Yielding dynamics of a Herschel-Bulkley fluid: a critical-like fluidization behaviour

TL;DR

This study investigates the shear-induced fluidization of a Herschel-Bulkley fluid, revealing a critical-like power-law behavior in the transient shear-banding process influenced by geometry and boundary conditions.

Contribution

It provides an exhaustive analysis of how shear rate, gap width, and boundary conditions affect fluidization dynamics, highlighting the robustness of power-law behavior and proposing a critical phenomena analogy.

Findings

Fluidization time decreases as a power law of shear rate.

Different shear band behaviors depend on shear rate and gap width.

Power-law behavior suggests critical-like dynamics in fluidization.

Abstract

The shear-induced fluidization of a carbopol microgel is investigated during long start-up experiments using combined rheology and velocimetry in Couette cells of varying gap widths and boundary conditions. As already described in [Divoux et al., {\it Phys. Rev. Lett.}, 2010, {\bf 104}, 208301], we show that the fluidization process of this simple yield stress fluid involves a transient shear-banding regime whose duration $\tau_f$ decreases as a power law of the applied shear rate $\gp$. Here we go one step further by an exhaustive investigation of the influence of the shearing geometry through the gap width $e$ and the boundary conditions. While slip conditions at the walls seem to have a negligible influence on the fluidization time $\tau_f$, different fluidization processes are observed depending on $\gp$ and $e$: the shear band remains almost stationary for several hours at low shear rates or small gap widths before strong fluctuations lead to a homogeneous flow, whereas at larger values of $\gp$ or $e$, the transient shear band is seen to invade the whole gap in a much smoother way. Still, the power-law behaviour appears as very robust and hints to critical-like dynamics. To further discuss these results, we propose (i) a qualitative scenario to explain the induction-like period that precedes full fluidization and (ii) an analogy with critical phenomena that naturally leads to the observed power laws if one assumes that the yield point is the critical point of an underlying out-of-equilibrium phase transition.