Extended μ(J)\mu(J)-rheology for dense suspensions at oscillatory shear flows

Recent studies have highlighted that oscillatory and time-dependent shear flows might help increase flowability of dense suspensions. While most focus has been on cross-flows we here study a simple two-dimensional suspensions where we apply simultaneously oscillatory and stationary shear along the same direction. We first show that the viscosities in this set-up significantly decrease with an increasing magnitude of the oscillations, contrary to previous claims. The decrease can be attributed to the large decrease in the number of contacts and an altered microstructure as the magnitude of the oscillation is increased. As a sub-result we find both an extension to the $\mu(J)$-rheology, a constitutive relationship between the shear stresses and the shear rate, valid for pure oscillatory flows and with a higher shear-jammed packing fraction for suspensions composed of frictional particles compared to steady-shear conditions.Comment: 5 pages, 5 figure

Classical van der Waals interactions between spherical bodies of dipolar fluid

The van der Waals interaction free energy Aint between two spherical bodies of Stockmayer fluid across a vacuum is calculated using molecular simulations and classical perturbation theory. The results are decomposed into their electrostatic and Lennard-Jones parts, and the former is shown to agree excellently with predictions from dielectric continuum theory. Aint is decomposed into its energetic and entropic contributions and the results are compared with analytical predictions. Finally, we expand the electrostatic part of Aint in a multipole expansion, and show that the surprisingly good agreement between the molecular and continuum descriptions is likely due to a cancellation of errors coming from the neglect of the discrete nature of the fluid within the dielectric description

Transition from viscous to inertial regime in dense suspensions

Non-Brownian suspensions present a transition from Newtonian behavior in the zero-shear limit to a shear thickening behaviour at a large shear rate, none of which is clearly understood so far. Here, we carry out numerical simulations of such an athermal dense suspension under shear, at an imposed confining pressure. This set-up is conceptually identical to the recent experiments of Boyer and co-workers [Phys. Rev. Lett. 107,188301 (2011)]. Varying the interstitial fluid viscosities, we recover the Newtonian and Bagnoldian regimes and show that they correspond to a dissipation dominated by viscous and contact forces respectively. We show that the two rheological regimes can be unified as a function of a single dimensionless number, by adding the contributions to the dissipation at a given volume fraction.Comment: 4 pages, 3 figure

A new dipolar potential for numerical simulations of polar fluids on the 4D4\mathrm{D} hypersphere

We present a new method for Monte Carlo or Molecular Dynamics numerical simulations of three dimensional polar fluids. The simulation cell is defined to be the surface of the northern hemisphere of a four-dimensional (hyper)sphere. The point dipoles are constrained to remain tangent to the sphere and their interactions are derived from the basic laws of electrostatics in this geometry. The dipole-dipole potential has two singularities which correspond to the following boundary conditions : when a dipole leaves the northern hemisphere at some point of the equator, it reappears at the antipodal point bearing the same dipole moment. We derive all the formal expressions needed to obtain the thermodynamic and structural properties of a polar liquid at thermal equilibrium in actual numerical simulation. We notably establish the expression of the static dielectric constant of the fluid as well as the behavior of the pair correlation at large distances. We report and discuss the results of extensive numerical Monte Carlo simulations for two reference states of a fluid of dipolar hard spheres and compare these results with previous methods with a special emphasis on finite size effects.Comment: 32 pages, 6 figures, 4 table

Local Rheology Relation with Variable Yield Stress Ratio across Dry, Wet, Dense, and Dilute Granular Flows

Dry, wet, dense, and dilute granular flows have been previously considered fundamentally different and thus described by distinct, and in many cases incompatible, rheologies. We carry out extensive simulations of granular flows, including wet and dry conditions, various geometries and driving mechanisms (boundary driven, fluid driven, and gravity driven), many of which are not captured by standard rheology models. For all simulated conditions, except for fluid-driven and gravity-driven flows close to the flow threshold, we find that the Mohr-Coulomb friction coefficient $\mu$ scales with the square root of the local P\'eclet number $\mathrm{Pe}$ provided that the particle diameter exceeds the particle mean free path. With decreasing $\mathrm{Pe}$ and granular temperature gradient $M$, this general scaling breaks down, leading to a yield condition with a variable yield stress ratio characterized by $M$

Relationships between postural orientation and self reported function, hop performance and muscle power in subjects with anterior cruciate ligament injury.

ABSTRACT: BACKGROUND: Injury to the anterior cruciate ligament (ACL) is associated not only with knee instability and impaired neuromuscular control, but also with altered postural orientation manifested as observable "substitution patterns". However, tests currently used to evaluate knee function in subjects with ACL injury are not designed to assess postural orientation. Therefore, we are in the process of developing an observational test set that measures postural orientation in terms of the ability to stabilize body segments in relation to each other and to the environment. The aim of the present study was to characterise correlations between this novel test set, called the Test for Substitution Patterns (TSP) and commonly used tests of knee function. METHODS: In a blinded set-up, 53 subjects (mean age 30 years, range 20-39, with 2-5 years since ACL injury) were assessed using the TSP, the Knee Injury and Osteoarthritis Outcome Score subscale sport/recreation (KOOS sport/rec), 3 hop tests and 3 muscle power tests. Correlations between the scores of the TSP and the other tests were determined. RESULTS: Moderate correlations were found between TSP scores and KOOS sport/rec (rs = -0.43; p = 0.001) and between TSP scores and hop test results (rs = -0.40 to -0.46; p </= 0.003), indicating that altered postural orientation was associated with worse self-reported KOOS sport/rec function and worse hop performance. No significant correlations were found between TSP scores and muscle power results. Subjects had higher TSP scores on their injured side than on their uninjured side (median 4 and 1 points; interquartile range 2-6 and 0-1.5, respectively; p < 0.0001). CONCLUSIONS: We conclude that the Test for Substitution Patterns is of relevance to the patient and measures a specific aspect of neuromuscular control not quantified by the other tests investigated. We suggest that the TSP may be a valuable complement in the assessment of neuromuscular control in the rehabilitation of subjects with ACL injury

Microrheology to probe non-local effects in dense granular flows

A granular material is observed to flow under the Coulomb yield criterion as soon as this criterion is satisfied in a remote but contiguous region of space. We investigate this non-local effect using discrete element simulations, in a geometry similar, in spirit, to the experiment of Reddy et al. (Phys. Rev. Lett., 106 (2011) 108301): a micro-rheometer is introduced to determine the influence of a distant shear band on the local rheological behaviour. The numerical simulations recover the dominant features of this experiment: the local shear rate is proportional to that in the shear band and decreases (roughly) exponentially with the distance to the yield conditions. The numerical results are in quantitative agreement with the predictions of the non-local rheology proposed by (Phys. Rev. Lett., 111 (2013) 238301) and derived from a gradient expansion of the rheology $\mu[I]$. The consequences of these findings for the dynamical mechanisms controlling non-locality are finally discussed.Comment: 6 pages, 5 figure

A non-local rheology for granular flows across yield conditions

The rheology of dense granular flows is studied numerically in a shear cell controlled at constant pressure and shear stress, confined between two granular shear flows. We show that a liquid state can be achieved even far below the yield stress, whose flow can be described with the same rheology as above the yield stress. A non-local constitutive relation is derived from dimensional analysis through a gradient expansion and calibrated using the spatial relaxation of velocity profiles observed under homogeneous stresses. Both for frictional and frictionless grains, the relaxation length is found to diverge as the inverse square-root of the distance to the yield point, on both sides of that point.Comment: 5 pages, 4 figure