Continuum Scale Non Newtonian Particle Transport Model for Hæmorheology
We present a continuum scale particle transport model for red blood cells following collision arguments, in a diffusive flux formulation. The model is implemented in FOAM, in a framework suitable for haemodynamics simulations and adapted to multi-scaling. Specifically, the framework we present is ab...
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| Format: | Article |
| Language: | English |
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MDPI AG
2021-08-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/9/17/2100 |
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| author | Torsten Schenkel Ian Halliday |
| author_facet | Torsten Schenkel Ian Halliday |
| author_sort | Torsten Schenkel |
| collection | DOAJ |
| description | We present a continuum scale particle transport model for red blood cells following collision arguments, in a diffusive flux formulation. The model is implemented in FOAM, in a framework suitable for haemodynamics simulations and adapted to multi-scaling. Specifically, the framework we present is able to ingest transport coefficient models to be derived, prospectively, from complimentary but independent meso-scale simulations. For present purposes, we consider modern semi-mechanistic rheology models, which we implement and test as proxies for such data. The model is verified against a known analytical solution and shows excellent agreement for high quality meshes and good agreement for typical meshes as used in vascular flow simulations. Simulation results for different size and time scales show that migration of red blood cells does occur on physiologically relevany timescales on small vessels below 1 mm and that the haematocrit concentration modulates the non-Newtonian viscosity. This model forms part of a multi-scale approach to haemorheology and model parameters will be derived from meso-scale simulations using multi-component Lattice Boltzmann methods. The code, haemoFoam, is made available for interested researchers. |
| first_indexed | 2024-03-10T08:06:33Z |
| format | Article |
| id | doaj.art-16ea64cbdff642c69aa789c2bc45f04c |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-10T08:06:33Z |
| publishDate | 2021-08-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-16ea64cbdff642c69aa789c2bc45f04c2023-11-22T10:57:54ZengMDPI AGMathematics2227-73902021-08-01917210010.3390/math9172100Continuum Scale Non Newtonian Particle Transport Model for HæmorheologyTorsten Schenkel0Ian Halliday1Department of Engineering and Mathematics, Sheffield Hallam University, Sheffield S1 1WB, UKDepartment of Infection, Immunity and Cardiovascular Disease, University of Sheffield, Sheffield S10 2RX, UKWe present a continuum scale particle transport model for red blood cells following collision arguments, in a diffusive flux formulation. The model is implemented in FOAM, in a framework suitable for haemodynamics simulations and adapted to multi-scaling. Specifically, the framework we present is able to ingest transport coefficient models to be derived, prospectively, from complimentary but independent meso-scale simulations. For present purposes, we consider modern semi-mechanistic rheology models, which we implement and test as proxies for such data. The model is verified against a known analytical solution and shows excellent agreement for high quality meshes and good agreement for typical meshes as used in vascular flow simulations. Simulation results for different size and time scales show that migration of red blood cells does occur on physiologically relevany timescales on small vessels below 1 mm and that the haematocrit concentration modulates the non-Newtonian viscosity. This model forms part of a multi-scale approach to haemorheology and model parameters will be derived from meso-scale simulations using multi-component Lattice Boltzmann methods. The code, haemoFoam, is made available for interested researchers.https://www.mdpi.com/2227-7390/9/17/2100haemorheologyblood flow modellingparticle transportnumerical fluid mechanics |
| spellingShingle | Torsten Schenkel Ian Halliday Continuum Scale Non Newtonian Particle Transport Model for Hæmorheology Mathematics haemorheology blood flow modelling particle transport numerical fluid mechanics |
| title | Continuum Scale Non Newtonian Particle Transport Model for Hæmorheology |
| title_full | Continuum Scale Non Newtonian Particle Transport Model for Hæmorheology |
| title_fullStr | Continuum Scale Non Newtonian Particle Transport Model for Hæmorheology |
| title_full_unstemmed | Continuum Scale Non Newtonian Particle Transport Model for Hæmorheology |
| title_short | Continuum Scale Non Newtonian Particle Transport Model for Hæmorheology |
| title_sort | continuum scale non newtonian particle transport model for haemorheology |
| topic | haemorheology blood flow modelling particle transport numerical fluid mechanics |
| url | https://www.mdpi.com/2227-7390/9/17/2100 |
| work_keys_str_mv | AT torstenschenkel continuumscalenonnewtonianparticletransportmodelforhæmorheology AT ianhalliday continuumscalenonnewtonianparticletransportmodelforhæmorheology |