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 (gamma) over dot. (i) At small strains (gamma < 1), sigma(t) increases linearly and the microgel undergoes homogeneous deformation. (ii) At a time t(m), 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 <= C <= 3% w/w). We further demonstrate that the maximum stress sigma(m) and the corresponding strain gamma(m) = (gamma) over dott(m) both depend on the applied shear rate (gamma) over dot and on the waiting time t(w) between preshear and shear start-up: they remain roughly constant as long as (gamma) over dot is smaller than some critical shear rate (gamma) over dot(w) similar to 1/t(w) and they increase as weak power laws of (gamma) over dot for (gamma) over dot > (gamma) over dot(w). Finally, by changing the boundary conditions from rough to smooth, we show that there exists a critical shear rate (gamma) over dot(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 (gamma) over dot(s) is observed to coincide with the shear rate below which the flow curve displays a kink attributed to wall slip.