Thibaut Divoux, Véronique Lapeyre, Valérie Ravaine, and Sébastien Manneville
Flows of suspensions are often affected by wall slip, that is, the fluid velocity Vf in the vicinity of a boundary differs from the wall velocity Vw due to the presence of a lubrication layer. While the slip velocity Vs = abs (Vf - Vw) robustly scales linearly with the stress S at the wall in dilute suspensions, there is no consensus regarding denser suspensions that are sheared in the bulk, for which slip velocities have been reported to scale as a Vs = k.(S)p with exponents p inconsistently ranging between 0 and 2. Here we focus on a suspension of soft thermoresponsive particles and show that Vs actually scales as a power law of the viscous stress (S - Sc), where Sc denotes the yield stress of the bulk material. By tuning the temperature across the jamming transition, we further demonstrate that this scaling holds true over a large range of packing fractions Phi on both sides of the jamming point and that the exponent p increases continuously with Phi, from 1 in the case of dilute suspensions to 2 for jammed assemblies. These results allow us to successfully revisit inconsistent data from the literature and pave the way for a continuous description of wall slip above and below jamming.