Refinement of a Poroelastic Model for Zero Porosity: Finite Element Implementation and Investigation of Fluid Mechanics in the Perivascular Space
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
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2025
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| _version_ | 1866918174682775552 |
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| author | Jannesari, Mohammad Ghitti, Beatrice Gluckman, Bruce J. Costanzo, Francesco |
| author_facet | Jannesari, Mohammad Ghitti, Beatrice Gluckman, Bruce J. Costanzo, Francesco |
| contents | In conventional formulations of poroelasticity, when the porosity approaches zero or vanishes in some parts of the poroelastic domain, if only temporarily, the governing equations degenerate to those for the solid phase thereby inhibiting a suitable determination of the fluid velocity field. To address this challenge, we reformulated a poroelastic model based on mixture theory to accommodate scenarios with zero porosity. We verified our model using the method of manufactured solutions and demonstrated its ability to handle extreme conditions in a sample test problem. As an application of our framework, we investigated peristaltic flow in the perivascular space of a penetrating arteriole in brain. Our analysis revealed that some literature-suggested parameters can drive the model to predict extreme non-physiological conditions. We further demonstrated that these extreme conditions can be somewhat mitigated by accounting for the deformation of the surrounding brain tissue. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2510_23683 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Refinement of a Poroelastic Model for Zero Porosity: Finite Element Implementation and Investigation of Fluid Mechanics in the Perivascular Space Jannesari, Mohammad Ghitti, Beatrice Gluckman, Bruce J. Costanzo, Francesco Fluid Dynamics 74A99, 76S05, 74S05, 76-10 In conventional formulations of poroelasticity, when the porosity approaches zero or vanishes in some parts of the poroelastic domain, if only temporarily, the governing equations degenerate to those for the solid phase thereby inhibiting a suitable determination of the fluid velocity field. To address this challenge, we reformulated a poroelastic model based on mixture theory to accommodate scenarios with zero porosity. We verified our model using the method of manufactured solutions and demonstrated its ability to handle extreme conditions in a sample test problem. As an application of our framework, we investigated peristaltic flow in the perivascular space of a penetrating arteriole in brain. Our analysis revealed that some literature-suggested parameters can drive the model to predict extreme non-physiological conditions. We further demonstrated that these extreme conditions can be somewhat mitigated by accounting for the deformation of the surrounding brain tissue. |
| title | Refinement of a Poroelastic Model for Zero Porosity: Finite Element Implementation and Investigation of Fluid Mechanics in the Perivascular Space |
| topic | Fluid Dynamics 74A99, 76S05, 74S05, 76-10 |
| url | https://arxiv.org/abs/2510.23683 |