Mathematical Modelling of Mechanical Alloying

This thesis applies Smoluchowski's coagulation-fragmentation equations to model the mechanical alloying process. Mechanisms operating during the milling process are reviewed. In the first instance, models are developed that predict the size distribution of a single milled powder while ignorin...

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Main Author: Harris, John Richard
Format: Thesis (University of Nottingham only)
Language:English
Published: 2002
Subjects:
Online Access:https://eprints.nottingham.ac.uk/10018/
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author Harris, John Richard
author_facet Harris, John Richard
author_sort Harris, John Richard
building Nottingham Research Data Repository
collection Online Access
description This thesis applies Smoluchowski's coagulation-fragmentation equations to model the mechanical alloying process. Mechanisms operating during the milling process are reviewed. In the first instance, models are developed that predict the size distribution of a single milled powder while ignoring mixing phenomena. A methodology is developed that allows experimentally measured sieve-fractions to be converted into volumetric cluster size distributions. Model parameters describing the rate of aggregation and fragmentation are obtained by fitting the model's predicted average particle size data over time to that measured in experiments. Different size-dependent aggregation and fragmentation rates are tested in many milling scenarios and the most realistic size-dependence of rates is found. In the second part of the thesis, the best size-dependent rates are generalised and used with a two-component version of \Smol's system of equations. This model also includes binary mixing phenomena by considering clusters that have two types of component. The two-component models are applied to experimental situations using the methods developed for one-component models. Comparing these multi-component models to experimental measurements verifies the modelling method and gives reasonable agreement. An improved fragmentation rate is suggested to enhance the model's accuracy in the prediction of mixing rates.
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format Thesis (University of Nottingham only)
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institution University of Nottingham Malaysia Campus
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language English
last_indexed 2025-11-14T18:21:42Z
publishDate 2002
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spelling nottingham-100182025-02-28T11:06:53Z https://eprints.nottingham.ac.uk/10018/ Mathematical Modelling of Mechanical Alloying Harris, John Richard This thesis applies Smoluchowski's coagulation-fragmentation equations to model the mechanical alloying process. Mechanisms operating during the milling process are reviewed. In the first instance, models are developed that predict the size distribution of a single milled powder while ignoring mixing phenomena. A methodology is developed that allows experimentally measured sieve-fractions to be converted into volumetric cluster size distributions. Model parameters describing the rate of aggregation and fragmentation are obtained by fitting the model's predicted average particle size data over time to that measured in experiments. Different size-dependent aggregation and fragmentation rates are tested in many milling scenarios and the most realistic size-dependence of rates is found. In the second part of the thesis, the best size-dependent rates are generalised and used with a two-component version of \Smol's system of equations. This model also includes binary mixing phenomena by considering clusters that have two types of component. The two-component models are applied to experimental situations using the methods developed for one-component models. Comparing these multi-component models to experimental measurements verifies the modelling method and gives reasonable agreement. An improved fragmentation rate is suggested to enhance the model's accuracy in the prediction of mixing rates. 2002 Thesis (University of Nottingham only) NonPeerReviewed application/pdf en arr https://eprints.nottingham.ac.uk/10018/1/thesis.pdf Harris, John Richard (2002) Mathematical Modelling of Mechanical Alloying. PhD thesis, University of Nottingham. Smoluchowski coagulation fragmentation coagulation-fragmentation
spellingShingle Smoluchowski
coagulation
fragmentation
coagulation-fragmentation
Harris, John Richard
Mathematical Modelling of Mechanical Alloying
title Mathematical Modelling of Mechanical Alloying
title_full Mathematical Modelling of Mechanical Alloying
title_fullStr Mathematical Modelling of Mechanical Alloying
title_full_unstemmed Mathematical Modelling of Mechanical Alloying
title_short Mathematical Modelling of Mechanical Alloying
title_sort mathematical modelling of mechanical alloying
topic Smoluchowski
coagulation
fragmentation
coagulation-fragmentation
url https://eprints.nottingham.ac.uk/10018/