Stress overshoot in a simple yield stress fluid: an extensive study combining rheology and velocimetry

We report a large amount of experimental data on the stress overshoot phenomenon which takes place during start-up shear flows in a simple yield stress fluid, namely a carbopol microgel. A combination of classical rheological measurements and ultrasonic velocimetry makes it possible to get physical insights on the transient dynamics of both the stress $σ(t)$ and the velocity field across the gap of a rough cylindrical Couette cell during the start-up of shear under an applied shear rate $\dotγ$. (i) At small strains ($γ<1$), $σ(t)$ increases linearly and the microgel undergoes homogeneous deformation. (ii) At a time $t_m$, the stress reaches a maximum value $σ_m$ which corresponds to the failure of the microgel and to the nucleation of a thin lubrication layer at the moving wall. (iii) The microgel then experiences a strong elastic recoil and enters a regime of total wall slip while the stress slowly decreases. (iv) Total wall slip gives way to a transient shear-banding phenomenon, which occurs on timescales much longer than that of the stress overshoot and has been described elsewhere [Divoux \textit{et al., Phys. Rev. Lett.}, 2010, \textbf{104}, 208301]. This whole sequence is very robust to concentration changes in the explored range ($0.5 \le C \le 3$ w/w). We further demonstrate that the maximum stress $σ_m$ and the corresponding strain $γ_m=\dotγt_m$ both depend on the applied shear rate $\dot γ$ and on the waiting time $t_w$ between preshear and shear start-up: they remain roughly constant as long as $\dotγ$ is smaller than some critical shear rate $\dotγ_w\sim 1/t_w$ and they increase as weak power laws of $\dot γ$ for $\dotγ> \dotγ_w$ [...].

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