Modeling of silica synthesis in a laminar flame by coupling an extended population balance model with computational fluid dynamics

References

• Ball, R. C., and R. Jullien. 1984. Finite size effects in cluster-cluster aggregation. J. Phyique Lett. 45 (21):1031–5. doi:10.1051/jphyslet:0198400450210103100.
   Web of Science ®Google Scholar
• Barlow, R. S., A. N. Karpetis, J. H. Frank, and J. Y. Chen. 2001. Scalar profiles and NO formation in laminar opposed-flow partially premixed methane/air flames. Combust. Flame. 127 (3):2102–18. doi:10.1016/S0010-2180(01)00313-3.
   Web of Science ®Google Scholar
• Buddhiraju, V. S., and V. Runkana. 2012. Simulation of nanoparticle synthesis in an aerosol flame reactor using a coupled flame dynamics–monodisperse population balance model. J. Aerosol Sci. 43 (1):1–13. doi:10.1016/j.jaerosci.2011.08.007.
   Web of Science ®Google Scholar
• Buesser, B., and A. J. Gröhn. 2012. Multiscale aspects of modeling gas-phase nanoparticle synthesis. Chem. Eng. Technol. 35 (7):1133–43. doi:10.1002/ceat.201100723.
   PubMed Web of Science ®Google Scholar
• Buesser, B., and S. E. Pratsinis. 2012. Design of nanomaterial synthesis by aerosol processes. Annu. Rev. Chem. Biomol. Eng. 3:103–27.
   PubMed Web of Science ®Google Scholar
• Camenzind, H., A. Schulz, G. Teleki, T. Beaucage, S. Narayanan, and E. Pratsinis. 2008. Nanostructure evolution: from aggregated to spherical SiO2 particles made in diffusion flames. Eur. J. Inorg. Chem. 2008 (6):911–8. doi:10.1002/ejic.200701080.
   Web of Science ®Google Scholar
• Chang H. and P. Biswas. 1992. In situ light scattering dissymmetry measurements of the evolution of the aerosol size distribution in flames. J. Colloid Interface Sci. 153 (1):157–66.
   Web of Science ®Google Scholar
• Cho, J., and M. Choi. 2000. Determination of number density, size and morphology of aggregates in coflow diffusion flames using light scattering and local sampling. J. Aerosol Sci. 31 (9):1077–95. doi:10.1016/S0021-8502(99)00574-1.
   Web of Science ®Google Scholar
• Choi, M., J. Cho, J. Lee, and H. W. Kim. 1999. Measurements of silica aggregate particle growth using light scattering and thermophoretic sampling in a coflow diffusion flame. J. Nanopart. Res. 1 (2):169–83. doi:10.1023/A:1010092113802.
   Web of Science ®Google Scholar
• Chung, S.-L., Y.-C. Sheu, and M.-S. Tsai. 1992. Formation of SiO2, Al2O3, and 3Al2O3 ·2SiO2 particles in a counterflow diffusion flame. J. Amer. Ceram. Soc. 75 (1):117–23.
   Web of Science ®Google Scholar
• Dasgupta, D., P. Pal, R. Torelli, S. Som, N. Paulson, J. Libera, and M. Stan. 2022. Computational fluid dynamics modeling and analysis of silica nanoparticle synthesis in a flame spray pyrolysis reactor. Combust. Flame. 236:111789. doi:10.1016/j.combustflame.2021.111789.
   Web of Science ®Google Scholar
• Ehrman, S. H. 1999. Effect of particle size on rate of coalescence of silica nanoparticles. J Colloid Interface Sci. 213 (1):258–61.
   PubMed Web of Science ®Google Scholar
• Ehrman, S. H., S. K. Friedlander, and M. R. Zachariah. 1998. Characteristics of SiO2/TiO2 nanocomposite particles formed in a premixed flat flame. J. Aerosol Sci. 29 (5–6):687–706. doi:10.1016/S0021-8502(97)00454-0.
   Web of Science ®Google Scholar
• Feroughi, O. M., L. Deng, S. Kluge, T. Dreier, H. Wiggers, I. Wlokas, and C. Schulz. 2017. Experimental and numerical study of a HMDSO-seeded premixed laminar low-pressure flame for SiO2 nanoparticle synthesis. Proc. Combust. Inst. 36 (1):1045–53. doi:10.1016/j.proci.2016.07.131.
   Web of Science ®Google Scholar
• Ford, J. 2004. Statistical mechanics of nucleation: A review. Proceedings Institution Mech. Engineer, Part C: J. Mech. Engng. Sci. 218 (8):883–99.
   Web of Science ®Google Scholar
• Frenkel. 1945. Viscous flow of crystalline bodies under the action of surface tension. J. Phys. 9 (385).
   Google Scholar
• Frenklach, M., H. Wang, M. Goldenberg, G. P. Smith, and D. M. Golden. GRI-MECH: An optimized detailed chemical reaction mechanism for methane combustion. Topical report, September 1992-August 1995. Technical report, SRI International, Menlo Park, CA (United States), 1995.
   Google Scholar
• Friedlander, S. K. 2000. Smoke, dust, and haze: Fundamentals of aerosol dynamics. 2nd ed. Oxford: Oxford University Press.
   Google Scholar
• Girshick, S. L., and C. P. Chiu. 1989. Homogeneous nucleation of particles from the vapor phase in thermal plasma synthesis. Plasma Chem. Plasma Process. 9 (3):355–69. doi:10.1007/BF01083672.
   Web of Science ®Google Scholar
• Goudeli, E., M. L. Eggersdorfer, and S. E. Pratsinis. 2015. Aggregate characteristics accounting for the evolving fractal-like structure during coagulation and sintering. J. Aerosol Sci. 89:58–68. doi:10.1016/j.jaerosci.2015.06.008.
   Web of Science ®Google Scholar
• Griffiths, P. R., and J. A. De Haseth. 2007. Fourier transform infrared spectrometry. Hoboken, NJ: John Wiley & Sons.
   Google Scholar
• Gröhn, J., B. Buesser, J. K. Jokiniemi, and S. E. Pratsinis. 2011. Design of turbulent flame aerosol reactors by mixing-limited fluid dynamics. Ind. Eng. Chem. Res. 50 (6):3159–68. doi:10.1021/ie1017817.
   Web of Science ®Google Scholar
• Grosshandler, W. L. 1993. Radcal: a narrow band model for radiation. Calculations in a Combustion Environment, NIST Technical Note, 1402.
   Google Scholar
• Heinson, W. R., C. M. Sorensen, and A. Chakrabarti. 2010. Does shape anisotropy control the fractal dimension in diffusion-limited cluster-cluster aggregation? Aerosol Sci. Tech. 44 (12):i–iv. doi:10.1080/02786826.2010.516032.
   Web of Science ®Google Scholar
• Hirschfelder, J. O., C. F. Curtiss, and R. B. Bird. 1955. Molecular theory of gases and liquids. Phys. today 8 (3):17. doi:10.1063/1.3061949.
   Google Scholar
• Iyer, S. S., T. A. Litzinger, S. Y. Lee, and R. J. Santoro. 2007. Determination of soot scattering coefficient from extinction and three-angle scattering in a laminar diffusion flame. Combust. Flame. 149 (1–2):206–16. doi:10.1016/j.combustflame.2006.11.009.
   Web of Science ®Google Scholar
• Jang, H. D. 2001. Experimental study of synthesis of silica nanoparticles by a bench-scale diffusion flame reactor. Powder Technol. 119 (2–3):102–8. doi:10.1016/S0032-5910(00)00407-1.
   Web of Science ®Google Scholar
• Ji, Y., H. Y. Sohn, H. D. Jang, B. Wan, and T. A. Ring. 2007. Computational fluid dynamic modeling of a flame reaction process for silica nanopowder synthesis from tetraethylorthosilicate. J American Ceramic Society. 0 (0):071019062949004–??? doi:10.1111/j.1551-2916.2007.02080.x.
   Web of Science ®Google Scholar
• Kammler, H. K., G. Beaucage, D. J. Kohls, N. Agashe, and J. Ilavsky. 2005. Monitoring simultaneously the growth of nanoparticles and aggregates by in situ ultra-small-angle x-ray scattering. J. Appl. Phys. 97 (5):054309. doi:10.1063/1.1855391.
   Web of Science ®Google Scholar
• Kammler, H. K., S. E. Pratsinis, P. W. Morrison, Jr., and B. Hemmerling. 2002. Flame temperature measurements during electrically assisted aerosol synthesis of nanoparticles. Combust. Flame. 128 (4):369–81. doi:10.1016/S0010-2180(01)00357-1.
   Web of Science ®Google Scholar
• Kennedy, M., and S. J. Harris. 1990. Enhancement of silica aerosol coagulation by van der Waals forces. Aerosol Sci. Tech. 12 (4):869–75. doi:10.1080/02786829008959399.
   Web of Science ®Google Scholar
• Kim, H. J., J. I. Jeong, Y. Park, Y. Yoon, and M. Choi. 2003. Modeling of generation and growth of non-spherical nanoparticles in a co-flow flame. J. Nanopart. Res. 5 (3/4):237–46. doi:10.1023/A:1025570125689.
   Web of Science ®Google Scholar
• Kim, H. W., and M. Choi. 2003. In situ line measurement of mean aggregate size and fractal dimension along the flame axis by planar laser light scattering. J. Aerosol Sci. 34 (12):1633–45. doi:10.1016/S0021-8502(03)00358-6.
   Web of Science ®Google Scholar
• Kim, S., and S. E. Pratsinis. 1988. Manufacture of optical waveguide preforms by modified chemical vapor deposition. AIChE J 34 (6):912–21. doi:10.1002/aic.690340603.
   Web of Science ®Google Scholar
• Kim, S., and S. E. Pratsinis. 1989. Modeling and analysis of modified chemical vapor deposition of optical fiber preforms. Chem. Eng. Sci. 44 (11):2475–82. doi:10.1016/0009-2509(89)85191-7.
   Web of Science ®Google Scholar
• Kirchhof, J., H. Förster, H. J. Schmid, and W. Peukert. 2012. Sintering kinetics and mechanism of vitreous nanoparticles. J. Aerosol Sci. 45:26–39. doi:10.1016/j.jaerosci.2011.10.006.
   Web of Science ®Google Scholar
• Koch, W., and S. K. Friedlander. 1990. The effect of particle coalescence on the surface area of a coagulating aerosol. J. Colloid Interface Sci. 140 (2):419–27. doi:10.1016/0021-9797(90)90362-R.
   Web of Science ®Google Scholar
• Kruis, F. E., K. A. Kusters, S. E. Pratsinis, and B. Scarlett. 1993. A simple model for the evolution of the characteristics of aggregate particles undergoing coagulation and sintering. Aerosol Sci. Tech. 19 (4):514–26. doi:10.1080/02786829308959656.
   Web of Science ®Google Scholar
• Lee, B. W., S. Oh, and M. Choi. 2001. Simulation of growth of nonspherical silica nanoparticles in a premixed flat flame. Aerosol Sci. Tech. 35 (6):978–89. doi:10.1080/027868201753306741.
   Web of Science ®Google Scholar
• Lee, J. 2011. Estimation of emission properties for silica particles using thermal radiation spectroscopy. Appl. Opt. 50 (22):4262–7.
   PubMed Web of Science ®Google Scholar
• Liu, A., and S. Rigopoulos. 2019. A conservative method for numerical solution of the population balance equation, and application to soot formation. Combust. Flame. 205:506–21. doi:10.1016/j.combustflame.2019.04.019.
   Web of Science ®Google Scholar
• Mathur, S., and S. C. Saxena. 1967. Methods of calculating thermal conductivity of binary mixtures involving polyatomic gases. Appl. Sci. Res. 17 (2):155–68. doi:10.1007/BF00419783.
   Google Scholar
• Meierhofer, F., and U. Fritsching. 2021. Synthesis of metal oxide nanoparticles in flame sprays: review on process technology, modeling, and diagnostics. Energy Fuel. 35 (7):5495–537. doi:10.1021/acs.energyfuels.0c04054.
   Web of Science ®Google Scholar
• Modest, F. 2003. Radiative Heat Transfer. Academic Press: Cambridge MA, USA, 2nd edition,
   Google Scholar
• Morrison, P. W., Jr., R. Raghavan, A. J. Timpone, C. P. Artelt, and S. E. Pratsinis. 1997. In situ fourier transform infrared characterization of the effect of electrical fields on the flame synthesis of TiO2 particles. Chem. Mater. 9 (12):2702–8. doi:10.1021/cm960508u.
   Web of Science ®Google Scholar
• Netzell, K., H. Lehtiniemi, and F. Mauss. 2007. Calculating the soot particle size distribution function in turbulent diffusion flames using a sectional method. Proc. Combust. Inst. 31 (1):667–74. doi:10.1016/j.proci.2006.08.081.
   Web of Science ®Google Scholar
• Neuber, G., C. E. Garcia, A. Kronenburg, B. A. Williams, F. Beyrau, O. T. Stein, and M. J. Cleary. 2019. Joint experimental and numerical study of silica particulate synthesis in a turbulent reacting jet. Proc. Combust. Inst. 37 (1):1213–20. doi:10.1016/j.proci.2018.06.074.
   Web of Science ®Google Scholar
• Olivas-Martinez, M., H. Y. Sohn, H. D. Jang, and K.-I. Rhee. 2015. Computational fluid dynamic modeling of the flame spray pyrolysis process for silica nanopowder synthesis. J. Nanopart Res. 17 (7):324. doi:10.1007/s11051-015-3109-z.
   Web of Science ®Google Scholar
• Park, H. K., and K. Y. Park. 2015. Control of particle morphology and size in vapor-phase synthesis of titania, silica and alumina nanoparticles. KONA 32 (0):85–101. doi:10.14356/kona.2015018.
   Google Scholar
• Poinsot, T., and D. Veynante. 2005. Theoretical and numerical combustion. Morningside, Australia: RT Edwards, Inc.,
   Google Scholar
• Pratsinis, S. E. 1988. Simultaneous nucleation, condensation, and coagulation in aerosol reactors. J. Colloid Interface Sci. 124 (2):416–27. doi:10.1016/0021-9797(88)90180-4.
   Web of Science ®Google Scholar
• Pratsinis, S. E., and K.-S. Kim. 1989. Particle coagulation, diffusion and thermophoresis in laminar tube flows. J. Aerosol Sci. 20 (1):101–11. doi:10.1016/0021-8502(89)90034-7.
   Web of Science ®Google Scholar
• Raman, V., and R. O. Fox. 2016. Modeling of fine-particle formation in turbulent flames. Annu. Rev. Fluid Mech. 48 (1):159–90. doi:10.1146/annurev-fluid-122414-034306.
   Web of Science ®Google Scholar
• Rigopoulos, S. 2007. PDF method for population balance in turbulent reactive flow. Chem. Eng. Sci. 62 (23):6865–78. doi:10.1016/j.ces.2007.05.039.
   Web of Science ®Google Scholar
• Rigopoulos, S. 2010. Population balance modelling of polydispersed particles in reactive flows. Prog. Energy Combust. Sci. 36 (4):412–43. doi:10.1016/j.pecs.2009.12.001.
   Web of Science ®Google Scholar
• Rittler, L., I. Deng, A. Wlokas, and M. Kempf. 2017. Large eddy simulations of nanoparticle synthesis from flame spray pyrolysis. Proc. Combust. Inst. 36 (1):1077–87. doi:10.1016/j.proci.2016.08.005.
   Web of Science ®Google Scholar
• Rodrigues, P., B. Franzelli, R. Vicquelin, O. Gicquel, and N. Darabiha. 2018. Coupling an LES approach and a soot sectional model for the study of sooting turbulent non-premixed flames. Combust. Flame 190:477–99. doi:10.1016/j.combustflame.2017.12.009.
   Web of Science ®Google Scholar
• Rogak, S. N. 1997. Modeling small cluster deposition on the primary particles of aerosol agglomerates. Aerosol Sci. Technol. 26 (2):127–40. doi:10.1080/02786829708965419.
   Web of Science ®Google Scholar
• Rosner, D. E. 2005. Flame synthesis of valuable nanoparticles: Recent progress/current needs in areas of rate laws, population dynamics, and characterization. Ind. Eng. Chem. Res. 44 (16):6045–55. doi:10.1021/ie0492092.
   Web of Science ®Google Scholar
• Scheckman, J. H., P. H. McMurry, and S. E. Pratsinis. 2009. Rapid characterization of agglomerate aerosols by in situ mass- mobility measurements. Langmuir. 25 (14):8248–54. doi:10.1021/la900441e.
   PubMed Web of Science ®Google Scholar
• Seto, T., A. Hirota, T. Fujimoto, M. Shimada, and K. Okuyama. 1997. Sintering of polydisperse nanometer-sized agglomerates. Aerosol Sci. Tech. 27 (3):422–38. doi:10.1080/02786829708965482.
   Web of Science ®Google Scholar
• Shekar, S., A. J. Smith, W. J. Menz, M. Sander, and M. Kraft. 2012. A multidimensional population balance model to describe the aerosol synthesis of silica nanoparticles. J. Aerosol Sci. 44:83–98. doi:10.1016/j.jaerosci.2011.09.004.
   Web of Science ®Google Scholar
• Sun, B., and S. Rigopoulos. 2022. Modelling of soot formation and aggregation in turbulent flows with the LES-PBE-PDF approach and a conservative sectional method. Combust. Flame. 242:112152. doi:10.1016/j.combustflame.2022.112152.
   Web of Science ®Google Scholar
• Sun, B., S. Rigopoulos, and A. Liu. 2021. Modelling of soot coalescence and aggregation with a two-population balance equation model and a conservative finite volume method. Combust. Flame 229:111382. doi:10.1016/j.combustflame.2021.02.028.
   Web of Science ®Google Scholar
• Sztucki, M., T. Narayanan, and G. Beaucage. 2007. In situ study of aggregation of soot particles in an acetylene flame by small-angle x-ray scattering. J. Appl. Phys. 101 (11):114304. doi:10.1063/1.2740341.
   Web of Science ®Google Scholar
• Tsagkaridis, M., S. Rigopoulos, and G. Papadakis. 2022. Analysis of turbulent coagulation in a jet with discretised population balance and DNS. J. Fluid Mech. 937 (A25) doi:10.1017/jfm.2022.57.
   Web of Science ®Google Scholar
• Tsantilis, S., and S. E. Pratsinis. 2000. Evolution of primary and aggregate particle-size distributions by coagulation and sintering. AIChE J. 46 (2):407–15. doi:10.1002/aic.690460218.
   Web of Science ®Google Scholar
• Tsantilis, S., H. Briesen, and S. E. Pratsinis. 2001. Sintering time for silica particle growth. Aerosol Sci. Tech. 34 (3):237–46. doi:10.1080/02786820119149.
   Web of Science ®Google Scholar
• Tsantilis, S., H. K. Kammler, and S. E. Pratsinis. 2002. Population balance modeling of flame synthesis of titania nanoparticles. Chem. Eng. Sci. 57 (12):2139–56. doi:10.1016/S0009-2509(02)00107-0.
   Web of Science ®Google Scholar
• Ulrich, G. D. 1971. Theory of particle formation and growth in oxide synthesis flames. Combust. Sci. Technol. 4 (1):47–57. doi:10.1080/00102207108952471.
   Web of Science ®Google Scholar
• Ulrich, G. D., and J. W. Rieh. 1982. Aggregation and growth of submicron oxide particles in flames. J. Colloid Interface Sci. 87 (1):257–65. doi:10.1016/0021-9797(82)90387-3.
   Web of Science ®Google Scholar
• Vo, S., A. Kronenburg, O. T. Stein, and M. J. Cleary. 2017. Multiple mapping conditioning for silica nanoparticle nucleation in turbulent flows. Proc. Combust. Inst. 36 (1):1089–97. doi:10.1016/j.proci.2016.08.088.
   Web of Science ®Google Scholar
• Wegner, K., and S. E. Pratsinis. 2003a. Nozzle-quenching process for controlled flame synthesis of titania nanoparticles. AIChE J. 49 (7):1667–75. doi:10.1002/aic.690490707.
   Web of Science ®Google Scholar
• Wegner, K., and S. E. Pratsinis. 2003b. Scale-up of nanoparticle synthesis in diffusion flame reactors. Chem. Eng. Sci. 58 (20):4581–9. doi:10.1016/j.ces.2003.07.010.
   Web of Science ®Google Scholar
• Wilke, C. R. 1950. A viscosity equation for gas mixtures. J. Chem. Phys. 18 (4):517–9. doi:10.1063/1.1747673.
   Web of Science ®Google Scholar
• Willeke, K. 1976. Temperature dependence of particle slip in a gaseous medium. J. Aerosol Sci. 7 (5):381–7. doi:10.1016/0021-8502(76)90024-0.
   Google Scholar
• Xiong, Y., and S. E. Pratsinis. 1991. Gas phase production of particles in reactive turbulent flows. J. Aerosol Sci. 22 (5):637–55. doi:10.1016/0021-8502(91)90017-C.
   Web of Science ®Google Scholar
• Xiong, Y., and S. E. Pratsinis. 1993. Formation of agglomerate particles by coagulation and sintering - Part I. A two-dimensional solution of the population balance equation. J. Aerosol Sci. 24 (3):283–300. doi:10.1016/0021-8502(93)90003-R.
   Web of Science ®Google Scholar
• Zachariah, M. R., D. Chin, H. G. Semerjian, and J. L. Katz. 1989. Silica particle synthesis in a counterflow diffusion flame reactor. Combust. Flame. 78 (3-4):287–98. doi:10.1016/0010-2180(89)90018-7.
   Web of Science ®Google Scholar