### Abstract

A model for the growth of lead sulphate particles in a gravity separation system from the crystal glassware industry is presented. The lead sulphate particles are an undesirable byproduct, and thus the model is used to ascertain the optimal system temperature configuration such that particle extraction is maximised. The model describes the evolution of a single, spherical particle due to the mass flux of lead particles from a surrounding acid solution. We divide the concentration field into two separate regions. Specifically, a relatively small boundary layer region around the particle is characterised by fast diffusion, and is thus considered quasi-static. In contrast, diffusion in the far-field is slower, and hence assumed to be time-dependent. The final system consisting of two nonlinear, coupled ordinary differential equations for the particle radius and lead concentration, is integrated numerically.

Language | English |
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Article number | 012001 |

Journal | Journal of Physics: Conference Series |

Volume | 811 |

Issue number | 1 |

DOIs | |

Publication status | Published - 3 Mar 2017 |

Externally published | Yes |

Event | MURPHYS-HSFS-2016: Workshop on Slow-Fast Systems with Hysteresis - Centre de Recerca Matemàtica, Barcelona, Spain Duration: 13 Jun 2016 → 17 Jun 2016 http://www.crm.cat/en/Activities/Curs_2015-2016/Documents/P%C3%B2ster%204.pdf (Link to Conference Poster) |

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*Journal of Physics: Conference Series*, vol. 811, no. 1, 012001. https://doi.org/10.1088/1742-6596/811/1/012001

**Slow and fast diffusion in a lead sulphate gravity separation process.** / Cregan, Vincent; Lee, William T.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Slow and fast diffusion in a lead sulphate gravity separation process

AU - Cregan, Vincent

AU - Lee, William T.

PY - 2017/3/3

Y1 - 2017/3/3

N2 - A model for the growth of lead sulphate particles in a gravity separation system from the crystal glassware industry is presented. The lead sulphate particles are an undesirable byproduct, and thus the model is used to ascertain the optimal system temperature configuration such that particle extraction is maximised. The model describes the evolution of a single, spherical particle due to the mass flux of lead particles from a surrounding acid solution. We divide the concentration field into two separate regions. Specifically, a relatively small boundary layer region around the particle is characterised by fast diffusion, and is thus considered quasi-static. In contrast, diffusion in the far-field is slower, and hence assumed to be time-dependent. The final system consisting of two nonlinear, coupled ordinary differential equations for the particle radius and lead concentration, is integrated numerically.

AB - A model for the growth of lead sulphate particles in a gravity separation system from the crystal glassware industry is presented. The lead sulphate particles are an undesirable byproduct, and thus the model is used to ascertain the optimal system temperature configuration such that particle extraction is maximised. The model describes the evolution of a single, spherical particle due to the mass flux of lead particles from a surrounding acid solution. We divide the concentration field into two separate regions. Specifically, a relatively small boundary layer region around the particle is characterised by fast diffusion, and is thus considered quasi-static. In contrast, diffusion in the far-field is slower, and hence assumed to be time-dependent. The final system consisting of two nonlinear, coupled ordinary differential equations for the particle radius and lead concentration, is integrated numerically.

UR - http://www.scopus.com/inward/record.url?scp=85016267296&partnerID=8YFLogxK

U2 - 10.1088/1742-6596/811/1/012001

DO - 10.1088/1742-6596/811/1/012001

M3 - Article

VL - 811

JO - Journal of Physics: Conference Series

T2 - Journal of Physics: Conference Series

JF - Journal of Physics: Conference Series

SN - 1742-6588

IS - 1

M1 - 012001

ER -