields and a Lagrangian approach is applied to track individual particles. A dispersion function is defined to represent the dispersion scale of the particle. The distributions of gas velocities and vortex blobs, the trajectories and dispersion functions as well as distributions for particles with various Stokes numbers ranging from 0.01 to 1000 are obtained. The numerical results show that: (1) very small sized particles with St = 0.01 can distribute both in the vortex core and around the vortex periphery, whereas intermediate sized particles with St = 1.0, 10 are distributed around the vortex periphery, and very large sized particles with St = 1000 do not feel the gas flow; (2) only at small Stokes number (St = 0.01, 0.1) the particles do not impact with the cylinder; (3) the particle's dispersion intensity decreases precipitously as St is increased from 0.01 to 10.     

Drag of non-spherical solid particles of regular and irregular shape

The drag of a non-spherical particle was reviewed and investigated for a variety of shapes (regular and irregular) and particle Reynolds numbers (Re_p). Point-force models for the trajectory-averaged drag were discussed for both the Stokes regime (Re_p ? 1) and Newton regime (Re_p ? 1 and sub-critical with approximately constant drag coefficient) for a particular particle shape. While exact solutions were often available for the Stokes regime, the Newton regime depended on: aspect ratio for spheroidal particles, surface area ratio for other regularly-shaped particles, and min-med-max area for irregularly shaped particles. The combination of the Stokes and Newton regimes were well integrated using a general method by Ganser (developed for isometric shapes and disks). In particular, a modified Clift-Gauvin expression was developed for particles with approximately cylindrical cross-sections relative to the flow, e.g. rods, prolate spheroids, and oblate spheroids with near-unity aspect ratios. However, particles with non-circular cross-sections exhibited a weaker dependence on Reynolds number, which is attributed to the more rapid transition to flow separation and turbulent boundary layer conditions. Their drag coefficient behavior was better represented by a modified Dallavalle drag model, by again integrating the Stokes and Newton regimes. This paper first discusses spherical particle drag and classification of particle shapes, followed by the main body which discusses drag in Stokes and Newton regimes and then combines these results for the intermediate regimes.     

Determination of the adhesion force between particles and a flat surface, using the centrifuge technique

By using a centrifuge technique, the influence of powdery material particle size on the adhesion force particle-surface was determined. In order to achieve this, the adhesion of phosphatic rock (ρ_p = 3.090 kg m^− 3) and of manioc starch particles (ρ_p = 1.480 kg m^− 3) on a steel surface were studied. A microcentrifuge that reached a maximum speed rotation of 14000 rpm and which contained specially designed centrifuge tubes was used. There tubes contained the flat surface where the test particles were deposited. The powder particles were dispersed on these disks and the particles detachment were performed using diverse centrifugal speeds. The graphics of particle percentages still adhering on the surface of the disks as a function of the applied detachment force showed that the profile of adhesion force followed a log-normal distribution. The adhesion force increased with particle size. The manioc starch particles presented adhesion forces greater than those for the phosphatic rock particles for all particle sizes studied. The results obtained were compared with the theory proposed by Derjaguin, Muller and Toporov whose theoretical adhesion presented values close to the experimental data for the phosphatic rock particles adhesion on the stainless steel surface. On the contrary, the theoretical values were lower than the experimental ones for the manioc starch particles maybe due to the small roughness of these particles, their physical properties (softer and deformable material) and/or specific chemical interactions since the organic composition of the manioc starch particles that can dominate the adhesion force. Finally, the separation distance among the surfaces in contact (Z₀) was estimated in approximately 1.0 × 10^− 9 m for the phosphatic rock and 5.0 × 10^− 10 m for the manioc starch. These results were weakly dependent on the particle size range.     

The effect of the generation and handling in the acquired electrostatic charge in airborne particles

The measurement of the charge distribution in laboratory generated aerosols particles was carried out. Four cases of electrostatic charge acquisition by aerosol particles were evaluated. In two of these cases, the charges acquired by the particles were naturally derived from the aerosol generation procedure itself, without using any additional charging method. In the other two cases, a corona charger and an impact charger were utilized as supplementary methods for charge generation. Two types of aerosol generators were used in the dispersion of particles in the gas stream: the vibrating orifice generator TSI model 3450 and the rotating plate generator TSI model 3433. In the vibrating orifice generator, a solution of methylene blue was used and the generated particles were mono-dispersed. Different mono-aerosols were generated with particle diameters varying from 6.0 × 10^− 6 m to 1.4 × 10^− 5 m. In the rotating plate generator, a poly-dispersed phosphate rock concentrate with Stokes mean diameter of 1.30 × 10^− 6 m and size range between 1.5 × 10^− 7 m and 8.0 × 10^− 6 m was utilized as powder material in all tests. In the tests performed with the mono-dispersed particles, the median charges of the particles varied between − 3.0 × 10^− 16 C and − 5.0 × 10^− 18 °C and a weak dependence between particle size and charge was observed. The particles were predominantly negatively charged. In the tests with the poly-dispersed particles the median charges varied fairly linearly with the particle diameter and were negative. The order of magnitude of the results obtained is in accordance with data reported in the literature. The charge distribution, in this case, was wider, so that an appreciable amount of particles were positively charged. The relative spread of the distribution varied with the charging method. It was also noticed that the corona charger acted very effectively in charging the particles.     

H2 production by steam-quenching of Zn vapor in a hot-wall aerosol flow reactor

Hydrogen production by steam-hydrolysis of zinc is investigated as part of a two-step water-splitting thermochemical cycle based on ZnO/Zn redox reactions. The hydrolysis reactor consists of a hot-wall tube containing a flow of Zn(g) that is steam-quenched to co-produce H₂ and Zn/ZnO nanoparticles. The effects of the quenching gas flow rate and reactor wall temperature on the Zn-to-ZnO chemical conversion and particle yield are examined. Solid products are characterized by X-ray diffraction, N₂ adsorption, and SEM microscopy. Quench rates of 2-6×10⁴ K/s yielded conversions of up to 95% at the expense of low particle yield due to significant wall deposition with subsequent hydrolysis. Aerosol particles with hexagonal structure were formed by Zn evaporation-condensation containing low ZnO mass fraction. In contrast, operation at quench rates up to 10⁶ K/s led to increased particle yield but lower conversion. Filamentary and rod-like particles were formed with high ZnO content by surface reaction and coagulation.     

Experimental study of acoustic agglomeration of coal-fired fly ash particles at low frequencies

This paper presents an experimental study of acoustic agglomeration of coal-fired fly ash particles in travelling sound waves. The ranges of variation of the main physical parameters are as follows: acoustic frequency, f = 700-3000 Hz; sound pressure level (SPL), SPL = 130-147 dB; residence time, t = 3-7 s; aerosol number concentration, N₀ = 1.0 × 10⁵-3.7 × 10⁵ /cm³. A 68.4% decrease in total number concentration is gained under an SPL of 147 dB and a frequency of 1400 Hz. Aggregates larger than 10 µm are observed in scanning electron microscopy photographs. The results show that the effect of sound waves is very sensitive to the frequency change, which means that orthokinetic interaction governs the process. There exists an optimum frequency for a given particle size distribution, which decreases slightly as SPL increases. The influences of SPL, residence time and initial total number concentration are also studied.     

CFD investigation of the pipe transport of coarse solids in laminar power law fluids

A numerical parametric study of the laminar pipe transport of coarse particles in non-Newtonian carrier fluids of the power law type has been conducted using an Eulerian-Eulerian computational fluid dynamics (CFD) model. The predicted flow fields have been successfully validated by experimental measurements of particle velocity profiles obtained using a positron emission particle tracking technique, whilst solid-liquid pressure drop has been validated using relevant correlations gleaned from the literature. The study is concerned with nearly-neutrally buoyant particles flowing in a horizontal or vertical pipe. The effects of various parameters on the flow properties of such mixtures have been investigated over a wide range of conditions. The variables studied are: particle diameter (2-9 mm), mean solids concentration (5-40% v/v), mean mixture velocity (25-125 mm s⁻¹), and rheological properties of the carrier fluid (k=0.15-20 Pa sⁿ; n=0.6-0.9). A few additional runs have been conducted for shear thickening fluids, i.e. n>1. Whilst the effects of varying the power law parameters and the mixture flowrate for shear thinning fluids are relatively small over the range of values considered, particle size and solids concentration have a significant bearing on the flow regime, the uniformity of the normalised particle radial distribution and of the normalised velocity profiles of both phases, and the magnitude of the solid-liquid pressure drop. The maximum particle velocity is always significantly less than twice the mean flow velocity for shear thinning fluids, but it can exceed this value in shear thickening fluids. In vertical down-flow, particles are uniformly distributed over the pipe cross-section, and particle diameter and concentration have little effect on the normalised velocity and concentration profiles. Pressure drop, however, is greatly influenced by particle concentration.     

Numerical simulation for the collision between a vortex ring and solid particles

This study is concerned with the numerical simulation for the collision between a vortex ring and an ensemble of small glass particles. The vortex ring, convecting with its self-induced velocity in a quiescent air, collides with the particles. The Reynolds number for the vortex ring is 2600, and the particle diameters are 50 and 200 μm. The Stokes number St for the 50 μm particle is 0.74, while the St for the 200 μm particle is 11.4. Immediately after the collision with the vortex ring, the 50 μm particles surround the vortex ring, forming a dome. It is parallel with the preferential distribution for the particle with St ? 1 around large-scale eddies, which has been measured experimentally and simulated numerically in various free turbulent flows. The 200 μm particles disperse more due to the collision with the vortex ring. This is attributable to the centrifugal effect of large-scale eddy, which has been reported by the numerical simulation for the motion of the particle with St = 10 in a wake flow. The collision between the vortex ring and the particles induces an organized three-dimensional vortical structure. It also reduces the strength and convective velocity of the vortex ring.     

Pyrolysis of wheat straw in a thermogravimetric analyzer: Effect of particle size and heating rate on devolatilization and estimation of global kinetics

The influence of different parameters such as particle size, initial weight of the sample, and heating rate on the devolatilization of wheat straw particles have been studied using thermogravimetric analysis. In addition, the variations in proximate analysis with different particle sizes of wheat straw have also been investigated. Results show that the curves corresponding to the third stage of pyrolysis differ for variations in particle size, initial weight, and heating rate of the pyrolysis process. A devolatilization model with three parallel nth-order reactions has been considered to determine the global kinetic parameters using thermogravimetric data. The kinetic parameters such as activation energy (kJ/mol), frequency factor (1/min), and order of the reaction for the three stages considered in devolatilization model were E₁ = 69, E₂ = 78, E₃ = 80; k₀₁ = 2.57 × 10¹², k₀₂ = 3.97 × 10⁷, k₀₃ = 3.17 × 10⁶; and n₁ = 2.3, n₂ = 0.65, n₃ = 2.7, respectively. It was noted from the order of the reaction that the second stage of the pyrolysis curve corresponds to the degradation of cellulose and hemicellulose, and the third stage to the lignin degradation.     

Elongated gas bubble dissolution under a turbulent liquid flow

Mass transfer between an elongated homogeneous gas bubble under a turbulent liquid flow in a duct is investigated experimentally. Elongated gas bubble dissolution is encountered in bioengineering tubular photobioreactors. Such reactors are interesting because they are compact, they have a low contamination risk and a low mechanical stress for a liquid phase containing fragile microalgae cells. It is demonstrated from experimental mass transfer measurements, that the interface of an immobilised elongated bubble can be approximated to a flat plane. Measured mass transfer experimental data, estimated using this simplification, appear to be well fitted by Sh_L = 1.76 × 10⁻⁵ × Re^1.506 × Sc^0.5, a correlation from Lamourelle and Sandall [8], given for a turbulent liquid flow in wetted-wall columns. A formula drawn from this hypothesis is proposed for mass transfer prediction in photobioreactors. For different applications, it is suggested that the results obtained for the studied geometry could be used to build mass transfer feedback control systems.     

Mass transfer in vertical liquid-solids flow of coarse particles

Wall-to-bed mass transfer in the hydraulic transport of spherical glass particles was studied. The experiments were performed by transporting spherical glass particles 1.20, 1.94 and 2.98 mm in diameter with water in a 25.4 mm I.D. tube. The mass transfer coefficients were determined by following rate of dissolution of a segment of the transport tube prepared from benzoic acid.In the runs in hydraulic transport, the Reynolds number of the tube varied between 1826 and 27597. The loading ratio (G_p/G_f) was between 0.026 and 0.474, and the fluid superficial velocity was between 0.267 · U_t and 4.904 · U_t, where U_t represents the single particle terminal velocity. For these ratios, the voidage ranged from 0.7123 to 0.9228.Also, wall-to-bed mass transfer in the single phase flow regime was studied. In the runs without particles, the Reynolds number of the tube varied between 122 and 39132. The data for the mass transfer factor (j_D) in single phase flow are correlated for turbulent flow regime, using the Chilton-Colburn's type equations, j_D = f(Re). Those investigations were conducted in aim to compare with results for wall-to-bed mass transfer in hydraulic transport.The data for wall-to-bed mass transfer (j_D) in hydraulic transport of spherical particles were correlated by treating the flowing fluid-particle suspension as a pseudofluid, by introducing a modified suspension-wall friction coefficient (f_w) and a modified Reynolds number (Re_m). The data for wall-to-bed mass transfer in the hydraulic transport of particles show that an analogy between mass and momentum transfer exists.     

Rear surface deposition of fine particles on spheres — eddy deposition or electrostatic effects?

The aim of this investigation is to show the demarcation of two possible mechanisms for surface deposition of fine particles on the rear surface of single spheres. By means of single particle trajectory computation, based on numerically determined flow fields (Re_max = 10³), it is shown that the mere existence of a wake is not in itself sufficient to produce eddy deposition. In addition, the particle's motion must undergo a lateral transfer promoted by fluid trubulence, in order to effect eddy deposition commencing at a Reynolds number of about 100. On the other hand, rear deposition, influenced by electrostatic forces, especially by the Coulomb force, is possible at any Reynolds number. Consequently, for Reynolds numbers of less than 100, only electrostatic effects can produce rear surface deposition. In the range of high Reynolds numbers, the coexistence of both mechanisms is possible. Very high Reynolds numbers (Re > 10³) and low Stokes numbers indicated the predominance of the electrostatic effect over eddy deposition, whereas at very high Reynolds numbers and medium to high Stokes numbers the electrostatic effect is only predominant in presence of high electrostatic charges.     

Simulation of SiO2/S coating deposition in a pilot plant set-up for coking inhibition

The anti-coking SiO₂/S coating was prepared on the inner surface of HK40 alloy tube in a pilot plant set-up by atmospheric pressure chemical vapour deposition (APCVD). The coating deposition was simulated using the computational fluid dynamics code, Fluent. The reaction parameters of the surface reaction for SiO₂ formation were determined based on the comparison between the experimental and the calculated values. Further, the influences of the inlet flow rate and mass concentration of source materials on the coating deposition rate were investigated. The simulated results showed that an increase of inlet flow rate led to the decrease of mass conversion of gas intermediates. The coating deposition rate along the reactor tube increased by 1–5 times as the inlet flow rate increased from 10 to 80 g min⁻¹. The mass conversion rate of the gas intermediate, Si(OH)₄, changed little at different inlet mass concentrations of source materials when the inlet flow rate was 30 g min⁻¹, and it had an increase for sulphide intermediates. The coating deposition rate along the reactor tube increased by about 10 times with increasing the inlet mass concentration from 0.2% to 2%. In the conditions we studied, SiO₂/S coating deposition was surface reaction rate limited. When the inlet flow rate was 30–40 g min⁻¹ with the resource material concentration of 1–1.6%, the SiO₂/S coating was about 15 μm at the tube outlet with the silicon-containing intermediate conversion rate of above 30% and a good uniformity of S along the reactor. This work provides a theoretical basis for optimisation of operational parameters of the anti-coking SiO₂/S coating preparation in the pilot plant set-up.     

Enhancement of mass transfer from particles by local shear-rate and correlations with application to drug dissolution

We analyze hydrodynamic enhancement of mass (or heat) release rate from small spherical particles within fluid flows from local flow shear-rate, with application to drug dissolution. Combining asymptotic theories in the high/low shear Peclet number limits in Stokes flow with 205 carefully-developed computational experiments, we develop accurate correlations for shear enhancement of Sherwood/Nusselt number (Sh/Nu) as a function of shear Peclet and Reynolds number (S^*, Re _S). The data spanned S^* from 0 to 500 and Re _S from 0 to 10. In Stokes flow our correlations are highly accurate over the entire S^* range, whereas for finite Re _S < 1 accuracy is good for S^* up to a few thousand. Shear enhancement results from highly three-dimensional spiraling flow created by particle spin. We develop a model for particle slip velocity that is inserted into the Ranz/Marshall correlation to show that shear-rate enhancement strongly dominates convection, a result important to drug dissolution.     

Solids mixing behavior in a nano-agglomerate fluidized bed

The nano-particles mixing behavior in a nano-agglomerate fluidized bed (NAFB) using R972, a kind of nano-SiO₂ powder, was investigated by the nano-particle coated phosphors tracer method. The axial and radial solids dispersion coefficients in this system were two orders of magnitude lower than those in fluid catalytic cracking (FCC) catalyst systems. The axial solids dispersion coefficient increased with increasing superficial gas velocities, and ranged between 9.1 × 10^− 4 and 2.6 × 10^− 3 m²/s. There was a step increase in the axial solids dispersion coefficient between the particulate fluidization regime and bubbling and turbulent fluidization regimes. As the superficial gas velocity increased, the radial solids dispersion coefficient increased gradually, from 1.2 × 10^− 4 to 4.5 × 10^− 4 m²/s. The much smaller D_a and D_r, compared to regular fluidized systems, is mainly due to the reduced density difference between the fluidized particles and fluidizing medium. To validate this, the solids dispersion coefficients in the NABF were compared with literature values for liquid-solid particulate systems in the particulate fluidization regime and FCC systems in the bubbling and turbulent fluidization regimes. The density difference between the fluidized particles and fluidizing medium and kinetic viscosity of the fluidizing medium, and other hydrodynamic factors like the superficial velocity of the fluidizing medium and the average diameters of the fluidized particles, were the key factors in the solids mixing in the fluidized beds. Empirical correlations are given to describe the results.     

Cross-linked latex particles grafted with polyisoprene as model rubber-compatible fillers

Model filler particles were obtained by grafting polyisoprene (PIP) chains onto spherical latex particles of polystyrene cross-linked with 12 mol% divinylbenzene. These particles, with a narrow size distribution and a diameter of ca. 400 nm, were synthesized by emulsifier-free starved-feed emulsion polymerization. Acetyl coupling sites were introduced randomly at either low (5 mol%) or high (30 mol%) target substitution levels on the latex particles by Friedel-Crafts acylation with acetyl chloride and AlCl₃ in nitrobenzene. ‘Living’ polyisoprenyllithium chains, generated from isoprene and sec-butyllithium (sec-BuLi), were then coupled with the acetylated particles. The PIP side chains had a high 1,4-polyisoprene microstructure content and a number-average molecular weight (M_n) of either 1.5 × 10³ (1.5 K), 5 × 10³ (5 K), or 3 × 10⁴ (30 K). The PIP content of the grafted particles was determined from the yield of isolated particles and by ¹H NMR spectroscopy analysis. The grafted latex particles were blended in solution with linear polyisoprene (M_n = 3.95 × 10⁵, 395 K). The influence of the filler-matrix interactions on the rheological behavior of the blends was determined by dynamic mechanical analysis for the different filler blends. Increases in complex viscosity and storage modulus, and decreased damping factors were observed in all cases relatively to the pure matrix polymer. The enhancements, decreasing in the order 30 mol% > 5 mol% acetylation, and with the grafted PIP chain length as 30 K > 5 K ≈ 1.5 K, are deemed to reflect the extent of interactions between the filler particles and the polymer matrix.     

Particle deposition behaviors of monolithic De-NO<Subscript><Emphasis Type="Italic">x</Emphasis></Subscript> catalysts for selective catalytic reduction (SCR)

A major issue when using selective catalytic reduction (SCR) De-NO _x catalysts is the risk of physical deactivation due to particle deposition and plugging of the monolithic catalysts. In the present study, numerical computations were carried out to investigate the particle deposition behaviors in monolithic SCR catalysts. Based on the calculation results, the effects of particle diameter, particle density, gas velocity, turbulent intensity, chemical reaction and channel size on particle deposition were analyzed in detail. Increasing gas velocity and equivalent diameter of channel can mitigate particle deposition. The increases of turbulent intensity and channel length both lead to the rise of particle deposition ratio. For particles with high Stokes number, particle deposition mainly takes place in the inlet section of catalysts. For particles with low Stokes number, sediment can be observed in the middle and outlet sections of catalysts. De-NO _x chemical reaction can mitigate particle deposition, but the effect of chemical reaction on particle deposition is inactive.     

Size-controlled synthesis of Fe-Ni alloy nanoparticles by hydrogen reduction of metal chlorides

We synthesized crystalline Fe-Ni nanoparticles with various particle sizes by reducing NiCl₂ and FeCl₂ vapors with hydrogen simultaneously. To control the primary particle size, processing variables of evaporator temperature, reaction zone temperature, and total gas flow rate were varied. The nanoparticles were nearly spherical and formed directional linkage between them due to magnetic interaction. The XRD patterns and elemental compositions measured by EDS showed that the Fe-Ni nanoparticles were mainly composed of cubic FeNi₃. With various evaporation temperatures from 800 to 900 °C, the reactant concentrations were estimated to range from 7.94 × 10^− 6 to 2.68 × 10^− 5 mol/l, which resulted in the specific surface area and Sauter diameter of the particles from 11.1 to 8.8 m²/g and from 65 to 82 nm, respectively. The geometric standard deviations of the primary particle sizes obtained from TEM micrographs ranged from 1.24 to 1.27, indicating very narrow particle size distribution. The increase in the reaction temperature from 850 to 950 °C led to the reduction of the Sauter diameter from 69 to 63 nm. As the total gas flow rate decreased from 5 to 3 l/min, the Sauter diameter increased from 56 to 69 nm.