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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| Format: | Thesis (University of Nottingham only) |
| Language: | English |
| Published: |
2002
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| Online Access: | https://eprints.nottingham.ac.uk/10018/ |
| _version_ | 1848791009878605824 |
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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. |
| first_indexed | 2025-11-14T18:21:42Z |
| format | Thesis (University of Nottingham only) |
| id | nottingham-10018 |
| institution | University of Nottingham Malaysia Campus |
| institution_category | Local University |
| language | English |
| last_indexed | 2025-11-14T18:21:42Z |
| publishDate | 2002 |
| recordtype | eprints |
| repository_type | Digital Repository |
| 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/ |