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| Format: | Preprint |
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2025
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| Online Access: | https://arxiv.org/abs/2511.18388 |
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| _version_ | 1866910129737170944 |
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| author | Yang, Shu Mahmood, Fahim Tanfeez Constante-Amores, C. Ricardo |
| author_facet | Yang, Shu Mahmood, Fahim Tanfeez Constante-Amores, C. Ricardo |
| contents | Capillary retraction of liquid ligaments is well understood for Newtonian fluids, whereas viscoplastic effects remain comparatively unexplored. Here, we consider Herschel-Bulkley fluids, which incorporate both yield stress and shear-rate-dependent viscosity, thereby introducing a spatially varying effective viscosity that is absent in simpler yield-stress models (e.g., Bingham models). We focus on the low-viscosity regime, where droplet detachment in Newtonian fluids is controlled by the end-pinching mechanism. Using fully resolved axisymmetric simulations, we show that viscoplasticity and shear-rate-dependent rheology reorganize the routes by which a retracting ligament may pinch off, escape break-up or stay motionless due to large yield stress. We identify two distinct routes by which a retracting Herschel-Bulkley ligament can escape end-pinching. In the shear-thickening regime, increased local viscosity during neck thinning leads to larger vorticity detachment from the curved neck, which opposes the capillary singularity. In the strongly shear-thinning regime, reopening is governed by curvature-induced pressure gradients. We show that this latter mechanism persists in the Newtonian limit of vanishing viscosity, yielding a purely inertial-capillary pathway for reopening. While previous Newtonian studies report end-pinching down to Ohnesorge number $Oh_K \approx 10^{-4}$, suggesting break-up as the asymptotic low-viscosity outcome (Anthony et al. 2019), our results demonstrate that a purely inertial-capillary reopening mechanism can arise as $Oh_K \to 0$, indicating that end-pinching is not the route in the inviscid limit. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_18388 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | End-pinching and inertial-capillary reopening in viscoplastic ligaments at low Ohnesorge number Yang, Shu Mahmood, Fahim Tanfeez Constante-Amores, C. Ricardo Fluid Dynamics Capillary retraction of liquid ligaments is well understood for Newtonian fluids, whereas viscoplastic effects remain comparatively unexplored. Here, we consider Herschel-Bulkley fluids, which incorporate both yield stress and shear-rate-dependent viscosity, thereby introducing a spatially varying effective viscosity that is absent in simpler yield-stress models (e.g., Bingham models). We focus on the low-viscosity regime, where droplet detachment in Newtonian fluids is controlled by the end-pinching mechanism. Using fully resolved axisymmetric simulations, we show that viscoplasticity and shear-rate-dependent rheology reorganize the routes by which a retracting ligament may pinch off, escape break-up or stay motionless due to large yield stress. We identify two distinct routes by which a retracting Herschel-Bulkley ligament can escape end-pinching. In the shear-thickening regime, increased local viscosity during neck thinning leads to larger vorticity detachment from the curved neck, which opposes the capillary singularity. In the strongly shear-thinning regime, reopening is governed by curvature-induced pressure gradients. We show that this latter mechanism persists in the Newtonian limit of vanishing viscosity, yielding a purely inertial-capillary pathway for reopening. While previous Newtonian studies report end-pinching down to Ohnesorge number $Oh_K \approx 10^{-4}$, suggesting break-up as the asymptotic low-viscosity outcome (Anthony et al. 2019), our results demonstrate that a purely inertial-capillary reopening mechanism can arise as $Oh_K \to 0$, indicating that end-pinching is not the route in the inviscid limit. |
| title | End-pinching and inertial-capillary reopening in viscoplastic ligaments at low Ohnesorge number |
| topic | Fluid Dynamics |
| url | https://arxiv.org/abs/2511.18388 |