Inertial migration of slender prolate and thin oblate spheroids in plane Poiseuille flow
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| Format: | Preprint |
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2025
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| _version_ | 1866911131784708096 |
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| author | Anand, Prateek Subramanian, Ganesh |
| author_facet | Anand, Prateek Subramanian, Ganesh |
| contents | We theoretically examine the inertial migration of a neutrally buoyant spheroid of aspect ratio $κ$ in wall-bounded plane Poiseuille flow at small particle Reynolds number ($Re_p$) and small confinement ratio ($λ$), with channel Reynolds number $Re_c = Re_p/λ^2$ arbitrary. For $λ\ll 1$, inertia rapidly drives the spheroid to the tumbling orbit ($C = \infty$), with migration governed by the time-averaged lift over orientations sampled in this orbit. Spheroids with $κ= O(1)$ follow Jeffery rotation closely, while deviations for slender rods and thin disks yield equilibrium positions distinct from the classical Segre-Silberberg result. Above a threshold $Re_c$, both rods and disks can undergo rotation arrest near walls, with these arrested regions expanding toward the centerline as $Re_c$ increases. Unlike spheres, the resulting equilibrium positions shift inward with increasing $Re_c$; for disks, these positions themselves become arrested beyond a threshold $Re_c$. The $κ$-dependence of equilibrium locations suggests passive shape-sorting strategies in microfluidic devices. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2509_00594 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Inertial migration of slender prolate and thin oblate spheroids in plane Poiseuille flow Anand, Prateek Subramanian, Ganesh Fluid Dynamics We theoretically examine the inertial migration of a neutrally buoyant spheroid of aspect ratio $κ$ in wall-bounded plane Poiseuille flow at small particle Reynolds number ($Re_p$) and small confinement ratio ($λ$), with channel Reynolds number $Re_c = Re_p/λ^2$ arbitrary. For $λ\ll 1$, inertia rapidly drives the spheroid to the tumbling orbit ($C = \infty$), with migration governed by the time-averaged lift over orientations sampled in this orbit. Spheroids with $κ= O(1)$ follow Jeffery rotation closely, while deviations for slender rods and thin disks yield equilibrium positions distinct from the classical Segre-Silberberg result. Above a threshold $Re_c$, both rods and disks can undergo rotation arrest near walls, with these arrested regions expanding toward the centerline as $Re_c$ increases. Unlike spheres, the resulting equilibrium positions shift inward with increasing $Re_c$; for disks, these positions themselves become arrested beyond a threshold $Re_c$. The $κ$-dependence of equilibrium locations suggests passive shape-sorting strategies in microfluidic devices. |
| title | Inertial migration of slender prolate and thin oblate spheroids in plane Poiseuille flow |
| topic | Fluid Dynamics |
| url | https://arxiv.org/abs/2509.00594 |