Wall slip across the jamming transition of soft thermoresponsive particles

Flows of suspensions are often affected by wall slip, that is, the fluid velocity nu(f) in the vicinity of a boundary differs from the wall velocity nu(w) due to the presence of a lubrication layer. While the slip velocity nu(s) = vertical bar nu(f) - nu(w)vertical bar robustly scales linearly with the stress sigma 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 nu(s) proportional to sigma(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 sigma - sigma(c), where sigma(c) 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 p = 1 in the case of dilute suspensions to p = 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.