Transient and asymptotic Taylor--Aris dispersion of Brownian rods in arbitrary regular-polygonal ducts
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arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866917522601672704 |
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| author | Feng, Jingsen Chu, Xu |
| author_facet | Feng, Jingsen Chu, Xu |
| contents | Taylor--Aris dispersion of Brownian rods in non-circular ducts is governed by a coupling absent from passive-scalar theory. Pressure-driven shear aligns the rods and makes translational diffusion tensorial, while duct geometry determines how this tensor is sampled across the cross-section. We formulate this problem for dilute rods in regular-polygonal ducts of arbitrary side number. At each cross-sectional point, a local shear-aligned Jeffery--Brownian closure gives four transport fields, namely two transverse diffusivities, a direct axial diffusivity and a signed shear--axial cross coefficient. Because the shear frame rotates through a polygon, these fields enter a conservative two-dimensional transverse operator rather than a radial scalar-diffusion problem. Its zero mode is a non-uniform invariant density, which replaces the area measure in the Taylor--Aris reduction and reduces, in the circular-pipe limit, to a weighting proportional to the inverse shear-direction diffusivity.
The resulting cell problem separates the effects of rod alignment on streamline sampling and transverse relaxation. Alignment produces only a small, non-monotone shift in mean speed, but gives a larger enhancement of the Taylor coefficient by reducing transverse mixing. Normalization by the same-geometry spherical coefficient removes most passive shape dependence and exposes the approach to the fully aligned transverse-mixing limit. Finite regular polygons converge smoothly to the circular-pipe branch, whereas low-sided polygons retain distinct shear-sampling signatures. A biorthogonal spectral formulation resolves finite-time releases. Localized, multi-peaked and broad injections excite different non-zero transverse modes and exhibit different pre-asymptotic variance growth, but modal decay selects the common long-time Taylor--Aris coefficient given by the cell problem. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_22982 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Transient and asymptotic Taylor--Aris dispersion of Brownian rods in arbitrary regular-polygonal ducts Feng, Jingsen Chu, Xu Fluid Dynamics Taylor--Aris dispersion of Brownian rods in non-circular ducts is governed by a coupling absent from passive-scalar theory. Pressure-driven shear aligns the rods and makes translational diffusion tensorial, while duct geometry determines how this tensor is sampled across the cross-section. We formulate this problem for dilute rods in regular-polygonal ducts of arbitrary side number. At each cross-sectional point, a local shear-aligned Jeffery--Brownian closure gives four transport fields, namely two transverse diffusivities, a direct axial diffusivity and a signed shear--axial cross coefficient. Because the shear frame rotates through a polygon, these fields enter a conservative two-dimensional transverse operator rather than a radial scalar-diffusion problem. Its zero mode is a non-uniform invariant density, which replaces the area measure in the Taylor--Aris reduction and reduces, in the circular-pipe limit, to a weighting proportional to the inverse shear-direction diffusivity. The resulting cell problem separates the effects of rod alignment on streamline sampling and transverse relaxation. Alignment produces only a small, non-monotone shift in mean speed, but gives a larger enhancement of the Taylor coefficient by reducing transverse mixing. Normalization by the same-geometry spherical coefficient removes most passive shape dependence and exposes the approach to the fully aligned transverse-mixing limit. Finite regular polygons converge smoothly to the circular-pipe branch, whereas low-sided polygons retain distinct shear-sampling signatures. A biorthogonal spectral formulation resolves finite-time releases. Localized, multi-peaked and broad injections excite different non-zero transverse modes and exhibit different pre-asymptotic variance growth, but modal decay selects the common long-time Taylor--Aris coefficient given by the cell problem. |
| title | Transient and asymptotic Taylor--Aris dispersion of Brownian rods in arbitrary regular-polygonal ducts |
| topic | Fluid Dynamics |
| url | https://arxiv.org/abs/2605.22982 |