Wall slip in suspensions of thermo-responsive particles

Flows of suspensions are affected by wall slip, i.e. the fluid velocity $v_{f}$ in the vicinity of a boundary differs from the velocity $v_{w}$ of the latter due to the presence of a lubrication layer. Wall slip is quantified by the slip velocity $v_s$, which is defined as $v_s=\mid v_{f}-v_{w}\mid $ and displays a power-law scaling with the stress $\sigma$ at the wall. If the slip velocity of dilute suspensions robustly follows $v_s \propto \sigma^p$ with $p\simeq 1$, there is no consensus regarding denser suspensions that are sheared in bulk, for which $v_s$ is reported to scale as a power-law of the stress with exponents inconsistently ranging between $p \simeq 0$ and 2. By means of extensive rheometry coupled to velocimetry on a suspension of thermo-responsive particles, we show that such discrepancy is only apparent, and demonstrate that $v_s$ scales as a power law of the viscous stress $\sigma-\sigma_c$, where $\sigma_c$ denotes the yield stress. Tunning the temperature reveals that such 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 $p=1$ (dilute suspensions) to $p=2$ (dense assemblies). Our results pave the way for a unified description of wall slip.