arXiv subjects

Abhinendra Singh

Publications and source records attributed to Abhinendra Singh.

26 records · Page 2Linked to original sources

arXiv2019

Interaction network analysis in shear thickening suspensions

Dense, stabilized, frictional particulate suspensions in a viscous liquid undergo increasingly strong continuous shear thickening (CST) as the solid packing fraction, $ϕ$, increases above a critical volume fraction, and discontinuous shear thickening (DST) is observed for even higher packing fractions. Recent studies have related shear thickening to a transition from mostly lubricated to predominantly frictional contacts with the increase in stress. The rheology and networks of frictional forces from two and three-dimensional simulations of shear-thickening suspensions are studied. These are analyzed using measures of the topology of the network, including tools of persistent homology. We observe that at low stress the frictional interaction networks are predominantly quasi-linear along the compression axis. With an increase in stress, the force networks become more isotropic, forming loops in addition to chain-like structures. The topological measures of Betti numbers and total persistence provide a compact means of describing the mean properties of the frictional force networks and provide a key link between macroscopic rheology and the microscopic interactions. A total persistence measure describing the significance of loops in the force network structure, as a function of stress and packing fraction, shows behavior similar to that of relative viscosity and displays a scaling law near the jamming fraction for both dimensionalities simulated.

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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.

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arXiv2018

From yielding to shear jamming in a cohesive frictional suspension

Simulations are used to study the steady shear rheology of dense suspensions of frictional particles exhibiting discontinuous shear thickening and shear jamming, in which finite-range cohesive interactions result in a yield stress. We develop a constitutive model that combines yielding behavior and shear thinning at low stress with the frictional shear thickening at high stresses, in good agreement with the simulation results. This work shows that there is a distinct difference between solids below the yield stress and in the shear-jammed state, as the two occur at widely separated stress levels, separated by a region of stress in which the material is flowable.

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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.

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arXiv2015

A contact model for sticking of adhesive meso-particles

The interaction between visco-elasto-plastic and adhesive particles is the subject of this study, where "meso-particles" are introduced, i.e., simplified particles, whose contact mechanics is not taken into account in all details. A few examples of meso-particles include agglomerates or groups of primary particles, or inhomogeneous particles with micro-structures of the scale of the contact deformation, such as core-shell materials. A simple, flexible contact model for meso-particles is proposed, which allows to model the bulk behavior of assemblies of many particles in both rapid and slow, quasi-static flow situations. An attempt is made to categorize existing contact models for the normal force, discuss all the essential mechanical ingredients that must enter the model (qualitatively) and finally solve it analytically. The model combines a short-ranged, non-contact part (resembling either dry or wet materials) with an elaborate, visco-elasto-plastic and adhesive contact law. Using energy conservation arguments, an analytical expression for the coefficient of restitution is derived in terms of the impact velocity (for pair interactions or, equivalently, without loss of generality, for quasi-static situations in terms of the maximum overlap or confining stress). Adhesive particles (or meso-particles) stick to each other at very low impact velocity, while they rebound less dissipatively with increasing velocity, in agreement with previous studies. For even higher impact velocities an interesting second sticking and rebound regime is reported. The low velocity sticking is due to non-contact adhesive forces, the first rebound regime is due to stronger elastic and kinetic energies with little dissipation, while the high velocity sticking is generated by the non-linearly increasing, history dependent plastic dissipation and adhesive contact force.

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arXiv2015

Micro-macro transition and simplified contact models for wet granular materials

Wet granular materials in a quasi-static steady state shear flow have been studied with discrete particle simulations. Macroscopic quantities, consistent with the conservation laws of continuum theory, are obtained by time averaging and spatial coarse-graining. Initial studies involve understanding the effect of liquid content and liquid properties like the surface tension on the macroscopic quantities. Two parameters of the liquid bridge contact model have been studied as the constitutive parameters that define the structure of this model (i) the rupture distance of the liquid bridge model, which is proportional to the liquid content, and (ii) the maximum adhesive force, as controlled by the surface tension of the liquid. Subsequently a correlation is developed between these micro parameters and the steady state cohesion in the limit of zero confining pressure. Furthermore, as second result, the macroscopic torque measured at the walls, which is an experimentally accessible parameter, is predicted from our simulation results as a dependence on the micro-parameters. Finally, the steady state cohesion of a realistic non-linear liquid bridge contact model scales well with the steady state cohesion for a simpler linearized irreversible contact model with the same maximum adhesive force and equal energy dissipated per contact.

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arXiv2014

Role of gravity or confining pressure and contact stiffness in granular rheology

The steady shear rheology of granular materials is investigated in slow quasi-static states and inertial flows. The effect of the gravity field and contact stiffness, which are conventionally trivialized is the focus of this study. Series of Discrete Element Method simulations are performed on a weakly frictional granular assembly in a split-bottom geometry considering various gravity fields and contact stiffnesses. While traditionally the inertial number, i.e., the ratio of stress to strain-rate timescales describes the flow rheology, we find that a second dimensionless number, the ratio of softness and stress timescales, must also be included to characterize the bulk flow behavior. For slow, quasi-static flows, the density increases while the macroscopic friction decreases with respective increase in particle softness and gravity. This trend is added to the $μ(I)$ rheology and can be traced back to the anisotropy in the contact network, displaying a linear correlation between macroscopic friction and deviatoric fabric in the steady state. Interestingly, the linear relation holds when the external rotation rate is increased for a given gravity field and contact stiffness.

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arXiv2014

Effect of cohesion on shear banding in quasi-static granular material

It is widely recognized in particle technology that adhesive powders show a wide range of different bulk behavior due to the peculiarity of the particle interaction. We use Discrete Element simulations to investigate the effect of contact cohesion on the steady state of dense powders in a slowly sheared split-bottom Couette cell, which imposes a wide stable shear band. The intensity of cohesive forces can be quantified by the {\em granular Bond number} ($Bo$), namely the ratio between maximum attractive force and average force due to external compression. We find that the shear banding phenomenon is almost independent of cohesion for Bond numbers $Bo<1$, but for $Bo \ge 1$ cohesive forces start to play an important role, as both width and center position of the band increase for $Bo > 1$. Inside the shear band, the mean normal contact force is always independent of cohesion and depends only on the confining stress. In contrast, when the behavior is analyzed focusing on the eigen-directions of the local strain rate tensor, a dependence on cohesion shows up. Forces carried by contacts along the compressive and tensile directions are symmetric about the mean force (larger and smaller respectively), while the force along the third, neutral direction follows the mean force. This anisotropy of the force network increases with cohesion, just like the heterogeneity in all (compressive, tensile and neutral) directions.

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