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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2507.11318 |
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| _version_ | 1866916844688900096 |
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| author | Bonnivard, Matthieu Pazanin, Igor Suarez-Grau, Francisco |
| author_facet | Bonnivard, Matthieu Pazanin, Igor Suarez-Grau, Francisco |
| contents | The lubrication theory is mostly concerned with the behavior of a lubricant flowing through a narrow gap. Motivated by the experimental findings from the tribology literature, we take the lubricant to be micropolar fluid and study its behavior in a thin domain with rough boundary. Instead of considering (commonly used) simple zero boundary condition, we impose physically relevant (nonzero) boundary condition for microrotation and perform asymptotic analysis of the corresponding 3D boundary value problem. We formally derive a simplified mathematical model acknowledging the roughness-induced effects and the effects of the nonzero boundary conditions on the macroscopic flow. Using the obtained asymptotic model, we study numerically the influence of the specific rugosity profile on the performance of a linear slider bearing. The numerical results clearly indicate that the use of the rough surfaces may contribute to enhance the mechanical performance of such device. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_11318 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Effects of rough boundary and nonzero boundary conditions on the lubrication process with micropolar fluid Bonnivard, Matthieu Pazanin, Igor Suarez-Grau, Francisco Analysis of PDEs Numerical Analysis 35B27 The lubrication theory is mostly concerned with the behavior of a lubricant flowing through a narrow gap. Motivated by the experimental findings from the tribology literature, we take the lubricant to be micropolar fluid and study its behavior in a thin domain with rough boundary. Instead of considering (commonly used) simple zero boundary condition, we impose physically relevant (nonzero) boundary condition for microrotation and perform asymptotic analysis of the corresponding 3D boundary value problem. We formally derive a simplified mathematical model acknowledging the roughness-induced effects and the effects of the nonzero boundary conditions on the macroscopic flow. Using the obtained asymptotic model, we study numerically the influence of the specific rugosity profile on the performance of a linear slider bearing. The numerical results clearly indicate that the use of the rough surfaces may contribute to enhance the mechanical performance of such device. |
| title | Effects of rough boundary and nonzero boundary conditions on the lubrication process with micropolar fluid |
| topic | Analysis of PDEs Numerical Analysis 35B27 |
| url | https://arxiv.org/abs/2507.11318 |