End-pinching and inertial-capillary reopening in viscoplastic ligaments at low Ohnesorge number

TL;DR

This study explores how viscoplastic effects influence liquid ligament retraction and pinch-off mechanisms, revealing new pathways for ligament reopening driven by shear-thinning and inertial-capillary effects.

Contribution

It introduces a detailed analysis of viscoplastic ligament retraction, identifying distinct shear-thickening and shear-thinning regimes affecting pinch-off and reopening pathways.

Findings

Increased viscosity in shear-thickening regime opposes capillary singularity.

Shear-thinning regime's reopening driven by curvature-induced pressure gradients.

Purely inertial-capillary pathway persists as viscosity approaches zero.

Abstract

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.