# Unified theoretical and experimental view on transient shear banding

## TL;DR

This paper presents a unified theoretical and experimental framework for understanding transient shear banding and fluidization in yield stress fluids, linking transient dynamics to steady-state flow behavior.

## Contribution

It introduces a continuum model based on free energy minimization that captures transient shear banding and unifies the description of yielding and steady flow in complex fluids.

## Key findings

- The model accurately predicts the decay of fluidization time with shear rate and stress.
- It reproduces the empirical relation between transient exponents and Herschel-Bulkley law.
- Provides a comprehensive framework linking transient and steady-state flow behaviors.

## Abstract

Dense emulsions, colloidal gels, microgels, and foams all display a solid-like behavior at rest characterized by a yield stress, above which the material flows like a liquid. Such a fluidization transition often consists of long-lasting transient flows that involve shear-banded velocity profiles. The characteristic time for full fluidization, $\tau_\text{f}$, has been reported to decay as a power-law of the shear rate $\dot \gamma$ and of the shear stress $\sigma$ with respective exponents $\alpha$ and $\beta$. Strikingly, the ratio of these exponents was empirically observed to coincide with the exponent of the Herschel-Bulkley law that describes the steady-state flow behavior of these complex fluids. Here we introduce a continuum model, based on the minimization of a "free energy", that captures quantitatively all the salient features associated with such \textit{transient} shear-banding. More generally, our results provide a unified theoretical framework for describing the yielding transition and the steady-state flow properties of yield stress fluids.