Élisabeth Guazzelli

We present particle-resolved simulations of dense frictional suspensions undergoing the viscous-inertial transition using pressure-imposed rheology. By varying the fluid viscosity, shear rate, and granular pressure, we demonstrate that the transition occurs at a Stokes number of ≈8 (close to the value of 10 found in the experiments of Tapia et al. [Viscous to inertial transition in dense granular suspension, Phys. Rev. Lett. 129, 078001 (2022).PRLTAO0031-900710.1103/PhysRevLett.129.078001]) and also that the shear stress exhibits a slower transition than the particle pressure. Using our highly resolved numerical simulations, we further demonstrate that this transitional behavior is related to the combined effect of tangential contact and lubrication forces, as the frictional particles concurrently shift from rolling to sliding contacts. This shift is controlled not only by the Stokes number, but also by the distance from jamming. Additionally, we examine the role of increasing interparticle friction on the viscous-inertial transition.

This study investigates the rheological behavior of soft spherical particles across the jamming transition and within both viscous and inertial flow regimes. We extend the established granular rheology for hard sphere suspensions to develop a soft granular rheology by adjusting the critical volume fraction and friction coefficient to account for pressure variations, and by incorporating the combined effiects of viscous and inertial stress scales. This framework effectively characterizes dense suspensions across a broad spectrum of sizes and flow conditions, from colloidal to granular. The implications for suspension flow dynamics and sediment transport processes are also explored.

Influence of small inertia on Jeffery orbits – CORRIGENDUM - Volume 1022

We experimentally investigate the rotational dynamics of neutrally buoyant flat bodies of revolution (spheroids, disks and rings with different cross-sectional shapes) in shear flows. In the Stokes regime, the axis of revolution of these rigid particles moves in one of a family of closed periodic Jeffery orbits. Inertia is able to lift the orbit degeneracy and induces drift among several rotations towards limiting stable orbits. Furthermore, permanent alignment can be achieved for disks and rings with triangular cross-sectional shapes, provided the inertia is sufficiently high. The bifurcations between the different dynamics are compared with those predicted by small-inertia asymptotic theories and numerical simulations.

Most sediment laden flows in nature are produced by strong local gradients in terms of a hillslope or a pressure gradient. Describing these kinds of complex flows from an engineering perspective (e.g. by means of macroscopic sediment transport models) requires in-depth knowledge of the rheology of the sheared sediment beds and the fluid-sediment mixture. In the present work, we review a previously derived macroscopic model that relies on a two-phase flow approach for the fluid and the sediment phase, respectively, as a promising avenue to predict such a complex flow. We apply this model to data that was generated by means of highly-resolved direct numerical simulations of a sediment bed sheared by a pressure driven viscous flow. We show that the rheology obtained in the numerical results obeys the scaling that has previously been derived for neutrally buoyant particles in rheometer cells. A two-phase flow model that is based on these scaling relations is therefore able to reproduce the simulation results of sheared sediment beds with high accuracy. Finally, we provide a list of open issues for future research that will be key to improve our understanding of the sediment bed rheology. Those are the role of higher particle inertia, transient behavior of sheared sediment beds, and cohesion.

The featured article ‘Break-up of a falling drop containing dispersed particles’ (Nitsche and Batchelor, J. Fluid Mech., 1997, vol. 340, pp. 161–175) is G. K. Batchelor's last published paper with his former postdoctoral associate J. M. Nitsche. The objective of the study was to investigate the randomness of the velocities of interacting rigid particles falling under gravity through a viscous fluid at a small Reynolds number and its consequence for the breakup of a falling cloud of particles. The study focused on a quintessential problem of the collective dynamics of interacting particles and has been an inspiration for subsequent work.

Concentration inhomogeneities occur in many flows of non-Brownian suspensions. Their modeling necessitates the description of the relative motion of the particle phase and of the fluid phase, as well as the accounting for their interaction, which is the object of the suspension balance model (SBM). We systematically investigate the dynamics and the steady state of shear-induced migration in a wide-gap Couette flow for a wide range of particle volume fraction, and we test the ability of the SBM to account for the observations. We use a model suspension for which macroscopic particle stresses are known. Surprisingly, the observed magnitude of migration is much lower than that predicted by the SBM when the particle stress in the SBM is equated to the macroscopic particle stress. Another noteworthy observation is the quasi-absence of migration for semidilute suspensions. From the steady-state volume fraction profiles, we derive the local particle normal stress responsible for shear-induced migration according to the SBM. However, the observed dynamics of migration is much faster than that predicted by the SBM when using this stress in the model. More generally, we show that it is not possible to build a local friction law consistent with both the magnitude and the dynamics of migration within the standard SBM framework. This suggests that there is a missing term in the usual macroscopic constitutive law for the particle normal stress driving migration. The SBM is indeed capable of accurately predicting both the magnitude and the dynamics of migration when a tentative phenomenological term involving a concentration gradient is added to the particle normal stresses determined in macroscopic experiments.

Dense granular suspensions, which consist of concentrated mixtures of non-Brownian particles suspended in a liquid, are ubiquitous in many natural phenomena (e.g., landslides, debris flows, and sediment transport) and industrial processes (e.g., concrete and pastes). Despite their prevalence, the rheology of these suspensions is not fully understood, and the establishment of a unified theoretical framework for different flow regimes remains a challenge. The present work reviews rheological measurements of granular suspensions in the dense regime, performed at imposed volume fractions and at imposed values of particle normal stress. It proposes a unified granular rheology over the viscous to inertial flow regime based on the superposition of inertial and viscous stress scales. This granular rheology, found for suspensions of hard spheres, can be extended to a soft granular rheology for soft particles. This soft granular rheology results in the approximate collapse of the rheological data into two branches when scaled with the distance to jamming, in a manner analogous to that found for viscous soft colloids, but now extended into the inertial regime.