arXiv subjects

Abhinendra Singh

Publications and source records attributed to Abhinendra Singh.

At least 19 recordsLinked to original sources

arXiv2026

Investigating the Nature of Discontinuous Shear Thickening: Beyond a Mean-Field Description

Dense suspensions can undergo a dramatic increase in viscosity at a critical value of the shear stress. This phenomenon, termed discontinuous shear thickening (DST), has been attributed to an increase in the fraction of particle interactions becoming frictional with increasing shear stress, and a successful mean-field theory has been developed to explain various accompanying rheological properties. On a microscopic scale, however, conventional structural analysis measures such as the grain-position pair correlation function show no significant changes with the onset of DST, though recent work has shown that similar analysis in the dual space of contact forces does lead to marked changes at this transition. Furthermore, experimental results have suggested the existence of higher-order microscopic correlations and the importance of incorporating fluctuations away from a mean-field description. To this end, we use a higher-order cluster analysis tool to study the force networks obtained from simulations of dense suspensions to construct an effective interaction potential in force space. We show that there are significant changes occurring in this potential as a function of density and stress close to DST. We discuss the implications of these observations on an emergent field theory of the DST transition.

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arXiv2026

Recent Modeling Advances in Dense Suspension Rheology

Dense suspensions of particles dispersed in liquids are central to industrial and geophysical processes and serve as model systems for out-of-equilibrium soft matter. At high particle concentrations, they exhibit stress-dependent rheology, including discontinuous shear thickening and shear jamming, arising from frictional contacts. Nonlinear physics arises from the interplay among direct contacts, interfacial chemistry, and fluid-mediated hydrodynamics. The relative importance of these mechanisms depends on the particle properties and flow conditions, making predictive modeling inherently multi-scale and, therefore, computationally challenging. Recent advances in computational methods have transformed our ability to simulate the physics of dense suspensions across different scales. In this Perspective, we primarily focus on state-of-the-art simulation frameworks that integrate the mechanics of dry granular materials, mediated by contact friction, with suspension hydrodynamics to provide predictive models of dense suspension rheology. We highlight recent computational developments for simulating dense, predominantly non-Brownian suspensions in the viscous limit at varying levels of fidelity, ranging from particle-resolved to continuum models, as well as models that investigate their mesoscale organization during flow. Together, these approaches reveal a hierarchical structure in which microscale constraints give rise to mesoscale frictional networks that ultimately govern the macroscopic flow. While our emphasis is on dense suspensions governed by near-field hydrodynamics and frictional interactions, we also briefly discuss complementary grid-based methods that can account for complex geometries and particle properties, and also enable continuum-scale descriptions.

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arXiv2026

Constraint ratio controls viscosity in shear thickening suspensions

The dramatic viscosity increase observed in dense suspensions under shear poses a major challenge in our understanding of how microscopic contact mechanics translate into macroscopic flow resistance. Here, we introduce a constraint-counting model that incorporates friction and dimensionality naturally without additional assumptions and allows for collapsing of rheological data onto a universal master curve. In this model, we borrow ideas from dry granular jamming physics and classify contacts as either locked or non-locked to define a single state variable, the constraint ratio, which measures the average strength of mechanical constraint per particle. By identifying the constraint ratio as the key control parameter, our framework provides a unifying route toward predictive modeling and rational design of shear-thickening materials.

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arXiv2026

Graph neural network for multitask prediction of rheological and microstructural behavior in suspensions

Fast prediction of suspension rheology is fundamental for optimizing process efficiency and performance in numerous industrial settings. However, traditional simulations are computationally demanding due to explicit evaluation of contact networks and stress tensors in dense regimes approaching shear thickening and jamming. This study presents a microstructure-informed multitask learning framework based on the graph neural network (GNN) that learns an implicit mapping between particle configurations and emergent microstructural and rheological properties of suspensions. This model simultaneously predicts particle pressure $Π$, viscosity $η$, and friction coordination $Z_μ$, in a dynamic steady-state, without explicit knowledge of interparticle forces. Here, semi-dilute to dense suspension systems in 2D were simulated across a wide range of shear stresses $σ$, spanning continuous, discontinuous shear thickening, and shear-jamming conditions. The trained models demonstrated high correlation coefficients ($R^2$ = 0.99) with narrow mean absolute error for packing fractions up to $ϕ\le ϕ_J^μ$ for all predictive targets. However, prediction scatter increases near jamming conditions, attributed to inherent fluctuations in suspension behavior as the critical packing fraction is approached, yet predictions remain in excellent agreement, closely following the trend of the simulated flow curves across stress evolution. Once trained, the model can infer rheological responses directly from structural topology, avoiding explicit stress evaluation during prediction. The approach yields computationally efficient mesoscale surrogates for accelerated simulation with potential for real-time exploration of particulate suspension behavior.

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arXiv2025

Quick starch guide: A perspective on shear thickening in dense non-Brownian suspensions

In this article, we provide a brief perspective on recent developments in the study of shear thickening in dense suspensions. We give a rapid overview of the state of the art and discuss current models aiming to describe this particular rheology. Although most of the experiments and simulation studies are conducted in "ideal" flows, where the sample is confined without an open boundary condition, we have decided to highlight more realistic flow conditions. We further provide an overview on how to relate the recently proposed constitutive models to these more practical flow conditions like pipe flow or flow down an incline.

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arXiv2025

Frictional Contact Network in Dense Suspension Flow

Dense particulate suspensions often exhibit a dramatic increase in viscosity in response to external deformation. This shear thickening behavior has been related to a transition from lubricated, unconstrained pairwise motion to a frictional contact network (FCN) at high stresses. Here, we study the characteristics of the FCN formed during shear thickening to investigate the role of constraints, emphasizing the impact of resistance to gear-like rolling. We contrast the FCN formed by sliding friction alone with that formed by particles with sliding and rolling constraints. Particles with sliding constraints only form a highly interconnected network with primary force chains in the compressive direction, which requires orthogonal support from other force chains. However, orthogonal support is not required for mechanical stability when particles have both sliding and rolling constraints. In addition, the force chains appear linear and longer, reducing the jamming volume fraction for rough/faceted particles. Finally, we propose a novel mechanical stability picture for rough/faceted particles with sliding and rolling constraints, which is crucial for understanding the flow behavior of real-life suspensions.

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arXiv2025

Robust Prediction of Frictional Contact Network in Near-Jamming Suspensions Employing Deep Graph Neural Networks

The viscosity of the suspension consisting of fine particles dispersed in a Newtonian liquid diverges close to the jamming packing fraction. The contact microstructure in suspensions governs this macroscopic behavior in the vicinity of jamming through a frictional contact network (FCN). FCN is composed of mechanical load-bearing contacts that lead to the emergence of rigidity near the jamming transition. The stress transmission and network topology, in turn, depend sensitively on constraints on the relative motion of the particles. Despite their significance, predicting the FCN, especially close to jamming conditions, remains challenging due to experimental and computational impediments. This study introduces a cost-effective machine learning approach to predict the FCN using a graph neural network (GNN), which inherently captures hidden features and underlying patterns in dense suspension by mapping interparticle interactions. Employing a variation of GNN called the Deep Graph Convolutional Network (DeepGCN) trained on data-driven simulations, this study demonstrates robust generalization and extrapolation capabilities, accurately predicting FCNs in systems with divergent flow parameters and phase spaces, despite each being trained exclusively on a single condition. The study covers a wide range of phase space, from semi-dilute to jammed states, spanning transient to steady states, while systematically varying parameters such as shear stress ($σ_{xy}$), packing fraction($ϕ$) and sliding and rolling friction (${μ_s, μ_r}$). The results of this research pave the way for innovative transferable techniques in predicting the properties of particulate systems, offering new avenues for advancement in material science and related fields.

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arXiv2025

Scalability of Graph Neural Network in Accurate Prediction of Frictional Contact Network in Suspensions

Dense suspensions often exhibit shear thickening, characterized by a dramatic increase in viscosity under large external forcing. This behavior has recently been linked to the formation of a system-spanning frictional contact network (FCN), which contributes to increased resistance during deformation. However, identifying these frictional contacts poses experimental challenges and is computationally expensive. This study introduces a Graph Neural Network (GNN) model designed to accurately predict FCNs in two dimensional simulations of dense shear thickening suspensions. The results demonstrate the robustness and scalability of the GNN model across various stress levels $(σ)$, packing fractions$(ϕ)$, system sizes, particle size ratios$(Δ)$, and amount of smaller particles. The model is further able to predict both the occurrence and structure of the FCN. The presented model is accurate and interpolates and extrapolates to conditions far from its control parameters. This machine learning approach provides an accurate, lower cost, and faster predictions of suspension properties compared to conventional methods, while it is trained using only small systems. Ultimately, the findings in this study pave the way for predicting frictional contact networks in real-life large-scale polydisperse suspensions, for which theoretical models are largely limited owing to computational challenges.

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arXiv2025

Topological insights into dense frictional suspension rheology: Third order loops drive discontinuous shear thickening

Dense suspensions exhibit significant viscosity changes under external deformation, a phenomenon known as shear thickening. Recent studies have identified a stress-induced transition from lubricated, unconstrained interactions to frictional contacts, which play a crucial role in shear thickening. This work investigates the rheological behavior and contact network evolution during continuous and discontinuous shear thickening (CST and DST) in two-dimensional simulations. We find that at low stress, during weak thickening, the frictional contact network is composed of quasilinear chains along the compression axis. With increasing stress, the contact network becomes more isotropic, and forms loop-like structures. We show that third-order loops within the frictional contact network are key to this behavior. Our findings revealed a strong correlation between the number of edges in the third-order loops and the viscosity of the suspension. Notably, this relationship remains independent of the packing fraction, applied stress, and interparticle friction, highlighting the fundamental role of the mesoscale network topology in governing macroscopic rheology.

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arXiv2024

Rheology of bidisperse non-Brownian suspensions

We study the rheology of bidisperse non-Brownian suspensions using particle-based simulation, mapping the viscosity as a function of the size ratio of the species, their relative abundance, and the overall solid content. The variation of the viscosity with applied stress exhibits shear thickening phenomenology irrespective of composition, though the stress-dependent limiting solids fraction governing the viscosity and its divergence point are non-monotonic in the mixing ratio. Contact force data demonstrate an asymmetric exchange in dominant stress contribution from large-large to small-small particle contacts as the mixing ratio of the species evolves. Combining a prior model for shear thickening with one for composition-dependent jamming, we obtain a full description of the rheology of bidisperse non-Brownian suspensions capable of predicting effects such as the viscosity reduction observed upon adding small particle fines to a suspension of large particles.

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arXiv2023

Hidden hierarchy in the rheology of dense suspensions

Dense suspensions of fine particles are significant in numerous biological, industrial, and natural phenomena. They also provide an ideal tool to develop statistical mechanics description for out-of-equilibrium systems. Predicting the bulk response of such materials has been challenging since these systems often undergo liquid-solid transitions upon a small change in solid concentration or applied loading. Developing an understanding of the mechanisms that drive these phenomena has over the last several years led to a surge in research activity at the intersection of fluid mechanics, granular materials, driven disordered systems, tribology, and soft condensed matter physics. One central aspect that emerged is that these phenomena are due to a shear-activated or deactivated network of contacts between particles. The perspective briefly presents the current state of understanding and challenges associated with relating the flow of material at the bulk scale with the microscopic physics at the particle scale.

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arXiv2023

Scaling relations between viscosity and diffusivity in shear-thickening suspensions

Dense suspensions often exhibit a dramatic response to large external deformation. The recent body of work has related this behavior to transition from an unconstrained lubricated to a constrained frictional state. Here, we use numerical simulations to study the flow behavior and shear-induced diffusion of frictional non-Brownian spheres in two dimensions under simple shear flow. We first show that both viscosity $η$ and diffusivity $D/\dotγ$ of the particles increase at characteristic shear stress, which is associated with lubrication to frictional transition. Subsequently, we propose a one-to-one relation between viscosity and diffusivity using the length scale $ξ$ associated with the size of collective motions (rigid clusters) of the particles. We demonstrate that $η$ and $D/\dotγ$ are controlled by $ξ$ in two distinct flow regimes, i.e. in the frictionless and frictional states, where the one-to-one relation is described as a crossover from $D/\dotγ\simη$ ({frictionless}) to $η^{1/3}$ ({frictional}). We also confirm the proposed power laws are insensitive to the interparticle friction and system size.

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arXiv2021

Stress-activated Constraints in Dense Suspension Rheology

Dispersing small particles in a liquid can produce surprising behaviors when the solids fraction becomes large: rapid shearing drives these systems out of equilibrium and can lead to dramatic increases in viscosity (shear-thickening) or even solidification (shear jamming). These phenomena occur above a characteristic onset stress when particles are forced into frictional contact. Here we show via simulations how this can be understood within a framework that abstracts details of the forces acting at particle-particle contacts into general stress-activated constraints on relative particle movement. We find that focusing on just two constraints, affecting sliding and rolling at contact, can reproduce the experimentally observed shear thickening behavior quantitatively, despite widely different particle properties, surface chemistries, and suspending fluids. Within this framework parameters such as coefficients of sliding and rolling friction can each be viewed as a proxy for one or more forces of different physical or chemical origin, while the parameter magnitudes indicate the relative importance of the associated constraint. In this way, a new link is established that connects features observable in macroscale rheological measurements to classes of constraints arising from micro- or nano-scale properties.

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arXiv2020

Shear thickening and jamming of dense suspensions: the "roll" of friction

Particle-based simulations of discontinuous shear thickening (DST) and shear jamming (SJ) suspensions are used to study the role of stress-activated constraints, with an emphasis on resistance to gear-like rolling. Rolling friction decreases the volume fraction required for DST and SJ, in quantitative agreement with real-life suspensions with adhesive surface chemistries and "rough" particle shapes. It sets a distinct structure of the frictional force network compared to only sliding friction, and from a dynamical perspective leads to an increase in the velocity correlation length, in part responsible for the increased viscosity. The physics of rolling friction is thus a key element in achieving a comprehensive understanding of strongly shear-thickening materials.

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arXiv2020

Structure and dynamics of hydrodynamically interacting finite-size Brownian particles in a spherical cavity: spheres and cylinders

The structure and dynamics of confined suspensions of particles of arbitrary shape is of interest in multiple disciplines, from biology to engineering. Theoretical studies are often limited by the complexity of long-range particle-particle and particle-wall forces, including many-body fluctuating hydrodynamic interactions. Here, we report a computational study on the diffusion of spherical and cylindrical particles confined in a spherical cavity. We rely on an Immersed-Boundary General geometry Ewald-like method to capture lubrication and long-range hydrodynamics, and include appropriate non-slip conditions at the confining walls. A Chebyshev polynomial approximation is used to satisfy the fluctuation-dissipation theorem for the Brownian suspension. We explore how lubrication, long-range hydrodynamics, particle volume fraction and shape affect the equilibrium structure and the diffusion of the particles. It is found that once the particle volume fraction is greater than $10\%$, the particles start to form layered aggregates that greatly influence particle dynamics. Hydrodynamic interactions strongly influence the particle diffusion by inducing spatially dependent short-time diffusion coefficients, stronger wall effects on the particle diffusion towards the walls, and a sub-diffusive regime --caused by crowding-- in the long-time particle mobility. The level of asymmetry of the cylindrical particles considered here is enough to induce an orientational order in the layered structure, decreasing the diffusion rate and facilitating a transition to the crowded mobility regime at low particle concentrations. Our results offer fundamental insights into the diffusion and distribution of globular and fibrillar proteins inside cells.

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arXiv2020

Shape induced segregation and anomalous particle transport under spherical confinement

Colloid or nanoparticle mobility under confinement is of central importance to a wide range of physical and biological processes. Here, we introduce a minimal model of particles in a hydrodynamic continuum to examine how particle shape and concentration affect the transport of particles in spherical confinement. Specifically, an immersed boundary-General geometry Ewald-like approach is adopted to simulate the dynamics of spheres and cylinders under the influence of short-and long-range fluctuating hydrodynamic interactions with appropriate non-slip conditions at the confining walls. An efficient $\it{O(N)}$ parallel finite element algorithm is used, thereby allowing simulations at high concentrations, while a Chebyshev polynomial approximation is implemented in order to satisfy the fluctuation-dissipation theorem. A concentration-dependent anomalous diffusion is observed for suspended particles. It is found that introducing cylinders in a background of spheres, i.e. particles with a simple degree of anisotropy, has a pronounced influence on the structure and dynamics of the particles. First, increasing the fraction of cylinders induces a particle segregation effect, where spheres are pushed towards the wall and cylinders remain near the center of the cavity. This segregation leads to lower mobility for the spheres relative to that encountered in a system of pure spheres at the same volume fraction. Second, the diffusive-to-anomalous transition and the degree of anomaly--quantified by the power-law exponent in the mean square displacement vs. time relation-both increase as the fraction of cylinders becomes larger. These findings are of relevance for studies of diffusion in the cytoplasm, where proteins exhibit a distribution of size and shapes that could lead to some of the effects identified in the simulations reported here.

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arXiv2019

Stress fluctuations and shear thickening in dense granular suspensions

We experimentally investigate the rheology and stress fluctuations of granules densely suspended in silicone oil. We find that both thickening strength and stress fluctuations significantly weaken with oil viscosity $η_0$. Comparison of our rheological results to the Wyart-Cates model for describing different dynamic jamming states suggests a transition from frictional contacts to lubrication interactions as $η_0$ increases. To clarify the contribution from viscous interactions to the rheology, we systematically measure stress fluctuations in various flow states. Reduction of stress fluctuations with $η_0$ indicates that a strong lubrication layer greatly inhibits force correlations among particles. Measuring stress fluctuations in the strong shear thickening regime, we observe a crossover from asymmetric Gamma to symmetric Gaussian distributions and associated with it a decrease of lateral (radial) correlation length $ξ$ with increasing shear rate.

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arXiv2019

Shear jamming and fragility in dense suspensions

The phenomenon of shear-induced jamming is a factor in the complex rheological behavior of dense suspensions. Such shear-jammed states are fragile, i.e., they are not stable against applied stresses that are incompatible with the stress imposed to create them. This peculiar flow-history dependence of the stress response is due to flow-induced microstructures. To examine jammed states realized under constant shear stress, we perform dynamic simulations of non-Brownian particles with frictional contact forces and hydrodynamic lubrication forces. We find clear signatures that distinguish these fragile states from the more conventional isotropic jammed states.

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