From transient fluidization processes to Herschel-Bulkley behavior in simple yield stress fluids

TL;DR

This study investigates the transient fluidization process of a simple yield stress fluid, revealing a scaling law for fluidization time and connecting it to the Herschel-Bulkley steady-state behavior.

Contribution

It provides a detailed analysis of the transient fluidization dynamics and links the fluidization exponents to the Herschel-Bulkley rheological law, offering a new understanding of yield stress fluid behavior.

Findings

Fluidization time scales as   (\u03c3 - c3_c)^{-}

Transient regime involves creep, wall slip, shear banding, then homogeneous flow

Herschel-Bulkley exponent is the ratio of transient fluidization exponents

Abstract

Stress-induced fluidization of a simple yield stress fluid, namely a carbopol microgel, is addressed through extensive rheological measurements coupled to simultaneous temporally and spatially resolved velocimetry. These combined measurements allow us to rule out any bulk fracture-like scenario during the fluidization process such as that suggested in [Caton {\it et al., Rheol Acta}, 2008, {\bf 47}, 601-607]. On the contrary, we observe that the transient regime from solidlike to liquidlike behaviour under a constant shear stress $\sigma$ successively involves creep deformation, total wall slip, and shear banding before a homogeneous steady state is reached. Interestingly, the total duration $\tau_f$ of this fluidization process scales as $\tau_f \propto 1/(\sigma - \sigma_c)^{\beta}$, where $\sigma_c$ stands for the yield stress of the microgel, and $\beta$ is an exponent which only depends on the microgel properties and not on the gap width or on the boundary conditions. Together with recent experiments under imposed shear rate [Divoux {\it et al., Phys. Rev. Lett.}, 2010, {\bf 104}, 208301], this scaling law suggests a route to rationalize the phenomenological Herschel-Bulkley (HB) power-law classically used to describe the steady-state rheology of simple yield stress fluids. In particular, we show that the {\it steady-state} HB exponent appears as the ratio of the two fluidization exponents extracted separately from the {\it transient} fluidization processes respectively under controlled shear rate and under controlled shear stress.