A hybrid discrete–continuum framework for modelling filtration
Typical mathematical frameworks for modelling the blocking behaviour of a filter due to particle deposition fall into one of two categories: a continuum approximation, whereby particle deposition is assumed to occur in such a way that all pores in the material are in the same state of blocking at an...
| Main Authors: | , |
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| Format: | Journal article |
| Language: | English |
| Published: |
Elsevier
2022
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| _version_ | 1797108687118008320 |
|---|---|
| author | Griffiths, IM Stewart, PS |
| author_facet | Griffiths, IM Stewart, PS |
| author_sort | Griffiths, IM |
| collection | OXFORD |
| description | Typical mathematical frameworks for modelling the blocking behaviour of a filter due to particle deposition fall into
one of two categories: a continuum approximation, whereby particle deposition is assumed to occur in such a way
that all pores in the material are in the same state of blocking at any given time; or a discrete model, where blocking is
treated as individual events in both space and time. While the former is computationally inexpensive, the latter allows
for variation from pore to pore. This pore-to-pore variation has been shown to provide a qualitative change in the
observed filtration behaviour that is essential to reproduce experimental observations. We present a hybrid model that
describes the location of particle depositions in a continuum manner while retaining a discrete, stochastic component
to capture the time at which a blocking event occurs. The model is able to grade between the aforementioned extreme
continuum and discrete cases through a parameter that controls the spatial extent of a blocking event. This enables us
to uncover the way in which the nature of the blocking process changes between these two pre-existing models. The
model also captures the key ingredients of a fully discrete stochastic model at a fraction of the computational cost,
making it ready to use to describe other complex filtration scenarios. |
| first_indexed | 2024-03-07T07:32:09Z |
| format | Journal article |
| id | oxford-uuid:92d206da-9e1c-4cfa-8c08-9aef10ff6dfd |
| institution | University of Oxford |
| language | English |
| last_indexed | 2024-03-07T07:32:09Z |
| publishDate | 2022 |
| publisher | Elsevier |
| record_format | dspace |
| spelling | oxford-uuid:92d206da-9e1c-4cfa-8c08-9aef10ff6dfd2023-01-23T09:31:38ZA hybrid discrete–continuum framework for modelling filtrationJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:92d206da-9e1c-4cfa-8c08-9aef10ff6dfdEnglishSymplectic ElementsElsevier2022Griffiths, IMStewart, PSTypical mathematical frameworks for modelling the blocking behaviour of a filter due to particle deposition fall into one of two categories: a continuum approximation, whereby particle deposition is assumed to occur in such a way that all pores in the material are in the same state of blocking at any given time; or a discrete model, where blocking is treated as individual events in both space and time. While the former is computationally inexpensive, the latter allows for variation from pore to pore. This pore-to-pore variation has been shown to provide a qualitative change in the observed filtration behaviour that is essential to reproduce experimental observations. We present a hybrid model that describes the location of particle depositions in a continuum manner while retaining a discrete, stochastic component to capture the time at which a blocking event occurs. The model is able to grade between the aforementioned extreme continuum and discrete cases through a parameter that controls the spatial extent of a blocking event. This enables us to uncover the way in which the nature of the blocking process changes between these two pre-existing models. The model also captures the key ingredients of a fully discrete stochastic model at a fraction of the computational cost, making it ready to use to describe other complex filtration scenarios. |
| spellingShingle | Griffiths, IM Stewart, PS A hybrid discrete–continuum framework for modelling filtration |
| title | A hybrid discrete–continuum framework for modelling filtration |
| title_full | A hybrid discrete–continuum framework for modelling filtration |
| title_fullStr | A hybrid discrete–continuum framework for modelling filtration |
| title_full_unstemmed | A hybrid discrete–continuum framework for modelling filtration |
| title_short | A hybrid discrete–continuum framework for modelling filtration |
| title_sort | hybrid discrete continuum framework for modelling filtration |
| work_keys_str_mv | AT griffithsim ahybriddiscretecontinuumframeworkformodellingfiltration AT stewartps ahybriddiscretecontinuumframeworkformodellingfiltration AT griffithsim hybriddiscretecontinuumframeworkformodellingfiltration AT stewartps hybriddiscretecontinuumframeworkformodellingfiltration |