Discrete population balance models of random agglomeration and cleavage in polymer pyrolysis

John E. J. Staggs; John E. J. Staggs

doi:10.3934/matersci.2017.3.614

AIMS Materials Science

2017, Volume 4, Issue 3: 614-637. doi: 10.3934/matersci.2017.3.614

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Discrete population balance models of random agglomeration and cleavage in polymer pyrolysis

John E. J. Staggs ^,

School of Chemical and Process Engineering, University of Leeds, Leeds LS2 9JT, United Kingdom

Received: 15 March 2017 Accepted: 16 May 2017 Published: 26 May 2017

The processes of random agglomeration and cleavage (both of which are important for the development of new models of polymer combustion, but are also applicable in a wide range of fields including atmospheric physics, radiation modelling and astrophysics) are analysed using population balance methods. The evolution of a discrete distribution of particles is considered within this framework, resulting in a set of ordinary differential equations for the individual particle concentrations. Exact solutions for these equations are derived, together with moment generating functions. Application of the discrete Laplace transform (analogous to the Z-transform) is found to be effective in these problems, providing both exact solutions for particle concentrations and moment generating functions. The combined agglomeration-cleavage problem is also considered. Unfortunately, it has been impossible to find an exact solution for the full problem, but a stable steady state has been identified and computed.
- agglomeration,
- recombination,
- cleavage,
- scission,
- population balance,
- polymer combustion
Citation: John E. J. Staggs. Discrete population balance models of random agglomeration and cleavage in polymer pyrolysis[J]. AIMS Materials Science, 2017, 4(3): 614-637. doi: 10.3934/matersci.2017.3.614

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Abstract

The processes of random agglomeration and cleavage (both of which are important for the development of new models of polymer combustion, but are also applicable in a wide range of fields including atmospheric physics, radiation modelling and astrophysics) are analysed using population balance methods. The evolution of a discrete distribution of particles is considered within this framework, resulting in a set of ordinary differential equations for the individual particle concentrations. Exact solutions for these equations are derived, together with moment generating functions. Application of the discrete Laplace transform (analogous to the Z-transform) is found to be effective in these problems, providing both exact solutions for particle concentrations and moment generating functions. The combined agglomeration-cleavage problem is also considered. Unfortunately, it has been impossible to find an exact solution for the full problem, but a stable steady state has been identified and computed.

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