arXiv subjects

Romain Mari

Publications and source records attributed to Romain Mari.

34 records · Page 2Linked to original sources

arXiv2018

Dynamic vorticity banding in discontinuously shear thickening suspensions

It has recently been argued that steady-state vorticity bands cannot arise in shear thickening suspensions, because the normal stress imbalance across the interface between the bands will set up particle migrations. In this Letter, we develop a simple continuum model that couples shear thickening to particle migration. We show by linear stability analysis that homogeneous flow is unstable towards vorticity banding, as expected, in the regime of negative constitutive slope. In full nonlinear computations, we show however that the resulting vorticity bands are unsteady, with spatiotemporal patterns governed by stress-concentration coupling. We furthermore show that these dynamical bands also arise in direct particle simulations, in good agreement with the continuum model.

cond-mat.soft↗

arXiv2018

Microscopic origin of frictional rheology in dense suspensions: correlations in force space

We develop a statistical framework for the rheology of dense, non-Brownian suspensions, based on correlations in a space representing forces, which is dual to position space. Working with the ensemble of steady state configurations obtained from simulations of suspensions in two dimensions, we find that the anisotropy of the pair correlation function in force space changes with confining shear stress ($σ_{xy}$) and packing fraction ($ϕ$). Using these microscopic correlations, we build a statistical theory for the macroscopic friction coefficient: the anisotropy of the stress tensor, $μ= σ_{xy}/P$. We find that $μ$ decreases (i) as $ϕ$ is increased and (ii) as $σ_{xy}$ is increased. Using a new constitutive relation between $μ$ and viscosity for dense suspensions that generalizes the rate-independent one, we show that our theory predicts a Discontinuous Shear Thickening (DST) flow diagram that is in good agreement with numerical simulations, and the qualitative features of $μ$ that lead to the generic flow diagram of a DST fluid observed in experiments.

cond-mat.soft↗

arXiv2018

Shaken and stirred: Random organization reduces viscosity and dissipation in granular suspensions

The viscosity of suspensions of large ($\geq10{μm}$) particles diverges at high solid fractions due to proliferation of frictional particle contacts. Reducing friction, to allow or improve flowability, is usually achieved by tuning the composition, either changing particle sizes and shapes or by adding lubricating molecules. We present numerical simulations that demonstrate a complementary approach whereby the viscosity divergence is shifted by driven flow tuning, using superimposed shear oscillations in various configurations to facilitate a primary flow. The oscillations drive the suspension towards an out-of-equilibrium, absorbing state phase transition, where frictional particle contacts that dominate the viscosity are reduced in a self-organizing manner. The method can allow otherwise jammed states to flow; even for unjammed states, it can substantially decrease the energy dissipated per unit strain. This creates a practicable route to flow enhancement across a broad range of suspensions where compositional tuning is undesirable or problematic.

cond-mat.soft↗

arXiv2017

A constitutive model for simple shear of dense frictional suspensions

Discrete particle simulations are used to study the shear rheology of dense, stabilized, frictional particulate suspensions in a viscous liquid, toward development of a constitutive model for steady shear flows at arbitrary stress. These suspensions undergo increasingly strong continuous shear thickening (CST) as solid volume fraction $ϕ$ increases above a critical volume fraction, and discontinuous shear thickening (DST) is observed for a range of $ϕ$. When studied at controlled stress, the DST behavior is associated with non-monotonic flow curves of the steady-state stress as a function of shear rate. Recent studies have related shear thickening to a transition between mostly lubricated to predominantly frictional contacts with the increase in stress. In this study, the behavior is simulated over a wide range of the dimensionless parameters $(ϕ,\tildeσ$, and $μ)$, with $\tildeσ = σ/σ_0$ the dimensionless shear stress and $μ$ the coefficient of interparticle friction: the dimensional stress is $σ$, and $σ_0 \propto F_0/ a^2$, where $F_0$ is the magnitude of repulsive force at contact and $a$ is the particle radius. The data have been used to populate the model of the lubricated-to-frictional rheology of Wyart and Cates [Phys. Rev. Lett.{\bf 112}, 098302 (2014)], which is based on the concept of two viscosity divergences or \textquotedblleft jamming\textquotedblright\ points at volume fraction $ϕ_{\rm J}^0 = ϕ_{\rm rcp}$ (random close packing) for the low-stress lubricated state, and at $ϕ_{\rm J} (μ) < ϕ_{\rm J}^0$ for any nonzero $μ$ in the frictional state; a generalization provides the normal stress response as well as the shear stress. A flow state map of this material is developed based on the simulation results.

cond-mat.soft↗

arXiv2017

Shear Reversal in Dense Suspensions: The Challenge to Fabric Evolution Models from Simulation Data

Despite the industrial importance of dense suspensions of hard particles, few constitutive models for them have been proposed or tested. Most of these are effectively "fabric evolution models" (FEMs) based on a stress rule connecting the bulk stress to a rank-2 microstructural fabric tensor Q and a closed time-evolution equation for Q. In dense suspensions most of the stress comes from short-ranged pairwise steric or lubrication interactions at near-contacts, so a natural choice for Q is the deviatoric 2nd moment of the distribution P(p) of the near-contact orientations p. Here we test directly whether a closed time-evolution equation for such a Q can exist for inertialess non-Brownian hard spheres in a Newtonian solvent. We perform extensive numerical simulations for the evolution of P(p) under shear reversal, providing a stringent test for FEMs. We consider a generic class of these as defined by Hand (1962) constrained only by frame indifference. Motivated by the small microstructural anisotropy in the dense regime, we start with linear models and successively consider increasingly nonlinear ones. Based on these results we suggest that no closed FEM properly describes the dynamics of Q under reversal. We attribute this to the fact that Q gives a poor description of the microstructure during large parts of the microstructural evolution following shear reversal. Specifically, the truncation of P(p) at 2nd spherical harmonic level describes two-lobed distributions of near-contact orientations, whereas on reversal we observe distributions that are markedly four-lobed; moreover dP/dt (p) has oblique axes, not collinear with those of Q in the shear plane. This structure likely precludes any adequate closure at second-rank level. Instead, our numerical data suggest that closures involving the coupled evolution of both a fabric tensor and a fourth-rank tensor might be reasonably accurate.

cond-mat.soft↗

arXiv2017

Shear-induced organization of forces in dense suspensions: signatures of discontinuous shear thickening

Dense suspensions can exhibit an abrupt change in their viscosity in response to increasing shear rate. The origin of this discontinuous shear thickening (DST) has been ascribed to the transformation of lubricated contacts to frictional, particle-on-particle contacts. Recent research on the flowing and jamming behavior of dense suspensions has explored the intersection of ideas from granular physics and Stokesian fluid dynamics to better understand this transition from lubricated to frictional rheology. DST is reminiscent of classical phase transitions, and a key question is how interactions between the microscopic constituents give rise to a macroscopic transition. In this paper, we extend a formalism that has proven to be successful in understanding shear jamming of dry grains to dense suspensions. Quantitative analysis of the collective evolution of the contact-force network accompanying the DST transition demonstrates clear changes in the distribution of microscopic variables, and leads to the identification of an "order parameter" characterizing DST.

cond-mat.soft↗

arXiv2016

Collective Influence Algorithm to find influencers via optimal percolation in massively large social media

We elaborate on a linear time implementation of the Collective Influence (CI) algorithm introduced by Morone, Makse, Nature 524, 65 (2015) to find the minimal set of influencers in a network via optimal percolation. We show that the computational complexity of CI is O(N log N) when removing nodes one-by-one, with N the number of nodes. This is made possible by using an appropriate data structure to process the CI values, and by the finite radius l of the CI sphere. Furthermore, we introduce a simple extension of CI when l is infinite, the CI propagation (CI_P) algorithm, that considers the global optimization of influence via message passing in the whole network and identifies a slightly smaller fraction of influencers than CI. Remarkably, CI_P is able to reproduce the exact analytical optimal percolation threshold obtained by Bau, Wormald, Random Struct. Alg. 21, 397 (2002) for cubic random regular graphs, leaving little improvement left for random graphs. We also introduce the Collective Immunization Belief Propagation algorithm (CI_BP), a belief-propagation (BP) variant of CI based on optimal immunization, which has the same performance as CI_P. However, this small augmented performance of the order of 1-2 % in the low influencers tail comes at the expense of increasing the computational complexity from O(N log N) to O(N^2 log N), rendering both, CI_P and CI_BP, prohibitive for finding influencers in modern-day big-data. The same nonlinear running time drawback pertains to a recently introduced BP-decimation (BPD) algorithm by Mugisha, Zhou, arXiv:1603.05781. For instance, we show that for big-data social networks of typically 200 million users (eg, active Twitter users sending 500 million tweets per day), CI finds the influencers in less than 3 hours running on a single CPU, while the BP algorithms (CI_P, CI_BP and BDP) would take more than 3,000 years to accomplish the same task.

physics.soc-ph↗

arXiv2015

Discontinuous Shear Thickening in Brownian Suspensions By Dynamic Simulation

Dynamic particle-scale numerical simulations are used to show that the shear thickening observed in dense colloidal, or Brownian, suspensions is of a similar nature to that observed in non-colloidal suspensions, i.e., a stress-induced transition from a flow of lubricated near-contacting particles to a flow of a frictionally contacting network of particles. Abrupt (or discontinuous) shear thickening is found to be a geometric rather than hydrodynamic phenomenon; it stems from the strong sensitivity of the jamming volume fraction to the nature of contact forces between suspended particles. The thickening obtained in a colloidal suspension of purely hard frictional spheres is qualitatively similar to experimental observations. However, the agreement cannot be made quantitative with only hydrodynamics, frictional contacts and Brownian forces. Therefore the role of a short-range repulsive potential mimicking the stabilization of actual suspensions on the thickening is studied. The effects of Brownian and repulsive forces on the onset stress can be combined in an additive manner. The simulations including Brownian and stabilizing forces show excellent agreement with experimental data for the viscosity $η$ and the second normal stress difference $N_2$.

cond-mat.soft↗

arXiv2015

Non-monotonic flow curves of shear thickening suspensions

The discontinuous shear thickening (DST) of dense suspensions is a remarkable phenomenon in which the viscosity can increase by several orders of magnitude at a critical shear rate. It has the appearance of a first order phase transition between two hypothetical "states" that we have recently identified as Stokes flows with lubricated or frictional contacts, respectively. Here we extend the analogy further by means of novel stress-controlled simulations and show the existence of a non-monotonic steady-state flow curve analogous to a non-monotonic equation of state. While we associate DST with an S-shaped flow curve, at volume fractions above the shear jamming transition the frictional state loses flowability and the flow curve reduces to an arch, permitting the system to flow only at small stresses. Whereas a thermodynamic transition leads to phase separation in the coexistence region, we observe a uniform shear flow all along the thickening transition. A stability analysis suggests that uniform shear may be mechanically stable for the small Reynolds numbers and system sizes in a rheometer.

cond-mat.soft↗

arXiv2014

Shear thickening, frictionless and frictional rheologies in non-Brownian suspensions

Particles suspended in a Newtonian fluid raise the viscosity and also generally give rise to a shear-rate dependent rheology. In particular, pronounced shear thickening may be observed at large solid volume fractions. In a recent article (R. Seto, R. Mari, J. F. Morris, and M. M. Denn., Phys. Rev. Lett., 111:218301, 2013) we have considered the minimum set of components to reproduce the experimentally observed shear thickening behavior, including Discontinuous Shear Thickening (DST). We have found frictional contact forces to be essential, and were able to reproduce the experimental behavior by a simulation including this physical ingredient along with viscous lubrication. In the present article, we thoroughly investigate the effect of friction and express it in the framework of the jamming transition. The viscosity divergence at the jamming transition has been a well known phenomenon in suspension rheology, as reflected in many empirical laws for the viscosity. Friction can affect this divergence, and in particular the jamming packing fraction is reduced if particles are frictional. Within the physical description proposed here, shear thickening is a direct consequence of this effect: as the shear rate increases, friction is increasingly incorporated as more contacts form, leading to a transition from a mostly frictionless to a mostly frictional rheology. This result is significant because it shifts the emphasis from lubrication hydrodynamics and detailed microscopic interactions to geometry and steric constraints close to the jamming transition.

cond-mat.soft↗

arXiv2014

Cavity method for force transmission in jammed disordered packings of hard particles

The force distribution of jammed disordered packings has always been considered a central object in the physics of granular materials. However, many of its features are poorly understood. In particular, analytic relations to other key macroscopic properties of jammed matter, such as the contact network and its coordination number, are still lacking. Here we develop a mean-field theory for this problem, based on the consideration of the contact network as a random graph where the force transmission becomes a constraint optimization problem. We can thus use the cavity method developed in the last decades within the statistical physics of spin glasses and hard computer science problems. This method allows us to compute the force distribution $\text P(f)$ for random packings of hard particles of any shape, with or without friction. We find a new signature of jamming in the small force behavior $\text P(f) \sim f^θ$, whose exponent has attracted recent active interest: we find a finite value for $\text P(f=0)$, along with $θ=0$. Furthermore, we relate the force distribution to a lower bound of the average coordination number $\, {\bar z}_{\rm c}^{\rm min}(μ)$ of jammed packings of frictional spheres with coefficient $μ$. This bridges the gap between the two known isostatic limits $\, {\bar z}_{\rm c}(μ=0)=2D$ (in dimension $D$) and $\, {\bar z}_{\rm c}(μ\to \infty)=D+1$ by extending the naive Maxwell's counting argument to frictional spheres. The theoretical framework describes different types of systems, such as non-spherical objects in arbitrary dimensions, providing a common mean-field scenario to investigate force transmission, contact networks and coordination numbers of jammed disordered packings.

cond-mat.dis-nn↗

arXiv2013

Calculation of the Voronoi boundary for lens-shaped particles and spherocylinders

We have recently developed a mean-field theory to estimate the packing fraction of non-spherical particles [A. Baule et al., Nature Commun. (2013)]. The central quantity in this framework is the Voronoi excluded volume, which generalizes the standard hard-core excluded volume appearing in Onsager's theory. The Voronoi excluded volume is defined from an exclusion condition for the Voronoi boundary between two particles, which is usually not tractable analytically. Here, we show how the technical difficulties in calculating the Voronoi boundary can be overcome for lens-shaped particles and spherocylinders, two standard prolate and oblate shapes with rotational symmetry. By decomposing these shapes into unions and intersections of spheres analytical expressions can be obtained.

cond-mat.soft↗

arXiv2013

Discontinuous Shear Thickening of Frictional Hard-Sphere Suspensions

Discontinuous shear thickening (DST) observed in many dense athermal suspensions has proven difficult to understand and to reproduce by numerical simulation. By introducing a numerical scheme including both relevant hydrodynamic interactions and granularlike contacts, we show that contact friction is essential for having DST. Above a critical volume fraction, we observe the existence of two states: a low viscosity, contactless (hence, frictionless) state, and a high viscosity frictional shear jammed state. These two states are separated by a critical shear stress, associated with a critical shear rate where DST occurs. The shear jammed state is reminiscent of the jamming phase of granular matter. Continuous shear thickening is seen as a lower volume fraction vestige of the jamming transition.

cond-mat.soft↗

arXiv2013

Mean-field theory of random close packings of axisymmetric particles

Finding the optimal random packing of non-spherical particles is an open problem with great significance in a broad range of scientific and engineering fields. So far, this search has been performed only empirically on a case-by-case basis, in particular, for shapes like dimers, spherocylinders and ellipsoids of revolution. Here, we present a mean-field formalism to estimate the packing density of axisymmetric non-spherical particles. We derive an analytic continuation from the sphere that provides a phase diagram predicting that, for the same coordination number, the density of monodisperse random packings follows the sequence of increasing packing fractions: spheres < oblate ellipsoids < prolate ellipsoids < dimers < spherocylinders. We find the maximal packing densities of 73.1% for spherocylinders and 70.7% for dimers, in good agreement with the largest densities found in simulations. Moreover, we find a packing density of 73.6% for lens-shaped particles, representing the densest random packing of the axisymmetric objects studied so far.

cond-mat.soft↗

arXiv2011

Dynamical transition of glasses: from exact to approximate

We introduce a family of glassy models having a parameter, playing the role of an interaction range, that may be varied continuously to go from a system of particles in d dimensions to a mean-field version of it. The mean-field limit is exactly described by equations conceptually close, but different from, the Mode-Coupling equations. We obtain these by a dynamic virial construction. Quite surprisingly we observe that in three dimensions, the mean-field behavior is closely followed for ranges as small as one interparticle distance, and still qualitatively for smaller distances. For the original particle model, we expect the present mean-field theory to become, unlike the Mode-Coupling equations, an increasingly good approximation at higher dimensions.

cond-mat.stat-mech↗

arXiv2011

Low energy modes and Debye behaviour in a colloidal crystal

We study the vibrational spectrum and the low energy modes of a three dimensional colloidal crystal using confocal microscopy. This is done in a two-dimensional cut through a three-dimensional crystal. We find that the observed density of states is incompatible with the standard Debye form in either two or three dimensions. These results are confirmed by numerical simulations. We show that an effective theory for the projections of the modes onto the two-dimensional cut describes the experimental and simulation data in a satisfactory way.

cond-mat.soft↗