Abstract
To control the particle size and morphology of nanoparticles is of crucial importance from a fundamental and an industrial point of view. Nanoparticle precipitation in the batch reactor is investigated experimentally as well as by simulations based on population balance equations combined with the model using titanium dioxide as the material under investigation. The superposition of the population balance models for agglomeration and disintegration with the different kernels leads to a system of partial differential equations, which can be numerically solved by various methods. This includes a comparison of the derived particle size distributions, moments and their accuracy depending on the initial particle size distribution. Furthermore, the capability of the precipitation model is evaluated, achieving good agreement of the particle sizes between experimental and simulation results. Finally, the computational effort of both methods in comparison to the prior mentioned parameters is evaluated in terms of practical applications.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Gratzel, M.: Light-induced redox reactions in nanocrystalline systems. Chem. Rev. 95, 49 (1995)
Granqvist, G.: Handbook of Inorganic Electrochromic Materials. Elsevier Science, Amsterdam (1995)
Janata, J., Josowicz, M., Vanysek, P., DeVaney, D.M.: Chemical Sensors. Anal. Chem. 70(12), 179R (1998)
Kupriyanov, L.Y. (ed.): Semiconductor Sensors in Physico-Chemical Studies: Handbook of Sensors and Actuators 4. Elsevier, Amsterdam (1996)
Kress-Rogers, E. (ed.): Handbook of Biosensors and Electronic Noses. CRC, Boca Raton (1997)
Manthiram, A., Kim, J.: Nanosized manganese oxide as cathode material for lithium batteries: Influence of carbon mixing and grinding on cyclability. Journal of power sources 146, 294–299 (2005)
Sarangapani, S., Tilak, B.V., Chen, C.P.: Materials for Electrochemical Capacitors. Journal of Electrochem. Soc. 143(11), 3791 (1996)
Vayssieres, L., Hagfeldt, A., Lindquist, S.E.: Purpose-built metal oxide nanomaterials. The emergence of a new generation of smart materials. Pure. Appl. Chem. 72(1), 47–52 (2000)
Schwarzer, H.C., Peukert, W.: Prediction of aggregation kinetics based on surface properties of nanoparticles. Chemical Engineering Science 60, 11–25 (2005)
Schuetz, S., Piesche, M.: A model of the coagulation process with solid particles and flocs in turbulent flow. Chemical Engineering Science 57, 4357–4368 (2002)
Schwarzer, H.C., Peukert, W.: Experimental investigation into the influence of mixing on nanoparticle precipitation. Chemical Engineering Technology 25(6), 657–661 (2002)
Schwarzer, H.C., Peukert, W.: Tailoring particle size through nanoparticle precipitation. Chemical Engineering Communication 191(4), 580–606 (2004)
Gregory, M., Odegard, S., Thomas, G., Lee, M., Nicholsonc, K., Wise, E.: Composites Science and Technology 62, 1869–1880 (2002)
Hintz, W., Nikolov, T., Jordanova, V., Tomas, J.: Preparation of titanium dioxide nanoparticles and their characterization. Nanoscience & nanotechnology - nanostructured materials, application and innovation transfer (Sofia) 3, 73–76 (2003)
Nikolov, T., Hintz, W., Jordanova, V., Tomas, J.: Synthesis and characterisation of titanium dioxide nanoparticles. Journal of the University of Chemical Technology and Metallurgy (Sofia) 38(3), 725–734 (2003)
McCoy, J.B.: A population balance framework for nucleation, growth, and aggregation. Chemical Engineering Science 57, 2279–2285 (2002)
Peukert, W., Schwarzer, H.C., Stenger, F.: Control of aggregation in production and handling of nanoparticles. Chemical Engineering and Processing 44, 245–252 (2005)
Ramkrishna, D.: Population balances. Theory and applications to particulate systems in engineering, 1st edn. Academic Press, New York (2000)
Kumar, J.: Numerical approximations of population balance equations in particulate systems, Ph.D. Thesis. Otto-von-Guericke-University Magdeburg, Germany (2006)
Sommer, M., Stenger, F., Peukert, W., Wagner, N.J.: Agglomeration and breakage of nanoparticles in stirred media mills a comparison of different methods and models. Chemical Engineering Science 61, 135–148 (2006)
Smoluchowski, M.V.: Versuch einer mathematischen theorie der koagulationskinetic kolloider losunggen. Z. Phys. Chem. 92, 129 (1917)
Thompson, P.D.: Proceedings International Conference Cloud Physics, Toronto, p. 115 (1968)
Fuchs, N.: Über die Stabilität und Aufladung der Aerosole. Z. Phys. 89, 736 (1934)
Melis, S., Verduyn, M., Storti, G., Morbidelli, M., Baldyga, J.: Effect of fluid motion on the aggregation of small particles subject to interaction forces. AIChE J. 45, 1383 (1999)
Kumar, S., Ramkrishna, D.: On the solution of population balance equations by discretization – I. A fixed pivot technique. Chemical Engineering Science 51, 1311–1332 (1996)
Seifert, A., Beheng, K.D.: A double-moment parameterization for simulating autoconversion, accreation and selfcollection. Atmospheric Research 59(60), 265–281 (2001)
Kumar, J., Peglow, M., Warnecke, G., Heinrich, S., Mörl, L.: Improved accuracy and convergence of discretized population balance for aggregation: the cell average technique. Chemical Engineering Science 61, 282–292 (2006)
Kumar, J., Peglow, M., Warnecke, G., Heinrich, S.: An efficient numerical technique for solving population balance equation involving aggregation, breakage, growth and nucleation. Powder Technology 182, 81–104 (2008)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2008 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
Gokhale, Y.P., Kumar, J., Hintz, W., Warnecke, G., Tomas, J. (2008). Population Balance Modelling for Agglomeration and Disintegration of Nanoparticles. In: Bertram, A., Tomas, J. (eds) Micro-Macro-interaction. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-85715-0_24
Download citation
DOI: https://doi.org/10.1007/978-3-540-85715-0_24
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-85714-3
Online ISBN: 978-3-540-85715-0
eBook Packages: EngineeringEngineering (R0)