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An analytical solution to the fixed pivot fragmentation population balance equation

Håkansson, Andreas LU (2019) In Chemical Engineering Science 208.
Abstract

Drop breakup in high-energy emulsification is often modelled using a population balance equation (PBE) framework. For cases with high emulsifier to disperse phase concentration, the PBE is dominated by the fragmentation term. Since there are no analytical solutions to the continuous PBE for physically reasonable fragmentation rate expressions, a discretization is often needed to evaluate the PBE, turning it into a set of ordinary differential equations that can be solved numerically. The fixed pivot technique (Kumar and Ramkrishna, 1996) is one of the most often applied class discretization methods. This contribution suggests an analytical solution to the fixed pivot technique fragmentation equation, that can be used instead of the... (More)

Drop breakup in high-energy emulsification is often modelled using a population balance equation (PBE) framework. For cases with high emulsifier to disperse phase concentration, the PBE is dominated by the fragmentation term. Since there are no analytical solutions to the continuous PBE for physically reasonable fragmentation rate expressions, a discretization is often needed to evaluate the PBE, turning it into a set of ordinary differential equations that can be solved numerically. The fixed pivot technique (Kumar and Ramkrishna, 1996) is one of the most often applied class discretization methods. This contribution suggests an analytical solution to the fixed pivot technique fragmentation equation, that can be used instead of the traditional numerical approach provided that the fragmentation rate is constant over time. The proposed solution compares favorably to two special cases where analytical solutions for the continuous PBE are available, and to two more realistic PBE emulsification problems (with varying fragmentation intensity and varying number of fragments formed per breakup), while offering a substantial reduction in computational time compared to the traditional approach of solving the discretized equations numerically.

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author
organization
publishing date
type
Contribution to journal
publication status
published
subject
keywords
Break-up, Emulsification, Fragmentation, Population balance equation, Population balance model
in
Chemical Engineering Science
volume
208
article number
115150
publisher
Elsevier
external identifiers
  • scopus:85070272619
ISSN
0009-2509
DOI
10.1016/j.ces.2019.08.008
language
English
LU publication?
yes
id
7ae40225-71c5-4991-8991-a6a6fe2869aa
date added to LUP
2019-08-19 07:08:22
date last changed
2020-01-13 02:17:17
@article{7ae40225-71c5-4991-8991-a6a6fe2869aa,
  abstract     = {<p>Drop breakup in high-energy emulsification is often modelled using a population balance equation (PBE) framework. For cases with high emulsifier to disperse phase concentration, the PBE is dominated by the fragmentation term. Since there are no analytical solutions to the continuous PBE for physically reasonable fragmentation rate expressions, a discretization is often needed to evaluate the PBE, turning it into a set of ordinary differential equations that can be solved numerically. The fixed pivot technique (Kumar and Ramkrishna, 1996) is one of the most often applied class discretization methods. This contribution suggests an analytical solution to the fixed pivot technique fragmentation equation, that can be used instead of the traditional numerical approach provided that the fragmentation rate is constant over time. The proposed solution compares favorably to two special cases where analytical solutions for the continuous PBE are available, and to two more realistic PBE emulsification problems (with varying fragmentation intensity and varying number of fragments formed per breakup), while offering a substantial reduction in computational time compared to the traditional approach of solving the discretized equations numerically.</p>},
  author       = {Håkansson, Andreas},
  issn         = {0009-2509},
  language     = {eng},
  month        = {11},
  publisher    = {Elsevier},
  series       = {Chemical Engineering Science},
  title        = {An analytical solution to the fixed pivot fragmentation population balance equation},
  url          = {http://dx.doi.org/10.1016/j.ces.2019.08.008},
  doi          = {10.1016/j.ces.2019.08.008},
  volume       = {208},
  year         = {2019},
}