Wall slip across the jamming transition of soft thermoresponsive particles

Flows of suspensions are often affected by wall slip, that is, the fluid velocity v(f) in the vicinity of a boundary differs from the wall velocity v(w) due to the presence of a lubrication layer. While the slip velocity v(s)=|v(f)-v(w)| robustly scales linearly with the stress σ 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 v(s)∝σ(p) with exponents p inconsistently ranging between 0 and 2. Here we focus on a suspension of soft thermoresponsive particles and show that v(s)) actually scales as a power law of the viscous stress σ-σ(c), where σ(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 ϕ on both sides of the jamming point and that the exponent p increases continuously with ϕ, 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.