Population Balance Modeling with Coupled Agglomeration and Disintegration Processes for TiO 2 Nanoparticles Formation an
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ORIGINAL PAPER
Population Balance Modeling with Coupled Agglomeration and Disintegration Processes for TiO2 Nanoparticles Formation and Experimental Validation Rajesh Kumar1 • Yashodhan Pramod Gokhale2 • Vikranth Kumar Surasani3 Received: 12 July 2020 / Accepted: 13 September 2020 Springer Science+Business Media, LLC, part of Springer Nature 2020
Abstract Particle size distribution of nanoparticles plays an important role in modelling many scientific and engineering problems. In this article, we proposed a Finite Volume Method (FVM) to model TiO2 nanoparticles formation using population balance equations (PBEs) by incorporating the simultaneous agglomeration and disintegration processes. The superposition of the PBEs for agglomeration and disintegration with different kernels leads to a system of partial-integro differential equations, which are numerically solved by using FVM. The precipitation of TiO2 nanoparticles in the batch reactor is studied experimentally as well as by numerical simulations based on Austin and Diemer disintegration kernels and Shear agglomeration kernel. Finally, the capability of the precipitation model is evaluated and the experimental results on particle sizes are compared with the numerical results. Keywords Population Balance Modeling TiO2 Nanoparticles Agglomeration Nomenclature B Disintegration function (m-3) D Particle size (l) S Selection function (s-1) T Time (s) x, y Particle volume (m3) Qr (d) Cumulative particle size distribution (%) Re Reynolds-Number b One-dimensional agglomeration kernel (m-3. s-1) e Turbulent energy dissipation rate (m2. s-3) t Kinematic viscosity of the fluid (m2. s-1) g Viscosity of the fluid (kg. m-1. s-1) k Wavelength (m) c_ Shear rate (s-1)
& Rajesh Kumar [email protected] 1
Department of Mathematics, Birla Institute of Technology and Science Pilani, Pilani Campus, Rajasthan 333031, India
2
Octillion Power Systems India Pvt. Ltd, Plot No. 302, Sector 10, Bhosari MIDC, Pune 411026, India
3
Department of Chemical Engineering, Birla Institute of Technology and Science Pilani, Hyderabad Campus, Hyderabad 500078, India
/ c
Dimensionless material constant Dimensionless material constant
Introduction There are tremendous high-tech applications of nanostructured metal oxide material devices such as dye-sensitized solar cells, displays and smart windows, chemical, gas and biosensors, lithium batteries, super capacitors and references therein [1, 2]. Both from the fundamental and the industrial point of view, it is crucial to control the particle size and morphology of nanoparticles. Indeed, further development, improvement, and optimization of such devices will be reached, if the following two factors exist. First, a better understanding of the unique physical properties and the complex electronic structure, and second, a better match of the materials design and the required device applications for the sake of miniaturization and performance [3]. One of the fundamental issues tha
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