Wall slip and bulk flow heterogeneity in a sludge under shear

We investigate the shear flow of a sludge mimicking slurries produced by the nuclear industry and constituted of a dispersion of non-Brownian particles into an attractive colloidal dispersion at a total solid volume fraction of about 10%. Combining rheometry and ultrasound flow imaging, we show that, upon decreasing the shear rate, the flow transitions from a homogeneous shear profile in the bulk to a fully arrested plug-like state with total wall slip, through an oscillatory regime where strong fluctuations of the slip velocity propagate along the vorticity direction. When the shear stress is imposed close to the yield stress, the shear rate presents large, quasi-periodic peaks, associated with the propagation of local stick-and-slip events along the vorticity direction. Such complex dynamics, reminiscent of similar phenomena reported in much denser suspensions, highlight the importance of local flow characterization to fully understand sludge rheology.

💡 Research Summary

This paper investigates the shear flow of a surrogate nuclear‑industry sludge composed of a dispersion of non‑Brownian particles (barium sulfate, perlite) in an attractive colloidal matrix (iron‑ and copper‑based hydroxides, cyanide complexes) at a total solid volume fraction of roughly 10 %. The authors combine conventional stress‑ or shear‑rate controlled rheometry with high‑frequency (15 MHz) ultrasound imaging to obtain spatially resolved velocity fields inside the opaque material. The experimental setup consists of a small‑gap (2 mm) concentric‑cylinder geometry with roughened PMMA surfaces; despite the roughness, significant wall slip is observed.

Two experimental protocols are employed. In the shear‑rate‑controlled tests, the sample is pre‑sheared at 200 s⁻¹, then subjected to a logarithmic sweep down to 0.2 s⁻¹, followed by a series of constant‑rate steps (200 → 0.5 s⁻¹). In each step, ultrasound velocity maps vθ(r, z, t) are recorded after a 60 s equilibration period. Slip velocities at the rotating bob (V_bob) and the stationary cup (V_cup) are extracted by linear extrapolation of the near‑wall velocity profiles, and an effective shear rate γ̇_eff is computed to correct the global rheometer reading for slip. In the stress‑controlled tests, a constant shear stress close to the measured yield stress σ_y is imposed, and the temporal evolution of the shear rate is monitored.

Key observations from the shear‑rate experiments are as follows: (1) At high imposed rates (>30 s⁻¹) the flow is homogeneous across the gap, with modest slip at both walls. (2) As the imposed rate is reduced below ≈10 s⁻¹, wall slip increases dramatically and the bulk velocity profile collapses into a plug‑like shape, indicating that the material behaves as a solid body that slides along the walls. (3) In an intermediate window (≈5–15 s⁻¹) the slip velocity exhibits strong, irregular oscillations. These oscillations are not random; they propagate along the vorticity (vertical) direction, forming wave‑like fronts of alternating stick and slip regions. This “slip‑wave” regime reveals a breakdown of translational invariance and points to a dynamic coupling between the wall and the bulk microstructure.

When the shear stress is held near σ_y, the shear rate does not settle to a steady value. Instead, it displays large, quasi‑periodic spikes separated by low‑rate intervals. Ultrasound imaging shows that each spike corresponds to a localized stick‑slip event that nucleates at one location and travels vertically, leaving behind a transiently fluidized band. The system therefore alternates between a nearly arrested state and brief episodes of rapid flow, a hallmark of bistability often reported in dense, shear‑thickening suspensions.

The authors emphasize that these phenomena—wall slip, plug formation, slip‑wave propagation, and stress‑controlled stick‑slip bursts—have previously been documented mainly in highly concentrated (ϕ > 40 %) suspensions. Their occurrence in a low‑concentration sludge underscores the pivotal role of strong inter‑particle attractions (enhanced by a high ionic strength of 0.5 M) and the presence of a broad size distribution of non‑Brownian particles. The attractive colloidal network provides a percolated gel that can support a finite yield stress, while the larger particles act as stress concentrators that facilitate slip at the boundaries.

Methodologically, the study demonstrates the necessity of coupling global rheometry with local velocimetry for opaque complex fluids. The ultrasound technique, relying on back‑scatter from the non‑Brownian particles, delivers time‑resolved, two‑dimensional velocity fields without requiring optical transparency. By correcting the engineering shear rate with the measured γ̇_eff, the authors obtain constitutive curves that faithfully represent the bulk material response, free from wall‑slip artefacts.

In conclusion, the work provides a comprehensive picture of sludge rheology: (i) a continuous transition from homogeneous shear to total wall slip and plug flow as the shear rate is lowered; (ii) an intermediate regime where slip velocity oscillates and propagates as a wave along the vorticity direction; (iii) a stress‑controlled regime near the yield stress where the system exhibits large, periodic shear‑rate spikes linked to traveling stick‑slip fronts. These findings have practical implications for the design and operation of pipelines and processing equipment handling nuclear sludges or similar industrial slurries, where unexpected wall slip or flow instabilities can lead to blockages or uneven transport. The study also highlights that even relatively dilute suspensions can display rich, non‑Newtonian dynamics when attractive forces and size polydispersity are significant, urging the broader rheology community to adopt local flow diagnostics in the analysis of complex, opaque materials.