Shear-induced force and dispersion due to buoyancy in a horizontal Hele-Shaw cell
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866915316340097024 |
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| author | Rajamanickam, Prabakaran |
| author_facet | Rajamanickam, Prabakaran |
| contents | This paper investigates shear flow in a Hele-Shaw cell, driven by varying horizontal buoyancy forces resulting from a horizontal density gradient induced by a scalar field. By employing asymptotic methods and taking the dependence of density and transport coefficients on the scalar field into account, effective two-dimensional hydrodynamic equations coupled with the scalar conservation equation are derived. These equations determine an effective diffusion coefficient for the scalar field accounting for shear-induced diffusion, and an effective shear-induced buoyancy force that modifies the classical Darcy's law. The derived equations provide a foundation for future research into various problems involving scalar transport in horizontal Hele-Shaw cells. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_04619 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Shear-induced force and dispersion due to buoyancy in a horizontal Hele-Shaw cell Rajamanickam, Prabakaran Fluid Dynamics This paper investigates shear flow in a Hele-Shaw cell, driven by varying horizontal buoyancy forces resulting from a horizontal density gradient induced by a scalar field. By employing asymptotic methods and taking the dependence of density and transport coefficients on the scalar field into account, effective two-dimensional hydrodynamic equations coupled with the scalar conservation equation are derived. These equations determine an effective diffusion coefficient for the scalar field accounting for shear-induced diffusion, and an effective shear-induced buoyancy force that modifies the classical Darcy's law. The derived equations provide a foundation for future research into various problems involving scalar transport in horizontal Hele-Shaw cells. |
| title | Shear-induced force and dispersion due to buoyancy in a horizontal Hele-Shaw cell |
| topic | Fluid Dynamics |
| url | https://arxiv.org/abs/2411.04619 |