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 [sigma](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 [small gamma, Greek, dot above]. (i) At small strains ([gamma] < 1), [sigma](t) increases linearly and the microgel undergoes homogeneous deformation. (ii) At a time tm, the stress reaches a maximum value [sigma]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 et al., Phys. Rev. Lett., 2010, 104, 208301]. This whole sequence is very robust to concentration changes in the explored range (0.5 [less-than-or-equal] C [less-than-or-equal] 3%w/w). We further demonstrate that the maximum stress [sigma]m and the corresponding strain [gamma]m = [small gamma, Greek, dot above]tm both depend on the applied shear rate [small gamma, Greek, dot above] and on the waiting time tw between preshear and shear start-up: they remain roughly constant as long as [small gamma, Greek, dot above] is smaller than some critical shear rate [small gamma, Greek, dot above]w [similar] 1/tw and they increase as weak power laws of [small gamma, Greek, dot above] for [small gamma, Greek, dot above] > [small gamma, Greek, dot above]w. Finally, by changing the boundary conditions from rough to smooth, we show that there exists a critical shear rate [small gamma, Greek, dot above]s fixed by the wall surface roughness below which slip at both walls allows for faster stress relaxation and for stress fluctuations strongly reminiscent of stick-slip. Interestingly, the value of [small gamma, Greek, dot above]s is observed to coincide with the shear rate below which the flow curve displays a kink attributed to wall slip.