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 $v_s=\vert v_{f}-v_{w}\vert$ 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 $v_s\propto\sigma^p$ 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 $\sigma-\sigma_c$, 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 paves the way for a continuous description of wall slip above and below jamming.