Contact tribology also affects the slow flow behavior of granular emulsions

Recent work on suspension flows has shown that contact mechanics plays a role in suspension flow dynamics. The contact mechanics between particulate matter in dispersions should depend sensitively on the composition of the dispersed phase: evidently emulsion droplets interact differently with each other than angular sand particles. We therefore ask: what is the role of contact mechanics in dispersed media flow? We focus on slow flows, where contacts are long-lasting and hence contact mechanics effects should be most visible. To answer our question, we synthesize soft hydrogel particles with different friction coefficients. By making the particles soft, we can drive them at finite confining pressure at all driving rates. For particles with a low friction coefficient, we obtain a rheology similar to that of an emulsion, yet with an effective friction much larger than expected from their microscopic contact mechanics. Increasing the friction coefficient of the particles, we find a flow instability in the suspension. Particle level flow and fluctuations are also greatly affected by the microscopic friction coefficient of the suspended particles. The specific rheology of our "granular emulsions" provides further evidence that a better understanding of microscopic particle interactions is of broad relevance for dispersed media flows

Universal fitness dynamics through an adaptive resource utilization model

The fitness of a species determines its abundance and survival in an ecosystem. At the same time, species take up resources for growth, so their abundance affects the availability of resources in an ecosystem. We show here that such species-resource coupling can be used to assign a quantitative metric for fitness to each species. This fitness metric also allows for the modeling of drift in species composition, and hence ecosystem evolution through speciation and adaptation. Our results provide a foundation for an entirely computational exploration of evolutionary ecosystem dynamics on any length or time scale. For example, we can evolve ecosystem dynamics even by initiating dynamics out of a single primordial ancestor and show that there exists a well defined ecosystem-averaged fitness dynamics that is resilient against resource shocks

Reynolds Pressure and Relaxation in a Sheared Granular System

We describe experiments that probe the evolution of shear jammed states, occurring for packing fractions $\phi_S \leq \phi \leq \phi_J$, for frictional granular disks, where above $\phi_J$ there are no stress-free static states. We use a novel shear apparatus that avoids the formation of inhomogeneities known as shear bands. This fixed $\phi$ system exhibits coupling between the shear strain, $\gamma$, and the pressure, $P$, which we characterize by the `Reynolds pressure', and a `Reynolds coefficient', $R(\phi) = (\partial ^2 P/\partial \gamma ^2)/2$. $R$ depends only on $\phi$, and diverges as $R \sim (\phi_c - \phi)^{\alpha}$, where $\phi_c \simeq \phi_J$, and $\alpha \simeq -3.3$. Under cyclic shear, this system evolves logarithmically slowly towards limit cycle dynamics, which we characterize in terms of pressure relaxation at cycle $n$: $\Delta P \simeq -\beta \ln(n/n_0)$. $\beta$ depends only on the shear cycle amplitude, suggesting an activated process where $\beta$ plays a temperature-like role.Comment: 4 pages, 4 figure

Refractive Index Matched Scanning and Detection of Soft Particle

We describe here how to apply the three dimensional imaging technique of refrecative index matched scanning to hydrogel spheres. Hydrogels are water based materials with a low refractive index, which allows for index matching with water-based solvent mixtures. We discuss here various experimental techniques required to handle specifically hydrogel spheres as opposed to other transparent materials. The deformability of hydrogel spheres makes their identification in three dimensional images non-trivial. We will also discuss numerical techniques that can be used in general to detect contacting, non-spherical particles in a three dimensional image. The experimental and numerical techniques presented here give experimental access to the stress tensor of a packing of deformed particles.Comment: 9 pages, 9 figures, submitted to review of scientific instruments, Issue 1

Rheology of Weakly Vibrated Granular Media

We probe the rheology of weakly vibrated granular flows as function of flow rate, vibration strength and pressure by performing experiments in a vertically vibrated split-bottom shear cell. For slow flows, we establish the existence of a novel vibration dominated granular flow regime, where the driving stresses smoothly vanish as the driving rate is diminished. We distinguish three qualitatively different vibration dominated rheologies, most strikingly a regime where the shear stresses no longer are proportional to the pressure.Comment: 14 pages, 19 figures, submitted to PR

Particle Diffusion in Slow Granular Bulk Flows

We probe the diffusive motion of particles in slowly sheared three dimensional granular suspensions. For sufficiently large strains, the particle dynamics exhibits diffusive Gaussian statistics, with the diffusivity proportional to the local strain rate - consistent with a local, quasi static picture. Surprisingly, the diffusivity is also inversely proportional to the depth of the particles within the flow - at the free surface, diffusivity is thus ill defined. We find that the crossover to Gaussian displacement statistics is governed by the same depth dependence, evidencing a non-trivial strain scale in three dimensional granular flows.Comment: 6 page

Darcy-Reynolds forces during intrusion into granular-fluid beds

We experimentally study intrusion into fluid-saturated granular beds by a free-falling sphere, varying particle size and fluid viscosity. We test our results against Darcy-Reynolds theory, where the deceleration of the sphere is controlled by Reynolds dilatancy and the Darcy flow resistance. We find the observed intruder dynamics are consistent with Darcy-Reynolds theory for varied particle size. We also find that our experimental results for varied viscosity are consistent with Darcy Reynolds theory, but only for a limited range of the viscosity. For large viscosities, observed forces begin to decrease with increasing viscosity, in contrast with the theoretical prediction.Office of Naval ResearchOffice of Naval Research Global Visiting Scientist Program VSP 19-7-001N0001419WX0151

Obtaining Self-similar Scalings in Focusing Flows

The surface structure of converging thin fluid films displays self-similar behavior, as was shown in the work by Diez et al [Q. Appl. Math 210, 155, 1990]. Extracting the related similarity scaling exponents from either numerical or experimental data is non-trivial. Here we provide two such methods. We apply them to experimental and numerical data on converging fluid films driven by both surface tension and gravitational forcing. In the limit of pure gravitational driving, we recover Diez' semi-analytic result, but our methods also allow us to explore the entire regime of mixed capillary and gravitational driving, up to entirely surface tension driven flows. We find scaling forms of smoothly varying exponents up to surprisingly small Bond numbers. Our experimental results are in reasonable agreement with our numerical simulations, which confirm theoretically obtained relations between the scaling exponents.Comment: 11 pages, 11 figures, accepted for Phys Rev

Spanning the Scales of Granular Materials: Microscopic Force Imaging

If you walk on sand, it supports your weight. How do the disordered forces between particles in sand organize, to keep you from sinking? This simple question is surprisingly difficult to answer experimentally: measuring forces in three dimensions, between deeply buried grains, is challenging. We describe here experiments in which we have succeeded in measuring forces inside a granular packing subject to controlled deformations. We connect the measured micro-scale forces to the macro-scale packing force response with an averaging, mean field calculation. This calculation explains how the combination of packing structure and contact deformations produce the unexpected mechanical response of the packing, and reveals a surprising microscopic particle deformation enhancement mechanism.Comment: Data and code available at http://www.phy.duke.edu/~nb108

Characterizing Granular Networks Using Topological Metrics

We carry out a direct comparison of experimental and numerical realizations of the exact same granular system as it undergoes shear jamming. We adjust the numerical methods used to optimally represent the experimental settings and outcomes up to microscopic contact force dynamics. Measures presented here range form microscopic, through mesoscopic to system-wide characteristics of the system. Topological properties of the mesoscopic force networks provide a key link between micro and macro scales. We report two main findings: the number of particles in the packing that have at least two contacts is a good predictor for the mechanical state of the system, regardless of strain history and packing density. All measures explored in both experiments and numerics, including stress tensor derived measures and contact numbers depend in a universal manner on the fraction of non-rattler particles, $f_{NR}$. The force network topology also tends to show this universality, yet the shape of the master curve depends much more on the details of the numerical simulations. In particular we show that adding force noise to the numerical data set can significantly alter the topological features in the data. We conclude that both $f_{NR}$ and topological metrics are useful measures to consider when quantifying the state of a granular system.Comment: 8 pages, 8 figure