Bulbul Chakraborty

Force transmission at large length scales is crucial for such biological functions as cell motility and morphogenesis. The networks that transmit these forces are malleable, patterned by active forces generated at the microscale by biological motors. In this paper we explore a simple model of a non-linear fiber network which has only two modes of deformation, but exhibits diverse mechanical phases with distinct large-scale response, tuned by the strength of a microscopic force dipole. We demonstrate, numerical simulations, that the network is remodeled by organized patterns of buckling. In addition, we use a mechanical screening theory of applied forces to extract an effective parameter that characterizes the spatial response of the stress field. This parameter shows strong variations that accompany changes in the buckling pattern. The emergent behavior at large length scales indicates that the medium screens out the details of the force dipole.

Tuning shear thickening behavior is a longstanding problem in the field of dense suspensions. Acoustic perturbations offer a convenient way to control shear thickening in real time, opening the door to a new class of smart materials. However, complete control over shear thickening requires a quantitative description for how suspension viscosity varies under acoustic perturbation. Here, we achieve this goal by experimentally probing suspensions with acoustic perturbations and incorporating their effect on the suspension viscosity into a universal scaling framework where the viscosity is described by a scaling function, which captures a crossover from the frictionless jamming critical point to a frictional shear jamming critical point. Our analysis reveals that the effect of acoustic perturbations may be explained by the introduction of an effective interparticle repulsion whose magnitude is roughly equal to the acoustic energy density. Furthermore, we show how this scaling framework may be leveraged to produce explicit predictions for the viscosity of a dense suspension under acoustic perturbation. Our results demonstrate the utility of the scaling framework for experimentally manipulating shear thickening systems.

Dense non-Brownian suspensions with conservative repulsive forces between the particles are known to exhibit shear thickening, where viscosity increases with applied stress due to a change in the dominant stress mechanism. At low stress, repulsion maintains liquid films that
lubricate particle interactions, while higher stress overcomes the repulsion to generate frictional contacts and leads to greater flow resistance.
Here, shear-thickened suspensions are studied in stress-controlled simulations incorporating hydrodynamic, electrostatic double-layer repulsion, and frictional forces; two-dimensional monolayers are studied for monodisperse and bidisperse suspensions with size ratios δ ¼ as=al
from 1.0 to 4.0, where as and al are the small and large particle radii. Small-particle fractions ζ ¼ fs=f ¼ 0:25, 0:50, and 0:75 are considered. Total area fractions of 0:71 f 0:82 are studied, with the larger values at greater size ratios. Flow curves for mono- and bidisperse
systems under varying stress are analyzed, along with detailed structural comparisons for different interparticle friction. We examine the
approach to shear jamming, through the emergence of rigid local clusters generated by the reduction of degrees of freedom by frictional contacts. The variance of the fraction of particles in rigid clusters increases sharply near the jamming solid fraction, consistent with a secondorder phase transition description of the phenomenon. The contact fabric tensor is determined to provide a measure of the structural anisotropy.

We demonstrate that the spatial correlations of microscopic stresses in 2D model colloidal gels obtained in computer simulations can be quantitatively
described by the predictions of a theory for emergent elasticity of pre-stressed solids (vector charge theory). By combining a rigidity analysis with the characterization provided by the stress correlations, we show that the theoretical predictions are able to distinguish rigid from floppy gels, and quantify that distinction in terms of the size of a pinch-point singularity emerging at large length scales, which, in the theory, directly derives from the constraints imposed by mechanical equilibrium on the internal forces. We also use the theoretical predictions to investigate the coupling between stress-transmission and rigidity, and we explore the possibility of a Debye-like screening mechanism that would modify the theory predictions below a characteristic length scale.

We demonstrate that the spatial correlations of microscopic stresses in 2D model colloidal gels obtained in computer simulations can be quantitatively described by the predictions of a theory for emergent elasticity of pre-stressed solids (vector charge theory). By combining a rigidity analysis with the characterization provided by the stress correlations, we show that the theoretical predictions are able to distinguish rigid from floppy gels, and quantify that distinction in terms of the size of a pinch-point singularity emerging at large length scales, which, in the theory, directly derives from the constraints imposed by mechanical equilibrium on the internal forces. We also use the theoretical predictions to investigate the coupling between stresstransmission and rigidity, and we explore the possibility of a Debye-like screening mechanism that would modify the theory predictions below a characteristic length scale. The loss of rigidity in particulate gels can be quantified by the disappearance of a characteristic pinch-point singularity in the gel stress-stress correlation function.

We study how the rigidity transition in a triangular lattice changes as a function of anisotropy by preferentially filling bonds on the lattice in one direction. We discover that the onset of rigidity in anisotropic spring networks on a regular triangular lattice arises in at least two steps, reminiscent of the two-step melting transition in two dimensional crystals. In particular, our simulations demonstrate that the percolation of stress-supporting bonds happens at different critical volume fractions along different directions. By examining each independent component of the elasticity tensor, we determine universal exponents and develop universal scaling functions to analyze isotropic rigidity percolation as a multicritical point. Our crossover scaling approach is applicable to anisotropic biological materials ( cellular cytoskeletons, extracellular networks of tissues like tendons), and extensions to this analysis are important for the strain stiffening of these materials.

The onset and growth of rigid clusters in a two-dimensional (2D) suspension in shear flow are studied by numerical simulations. The suspension exhibits the lubricated-to-frictional rheology transition, but the key results here are for stresses above the levels that cause extreme shear thickening. At large solid fraction, ϕ, but below the stress-dependent jamming fraction, we find a critical ϕ_{c}(σ,μ) where σ is a dimensionless shear stress and μ is the interparticle friction coefficient. For ϕ>ϕ_{c}, the proportion of particles in rigid clusters grows sharply, as f_{rig}∼|ϕ−ϕ_{c}|^{β} with β=1/8. The fluctuations in the fraction of particles in rigid clusters yield a susceptibility measure χ_{rig}∼|ϕ−ϕ_{c}|^{−γ} with γ=7/4. The system is thus found to exhibit criticality. The results are shown to depend on an effective field h(μ), which provides data collapse near ϕ_{c} for both f_{rig} and χ_{rig}. This behavior occurs over a range of stresses, with ϕ_{c}(σ,μ) increasing as the stress decreases.

Recently, we proposed a universal scaling framework that shows shear thickening in dense suspensions is governed by the crossover between two critical points: one associated with frictionless isotropic jamming and a second corresponding to frictional shear jamming. Here, we show that orthogonal perturbations to the flows, an effective method for tuning shear thickening, can also be folded into this universal scaling framework. Specifically we show that the effect of adding orthogonal shear perturbations can be incorporated into the scaling variable via a multiplicative function, determined through our measurements, to achieve collapse of the entire thickening and dethickening dataset onto a single universal curve. We then show that this universal scaling framework can be used to control the phase behavior in thickening and jamming suspensions.

Nearly, all dense suspensions undergo dramatic and abrupt thickening transitions in their flow behavior when sheared at high stresses. Such transitions occur when the dominant interactions between the suspended particles shift from hydrodynamic to frictional. Here, we interpret abrupt shear thickening as a precursor to a rigidity transition and give a complete theory of the viscosity in terms of a universal crossover scaling function from the frictionless jamming point to a rigidity transition associated with friction, anisotropy, and shear. Strikingly, we find experimentally that for two different systems—cornstarch in glycerol and silica spheres in glycerol—the viscosity can be collapsed onto a single universal curve over a wide range of stresses and volume fractions. The collapse reveals two separate scaling regimes due to a crossover between frictionless isotropic jamming and frictional shear jamming, with different critical exponents. The material-specific behavior due to the microscale particle interactions is incorporated into a scaling variable governing the proximity to shear jamming, that depends on both stress and volume fraction. This reformulation opens the door to importing the vast theoretical machinery developed to understand equilibrium critical phenomena to elucidate fundamental physical aspects of the shear thickening transition.