Continuum modelling of shear start-up in soft glassy materials

Abstract

Yield stress fluids (YSFs) display a dual nature highlighted by the existence of a yield stress such that YSFs are solid below the yield stress, whereas they flow like liquids above it. Under an applied shear rate $\dot{\gamma }$, the solid-to-liquid transition is associated with a complex spatiotemporal scenario. Still, the general phenomenology reported in the literature boils down to a simple sequence that can be divided into a short-time response characterized by the so-called "stress overshoot", followed by stress relaxation towards a steady state. Such relaxation can be either long-lasting, which usually involves the growth of a shear band that can be only transient or that may persist at steady-state, or abrupt, in which case the solid-to-liquid transition resembles the failure of a brittle material, involving avalanches. Here we use a continuum model based on a spatially-resolved fluidity approach to rationalize the complete scenario associated with the shear-induced yielding of YSFs. Our model provides a scaling for the coordinates of the stress maximum as a function of $\dot{\gamma }$, which shows excellent agreement with experimental and numerical data extracted from the literature. Moreover, our approach shows that such a scaling is intimately linked to the growth dynamics of a fluidized boundary layer in the vicinity of the moving boundary. Yet, such scaling is independent of the fate of that layer, and of the long-term behavior of the YSF. Finally, when including the presence of "long-range" correlations, we show that our model displays a ductile to brittle transition, i.e., the stress overshoot reduces into a sharp stress drop associated with avalanches, which impacts the scaling of the stress maximum with $\dot{\gamma }$. Our work offers a unified picture of shear-induced yielding in YSFs, whose complex spatiotemporal dynamics are deeply connected to non-local effects.

24 pages, 19 figures

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• Microscopic Activated Dynamics Theory of the Shear Rheology and Stress Overshoot in Ultra-Dense Glass-Forming Fluids and Colloidal Suspensions
• Rheology of Wormlike Micellar Gels Formed By Long-Chained Zwitterionic Surfactants
• Interplay between wall slip and shear banding in a thixotropic yield stress fluid
• Continuum modeling of Soft Glassy Materials under shear
• Dynamical regimes of thermally convective emulsions