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The instability of an iso-dense non-Brownian suspension of polystyrene beads of diameter 40 μm dispersed in a water-glycerol mixture submitted to a periodic square wave oscillating flow in a Hele-Shaw cell is studied experimentally. The instability gives rise to stationary bead concentration waves transverse to the flow. It has been observed for average particle volume fractions between 0.25 and 0.4, for periods of the square wave flow variation between 0.4 and 10 s and in finite intervals of the amplitude of the fluid displacement. The study shows that the wavelength λ increases roughly linearly with the amplitude of the oscillatory flow; on the other hand, λ is independent of the particle concentration and of the period of oscillation of the flow although the minimum threshold amplitude for observing the instability increases with the period.

Shear thickening fluids are liquids that stiffen as the applied stress increases. If many of these types of fluids follow a monotonic rheological curve, some experimental and numerical studies suggest that certain fluids, like cornstarch, may exhibit a non-monotonic, S-shaped rheology. Such non-monotonic behavior has however proved very difficult to observe experimentally in classical rheometer. To explain such difficulties, the possible presence of vorticity banding in the rheometer has been considered. To prevent such instabilities, we use a capillary rheometer, which is a cylindrical tube, measuring the flow rate versus the applied pressure drop. With this setup, we indeed observe a non-monotonic behavior: the flow rate increases monotonically at low pressure drops up to a maximum, after which it abruptly decreases to an almost constant flow rate regardless of further increases in pressure drop. This maximum-jump-plateau behavior occurs over a wide range of concentrations and is reproducible without hysteresis, which is in agreement with an S-shaped rheology. However, the obtained flow versus pressure difference function Q ( Δ P ) does not agree with the classical Wyart-Cates rheological model, which predicts an S-shaped non-monotonic function, but with neither a jump nor a plateau. To understand this jump-plateau behavior, we remark that any rheological model would establish a relationship between the flow rate and the local pressure gradient, but not the total pressure drop. We thus discuss and analyze the implications of having an S-shaped non-monotonic flow rate-pressure gradient in Poiseuille flow. In particular, we discuss the possibility of a non-uniform pressure gradient in the direction of the flow, i.e., a kind of streamwise banding. The key issue is then the selection of the gradient pressure distribution along the tube. One solution could arise from an analogy of this problem with the spinodal decomposition. It, however, leads to an increase in flow rate with ∂ x P up to a plateau between two values of ∂ x P as determined by the Maxwell construction. To account for the bump-jump behavior, we have implemented a simple dynamical stochastic version of the Wyart-Cates model, where the thickening occurs with a characteristic time. As a result, with increasing the total pressure drop, the flow rate increases monotonically up to a maximum value. Beyond this point, the flow rate drops abruptly to a lower value, forming a slowly decreasing plateau. This behavior is likely to account for the maximum-jump-plateau observed in the experiments. We also show that in such a system, the final state is quite sensitive to the initial state of the fluid, especially its homogeneity. Our results then demonstrate that the mere presence of a non-monotonic rheological curve is sufficient to predict the occurrence of stress banding in the streamwise direction and a plateau flow rate, even if the suspension remains homogeneous., (© 2024. The Author(s), under exclusive licence to EDP Sciences, SIF and Springer-Verlag GmbH Germany, part of Springer Nature.)

The extension of a gravity current in a lock-exchange problem, proceeds as square root of time in the viscous-buoyancy phase, where there is a balance between gravitational and viscous forces. In the presence of particles however, this scenario is drastically altered, because sedimentation reduces the motive gravitational force and introduces a finite distance and time at which the gravity current halts. We investigate the spreading of low Reynolds number suspension gravity currents using a novel approach based on the Lattice-Boltzmann (LB) method. The suspension is modeled as a continuous medium with a concentration-dependent viscosity. The settling of particles is simulated using a drift flux function approach that enables us to capture sudden discontinuities in particle concentration that travel as kinematic shock waves. Thereafter a numerical investigation of lock-exchange flows between pure fluids of unequal viscosity, reveals the existence of wall layers which reduce the spreading rate substantially compared to the lubrication theory prediction. In suspension gravity currents, we observe that the settling of particles leads to the formation of two additional fronts: a horizontal front near the top that descends vertically and a sediment layer at the bottom which aggrandises due to deposition of particles. Three phases are identified in the spreading process: the final corresponding to the mutual approach of the two horizontal fronts while the laterally advancing front halts indicating that the suspension current stops even before all the particles have settled. The first two regimes represent a constant and a decreasing spreading rate respectively. Finally we conduct experiments to substantiate the conclusions of our numerical and theoretical investigation.