Transition in elastic Dean flow: the centre-mode versus hoop-stress pathways
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| Format: | Preprint |
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2025
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| _version_ | 1866911310165311488 |
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| author | Tej, P. S. D. Surya Phani Subramanian, Ganesh Shankar, V. |
| author_facet | Tej, P. S. D. Surya Phani Subramanian, Ganesh Shankar, V. |
| contents | We analyse the stability of viscoelastic Dean flow (flow of an elastic fluid through a curved two-dimensional channel, driven by an azimuthal pressure gradient) in the absence of fluid inertia. This configuration is well known to exhibit a hoop-stress-driven `purely elastic' instability (referred to henceforth as the hoop-stress mode -- `HSM') on account of the base-flow streamline curvature. The objective of this study is to demonstrate the existence and importance of a distinct elastic instability in this flow configuration, which is not driven by hoop-stresses, but instead is a continuation of a novel `centre-mode' (CM) instability recently identified in rectilinear shear flows. We use both the Oldroyd-B and FENE-P models to map out parameter regimes in the $W\!i$--$ε$--$β$ space where the aforementioned instabilities are present. Here, $W\!i$ is a suitably defined Weissenberg number that characterizes fluid elasticity, $β$ is the ratio of solvent to total solution viscosity, and $ε$ is the ratio of the gap (channel) width to the radius of curvature. For FENE-P model, decreasing the finite extensibility parameter $L$ has opposing effects on the HSM and CM instabilities -- stabilising the former, but destabilising the latter. In the dilute solution regime ($β> 0.95$), and for realistic values of $L \sim O(100)$, corresponding to polymer molecular weights of $O(10^{5-6})$g/mol, the CM remains the most unstable mode for $ε\leq 0.25$, rendering it potentially relevant to the onset of elastic turbulence in the flow of such polymer solutions through curved channels. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2512_08456 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Transition in elastic Dean flow: the centre-mode versus hoop-stress pathways Tej, P. S. D. Surya Phani Subramanian, Ganesh Shankar, V. Fluid Dynamics Soft Condensed Matter We analyse the stability of viscoelastic Dean flow (flow of an elastic fluid through a curved two-dimensional channel, driven by an azimuthal pressure gradient) in the absence of fluid inertia. This configuration is well known to exhibit a hoop-stress-driven `purely elastic' instability (referred to henceforth as the hoop-stress mode -- `HSM') on account of the base-flow streamline curvature. The objective of this study is to demonstrate the existence and importance of a distinct elastic instability in this flow configuration, which is not driven by hoop-stresses, but instead is a continuation of a novel `centre-mode' (CM) instability recently identified in rectilinear shear flows. We use both the Oldroyd-B and FENE-P models to map out parameter regimes in the $W\!i$--$ε$--$β$ space where the aforementioned instabilities are present. Here, $W\!i$ is a suitably defined Weissenberg number that characterizes fluid elasticity, $β$ is the ratio of solvent to total solution viscosity, and $ε$ is the ratio of the gap (channel) width to the radius of curvature. For FENE-P model, decreasing the finite extensibility parameter $L$ has opposing effects on the HSM and CM instabilities -- stabilising the former, but destabilising the latter. In the dilute solution regime ($β> 0.95$), and for realistic values of $L \sim O(100)$, corresponding to polymer molecular weights of $O(10^{5-6})$g/mol, the CM remains the most unstable mode for $ε\leq 0.25$, rendering it potentially relevant to the onset of elastic turbulence in the flow of such polymer solutions through curved channels. |
| title | Transition in elastic Dean flow: the centre-mode versus hoop-stress pathways |
| topic | Fluid Dynamics Soft Condensed Matter |
| url | https://arxiv.org/abs/2512.08456 |