Pinch-off of non-Brownian rod suspensions: onset of heterogeneity and effective extensional viscosity

TL;DR

This study investigates how suspensions of rigid rods behave during liquid bridge pinch-off, revealing regimes, effective viscosity changes, and the influence of rod length and volume fraction on heterogeneity onset.

Contribution

It introduces a detailed analysis of pinch-off regimes in rod suspensions, highlighting the role of rod length and volume fraction in continuum breakdown and heterogeneity formation.

Findings

Three regimes observed during pinch-off: equivalent-fluid, dislocation, and liquid-controlled.

Effective extensional viscosity increases with volume fraction and aspect ratio.

Critical volume fraction decreases with aspect ratio, following an empirical law.

Abstract

The stretching and pinch-off of a liquid bridge is a simple way to probe when a suspension of particles stops behaving as a continuum. In this study, we consider density-matched suspensions of rigid nylon fibers with aspect ratios (length over diameter) ranging from 2 to 84, and volume fractions $\phi$ spanning the dilute to dense regimes. High-speed imaging of pendant-drop breakup reveals three successive regimes, as previously observed for spherical particles: an equivalent-fluid regime at early times, a dislocation regime corresponding to the separation of the rods, and a final regime controlled by the interstitial liquid once the neck is devoid of rods. The thresholds between these regimes follow the previously proposed scaling for spherical particles, in which the rod length, rather than the rod diameter, is used as the relevant discrete scale. In the equivalent-fluid regime, pinch-off also leads to an effective extensional viscosity that increases with both volume fraction and aspect ratio. This viscosity is not equal to the shear viscosity measured in a parallel-plate rheometer, but both sets of data are well described by Mills' law using a critical volume fraction $\phi_c$. Finally, the critical volume fraction $\phi_c$ decreases monotonically with the aspect ratio and is well captured by an empirical law. These results show that pinch-off is a sensitive probe of continuum breakdown in anisotropic suspensions and that, for rigid rods, the rod length controls the onset of heterogeneous thinning.