Dissolution-driven transport in a rotating horizontal cylinder
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arXiv
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| Auteurs principaux: | , , , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866908955656060928 |
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| author | Nandi, Subhankar Kalita, Jiten C. Yedida, Sanyasiraju VSS Pramanik, Satyajit |
| author_facet | Nandi, Subhankar Kalita, Jiten C. Yedida, Sanyasiraju VSS Pramanik, Satyajit |
| contents | We study the combined effects of natural convection and rotation on the dissolution of a solute in a solvent-filled circular cylinder. The density of the fluid increases with the increasing concentration of the dissolved solute, and we model this using the Oberbeck-Boussinesq approximation. The underlying moving-boundary problem has been modelled by combining the Navier-Stokes equations with the advection-diffusion equation and a Stefan condition for the evolving solute-fluid interface. We use highly resolved numerical simulations to investigate the flow regimes, dissolution rates, and mixing of the dissolved solute for $Sc = 1$, $Ra \in [10^5, 10^8]$ and $Ω\in [0, 2.5]$. In the absence of rotation and buoyancy, the distance of the interface from its initial position follows a square root relationship with time ($r_d \propto \sqrt{t}$), which ceases to exist at a later time due to the finite-size effect of the liquid domain. We then explore the rotation parameter, considering a range of rotation frequency -- from smaller to larger, relative to the inverse of the buoyancy-induced timescale -- and Rayleigh number. We show that the area of the dissolved solute varies nonlinearly with time depending on $Ra$ and $Ω$. The symmetry breaking of the interface is best described in terms of $Ra/Ω^2$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_05771 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Dissolution-driven transport in a rotating horizontal cylinder Nandi, Subhankar Kalita, Jiten C. Yedida, Sanyasiraju VSS Pramanik, Satyajit Fluid Dynamics 76M20, 76U99, 76D05, 76R05, 76R50 We study the combined effects of natural convection and rotation on the dissolution of a solute in a solvent-filled circular cylinder. The density of the fluid increases with the increasing concentration of the dissolved solute, and we model this using the Oberbeck-Boussinesq approximation. The underlying moving-boundary problem has been modelled by combining the Navier-Stokes equations with the advection-diffusion equation and a Stefan condition for the evolving solute-fluid interface. We use highly resolved numerical simulations to investigate the flow regimes, dissolution rates, and mixing of the dissolved solute for $Sc = 1$, $Ra \in [10^5, 10^8]$ and $Ω\in [0, 2.5]$. In the absence of rotation and buoyancy, the distance of the interface from its initial position follows a square root relationship with time ($r_d \propto \sqrt{t}$), which ceases to exist at a later time due to the finite-size effect of the liquid domain. We then explore the rotation parameter, considering a range of rotation frequency -- from smaller to larger, relative to the inverse of the buoyancy-induced timescale -- and Rayleigh number. We show that the area of the dissolved solute varies nonlinearly with time depending on $Ra$ and $Ω$. The symmetry breaking of the interface is best described in terms of $Ra/Ω^2$. |
| title | Dissolution-driven transport in a rotating horizontal cylinder |
| topic | Fluid Dynamics 76M20, 76U99, 76D05, 76R05, 76R50 |
| url | https://arxiv.org/abs/2504.05771 |