Capillary flow of a suspension in the presence of discontinuous shear thickening

TL;DR

This study investigates the capillary flow behavior of suspensions exhibiting discontinuous shear thickening, combining experimental measurements with theoretical modeling to better understand flow cessation and the effects of shear stress.

Contribution

It introduces a modified Wyart-Cates theory that accounts for contact relaxation, improving predictions of suspension flow in capillaries during shear thickening.

Findings

Flow rate decreases progressively rather than abruptly at critical stress.

Modified theory accurately predicts flow behavior and high-stress flow persistence.

Propagation of DST transition inside the capillary is supported by experimental data.

Abstract

The rheology of suspensions showing discontinuous shear thickening (DST) is well documented in conventional rheometer with rotating tools, but their study in capillary flow is still lacking. We present results obtained in a homemade capillary rheometer working in an imposed pressure regime. We show that the shape of the experimental curve giving the volume flow rate versus the wall stress in a capillary can be qualitatively reproduced from the curve obtained in rotational geometry at imposed stress but instead of a sharp decrease of the volume flow rate observed at a critical stress, this transposition predicts a progressive decrease in flow rate. The Wyart-Cates theory is used to reproduce the stress-shear rate curve obtained in rotational geometry and then applied to predict the volume flow rate at imposed pressure. The theoretical curve predicts a total stop of the flow at high stress, whereas experimentally it remains constant. We propose a modification of the theory which, by taking into account the relaxation of the frictional contacts in the absence of shear rate, well predicts the high stress behavior. We also hypothesized that the DST transition propagates immediately inside the capillary, once the wall shear stress has reached its critical value: $\tau_R=\tau_c$, even if the internal shear stress $\tau(r<R)$ is below the critical one. In this way the whole experimental curve can be well reproduced by the modified W-C model.