# Unified theoretical and experimental view on transient shear banding

Roberto Benzi, Thibaut Divoux, Catherine Barentin, Sébastien Manneville, Mauro Sbragaglia, Federico Toschi

Research output: Contribution to journalArticleAcademic

## 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 an out-of-equilibrium 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.
Original language English 1907.08846vl 10 arXiv Published - 20 Jul 2019

### Bibliographical note

5 pages, 4 figures - supplemental 5 pages, 4 figures

## Keywords

• cond-mat.soft
• cond-mat.stat-mech
• physics.flu-dyn

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