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Population Balance Modeling with Coupled Agglomeration and Disintegration Processes for TiO2 Nanoparticles Formation and Experimental Validation

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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.

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Abbreviations

B:

Disintegration function (m−3)

D:

Particle size (µ)

S:

Selection function (s−1)

T:

Time (s)

x, y:

Particle volume (m3)

Qr (d):

Cumulative particle size distribution (%)

Re:

Reynolds-Number

β:

One-dimensional agglomeration kernel (m−3. s−1)

ε:

Turbulent energy dissipation rate (m2. s−3)

\( \upsilon \) :

Kinematic viscosity of the fluid (m2. s−1)

\( \eta \) :

Viscosity of the fluid (kg. m−1. s−1)

λ:

Wavelength (m)

\( \dot{\gamma } \) :

Shear rate (s−1)

\( \,\phi \) :

Dimensionless material constant

\( \gamma \) :

Dimensionless material constant

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Authors and Affiliations

  1. Department of Mathematics, Birla Institute of Technology and Science Pilani, Pilani Campus, Rajasthan, 333031, India

    Rajesh Kumar

  2. Octillion Power Systems India Pvt. Ltd, Plot No. 302, Sector 10, Bhosari MIDC, Pune, 411026, India

    Yashodhan Pramod Gokhale

  3. Department of Chemical Engineering, Birla Institute of Technology and Science Pilani, Hyderabad Campus, Hyderabad, 500078, India

    Vikranth Kumar Surasani

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  1. Rajesh Kumar
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  2. Yashodhan Pramod Gokhale
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  3. Vikranth Kumar Surasani
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Correspondence to Rajesh Kumar.

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Kumar, R., Gokhale, Y.P. & Surasani, V.K. Population Balance Modeling with Coupled Agglomeration and Disintegration Processes for TiO2 Nanoparticles Formation and Experimental Validation. J Clust Sci 32, 1361–1369 (2021). https://doi.org/10.1007/s10876-020-01895-4

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