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| Main Authors: | , , , , , , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2408.13824 |
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| _version_ | 1866914923538284544 |
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| author | Farutin, Alexander Nait-Ouhra, Abdessamad Dixit, Gopal Abbasi, Mehdi Aouane, Othmane Harting, Jens Misbah, Chaouqi |
| author_facet | Farutin, Alexander Nait-Ouhra, Abdessamad Dixit, Gopal Abbasi, Mehdi Aouane, Othmane Harting, Jens Misbah, Chaouqi |
| contents | Despite decades of research on blood flow, an analogue of Navier-Stokes equations that accurately describe blood flow properties has not been established yet. The reason behind this is that the properties of blood flow seem à priori non universal as they depend on various factors such as global concentration of red blood cells (RBCs) and channel width. Here, we have discovered a universal law when the stress and strain rate are measured at a given local RBCs concentration. However, the local concentration must be determined in order to close the problem. We propose a non-local diffusion equation of RBCs concentration that agrees with the full simulation. The universal law is exemplified for both shear and pressure driven flows. While the theory is restricted to a simplistic geometry (straight channel) it provides a fundamental basis for future research on blood flow dynamics and could lead to the development of a new theory that accurately describes blood flow properties under various conditions, such as in complex vascular networks. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_13824 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Towards a universal law for blood flow Farutin, Alexander Nait-Ouhra, Abdessamad Dixit, Gopal Abbasi, Mehdi Aouane, Othmane Harting, Jens Misbah, Chaouqi Fluid Dynamics Despite decades of research on blood flow, an analogue of Navier-Stokes equations that accurately describe blood flow properties has not been established yet. The reason behind this is that the properties of blood flow seem à priori non universal as they depend on various factors such as global concentration of red blood cells (RBCs) and channel width. Here, we have discovered a universal law when the stress and strain rate are measured at a given local RBCs concentration. However, the local concentration must be determined in order to close the problem. We propose a non-local diffusion equation of RBCs concentration that agrees with the full simulation. The universal law is exemplified for both shear and pressure driven flows. While the theory is restricted to a simplistic geometry (straight channel) it provides a fundamental basis for future research on blood flow dynamics and could lead to the development of a new theory that accurately describes blood flow properties under various conditions, such as in complex vascular networks. |
| title | Towards a universal law for blood flow |
| topic | Fluid Dynamics |
| url | https://arxiv.org/abs/2408.13824 |