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Uniaxial compression of a strongly aggregated colloidal dispersion.: The image on the left is taken from the simulation while the schematic on the right shows the structure of the particle network that contains flocs, which are formed by aggregation of particles. The correlation length of the flocs is identified as the end-to-end distance of chains, q. The shaded particles in the flocs are the elastically active particles in the chain that support stress. (Soft Matter 12 (47), 9402-9406 )

1. Yielding in a Strongly Aggregated Colloidal Gel: Simulation, Theory and Experiments

Consolidation of colloidal dispersions under external load is a complex process involving inter-particle interactions, thermal forces and hydrodynamics. Despite its importance in diverse industrial applications, past studies involving experiments, scaling approaches and simulations are yet to provide a comprehensive understanding of how the microstructure determines the mechanical response in three dimensional colloidal gels. In our previous work, a constitutive model is developed which accounts for the microstructural details and predicts the mechanical response under slow, uniaxial compression of a strongly aggregated colloidal gel both in two and three dimensions. The particle network assumes a fractal structure that is independent of the strength of inter-particle interactions. While the yield strain changes negligibly during the entire process, the yield stress increases by several orders of magnitude. The predicted yield stress and strain are in close agreement with those observed in simulations and experiments with diverse colloidal systems, suggesting a universality in the consolidation process. Although we have been able to successfully model the consolidation process, there is still a lot of room to improve upon the theory . We currently aim to do large scale simulations as well as experiments to understand the mechanical properties of the colloidal gel under different loading conditions.

2. Study of Frictional Granular Matter via Discrete Element Simulation, Theory and Experiments

Granular World

Granular matter is a many body complex system and due to its large size, it does not move under the ambient thermal fluctuations unlike the colloidal particles. As the thermal fluctuations are negligible for granular matter, it can not explore different points in phase space. External driving is required to move the system from one point to another. This system is also not conservative as it dissipates energy via friction. One of the interesting features of granular matter is that it is neither solid nor fluid. Depending on the external driving and the volume fraction of the constituent particles, the system can either flow or get stuck. When the volume fraction increases above a threshold, the system jams into a disordered solid and posses a finite yield stress. This transition from fluid to solid is nothing but the famous Jamming transition where a many body system jam into an amorphous solid with no clear structural signature that is observed in an ordinary phase transition.

Training, Memory and Universal Scaling in non-equilibrium Amorphous Matter:

We carry out experimental and theoretical investigation of cyclic training of amorphous frictional granular assemblies, with special attention to memory formation and retention. Measures of dissipation and compactification are introduced, culminating with a proposed scaling law for the reducing dissipation and increasing memory. This scaling law is expected to be universal, and insensitive to the details of the elastic and frictional interactions between the granules.

Memory in crude sense is the ability of any system to remember its past history which can either be read out in later times or be erased. Now, studying the memory formation in materials is of broad importance as it can be observed across many disciplines: physics, chemistry, biology and computer science. Memory is typically linked to the transient response of non-equilibrium systems as the system in equilibrium forgets its past evolution. There can be many types of memory observed for diverse systems: glasses can remember their past history of deformation, rubbers and rocks can retain the memory of the largest strain amplitude, magnets can have return point memory. Although memory formation is so common in non-equilibrium systems, there is no clear and coherent understanding behind the formation of the memory and its connection to the self-organization of system constituents. So, we will undertake large scale simulations as well as careful experiments to unravel the physics behind memory formation and random organization in cyclically trained non-equilibrium systems (like non-Brownian suspension, granular materials and many more) and find efficient ways to train a disordered system to produce a specific mechanical response. The study will also shed light on the role of noise in formation of multiple transient memories in these types of systems.

A succession of hysteresis loops as measured in the numerical simulation of granular matter. Blue symbols are compression legs and red symbols decompression legs.(EPL (Europhysics Letters) 122 (3), 38003 )

Force Distributions in Frictional Granular Media:

In compressed frictional amorphous granular media the external pressure is balanced by normal and tangential (frictional) forces acting at the contacts between the grains. The forces are very inhomogeneous, with a wide distribution of magnitude, resulting in the appearance of force chains which represent the largest forces which are percolating from wall to wall.

We perform a joint experimental and theoretical investigation of the probability distribution functions (PDFs) of the normal and tangential (frictional) forces in amorphous frictional media. We consider both the joint PDF of normal and tangential forces together, and the marginal PDFs of normal forces separately and tangential forces separately. A maximum entropy formalism is utilized for all these cases after identifying the appropriate constraints. We find excellent agreements between experimental and simulation data. The proposed joint PDF predicts giant slip events at low pressures, again in agreement with observations.

Although the maximum entropy formalism was a great success for the case we considered, it will be interesting to find out whether same formalism works for different loading scenarios (shear and oscillations) or not. We also aim to carry out numerical simulations as well as granular experiments to check the range of applicability of this formalism.

A typical visualization of the force chains that hold together a compressed assembly of frictional granular photoelastic disks in two dimensions.(Physical Review E 98 (1), 012905 )

Plot of the joint probability of normal and tangential forces at high(top) and low pressure(bottom) (Physical Review E 98 (1), 012905 )

Diffusion in Agitated Frictional Granular Matter Near the Jamming Transition:

We study agitated frictional disks in two dimensions with the aim of developing a scaling theory for their diffusion over time. As a function of the area fraction and mean-square velocity fluctuations, the mean-square displacement of the disks spans 4-5 orders of magnitude. The motion evolves from a sub-diffusive form to a complex diffusive behavior at long times. Even where a diffusion constant can be identified it is a complex function of area fraction and mean-square velocity fluctuations. By identifying the relevant length and time scales and their interdependence one can re-scale the data for the mean square displacement and the probability density function of displacements into collapsed scaling functions for all area fractions and mean-square velocity fluctuations. These scaling functions provide a predictive tool, allowing to infer from one set of measurements (at a given area fractions and mean-square velocity fluctuations) what are the expected results at any value of area fractions and mean-square velocity fluctuations.

For high enough temperatures , diffusion continues also at packing fraction greater than the jamming packing fraction. We aim to study this regime via simulations to achieve complete understanding of the transport properties of granular matter over the whole range of area fraction and temperature.

Displacement field in an agitated granular medium(Physical Review E 100 (4), 042902 )

Stress correlations in Frictional Granular Media:

In this work, we investigate whether in frictional granular packings, like in Hamiltonian amorphous elastic solids, the stress autocorrelation matrix presents long range anisotropic contributions just as elastic Green's functions. We find that in a standard model of frictional granular packing this is not the case. We prove quite generally that mechanical balance and material isotropy constrain the stress auto-correlation matrix to be fully determined by two spatially isotropic functions: the pressure and torque auto-correlations. The pressure and torque fluctuations being respectively normal and hyper-uniform force the stress autocorrelation to decay as the elastic Green's function. Since we find the torque fluctuations to be hyper-uniform, the culprit is the pressure whose fluctuations decay slower than normally as a function of the system's size. Investigating the reason for these abnormal pressure fluctuations we discover that anomalous correlations build up already during the compression of the dilute system before jamming. Once jammed these correlations remain frozen.

Whether this is true for frictional matter in general or is it the consequence of the model properties is a question that must await experimental scrutiny and possible alternative models.

Fourier space stress correlations

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