Session V53: Wet and Cohesive Granular Materials

An analytical framework for aeolian saltation

We construct an analytical framework for steady state aeolian saltation, using experimentally-derived splash function relationships and the additional constraint of a threshold height, above which the wind velocity is strong enough to carry a grain from reptation into saltation. This threshold height rises as the wind profile magnitude is lowered by the increasing number of saltating grains being accelerated by the wind, until the number of grains being demoted below this threshold due to loss of energy to collisions with the bed equals the number being promoted. The balance of these populations at steady state determines both the flux of grains in saltation and the saturated wind velocity profile, while the approach to this balance describes the transient evolution to this state. We also formulate the difference between the critical impact Shields stress, defined as the stress below which transport ceases, and the higher critical fluid Shields stress, at which transport is initiated. Finally, we test the dependence of grain flux and trajectory lengths and speeds on the erodibility of the bed, and compare these results with observed differences in scaling. We also compare our results to findings for saltation under water.   

X-Ray Fluoroscopy of Sedimentation in Elastic Fluids

Dispersions of spheres in a Newtonian fluid will sediment until all grains form a packing. While the system approaches its final configuration, the dispersion is roughly homogenous in space and time except at two well-defined interfaces: a dispersion-supernatant interface, and an interface below the dispersion at which grains stack to form a packing. In order to better understand this packing process we perturb the dynamics at the lower interface by adding a flexible, high molecular weight polymer that enhances fluid elasticity. The fluid strain-rate between spheres has an extensional component that is inversely proportional to grain separation, so elasticity dominates the fluid forces as the grain separation becomes small, thus frustrating the packing process. In order to observe the effect of this perturbation, we utilize x-ray fluoroscopy. In the case of a system without polymer we observe settling rates in accordance with a typical Stokes' model until all grains have settled into a random packing. In the polymeric case we see that, alongside the Newtonian-like settling, there's a time- and depth-dependent compression of the disperse phase, resulting in a smooth transition between dispersion and packing rather than the sharp interface observed in the Newtonian case.   

Three dimensional imaging of soft sphere packings under shear

The (microscopic) flow of three dimensional disordered athermal granular packings remains poorly understood. However, experimentally studying flow and deformations in a three dimensional packing of grains is challenging due to the opacity of such packings. We use refractive index matched scanning with hydrogel spheres to image such flows. Hydrogel is soft and has low friction, which allows for the study of contact forces via contact deformations. We look at how force networks develop in sheared packings close to the onset of mechanical rigidity.   

Fluidization of wet granulates under hydrodynamic shear - experiments

Very recently, the fluidization threshold of a wet granular bed under hydrodynamic shear forces were predicted theoretically [1]. This theory described the flow through a wet granular bed by a continuum model and provides analytical expressions for the averaged drag foce on a single particle. Moreover, the theory predicts the stability of the granular bed in dependence of the strength of the capillary and buoyancy forces. These theoretical predictions are tested in the present study by a newly designed flow channel. We will present our first experimental results for the fluidization onset of granular beds. \\[4pt] [1] I. Battiato, and J. Vollmer,``Fluidization of wet granulates under hydrpdynamic shear,'' submitted for pubblication.   

Building designed granular towers one drop at a time

The impact of a drop on a surface leads to beautiful dynamical shapes that result from a subtle interplay between inertial effects, fluid properties and substrate characteristics. In this talk, we will present an experiment where the successive impacts of drops lead to surprisingly slender mechanically stable structures that we called granular towers. They are created by dripping a dense granular suspension on a liquid absorbing surface such as a blotter paper or a dry granular bed. These towers formed by rapid solidification of the drop upon impact are analogous to many natural structures found in nature including frozen lava flows, icicles and stalagmites. We find that the height can be determined by balancing the excess liquid flux and the drainage through the granular tower. The velocity impact, the free fall time and the density of the suspension are found to control the tower width and its detailed morphology. We show that these facts can be manipulated to obtain various symmetric, smooth, corrugated, zigzag, and chiral structures. Further, the shape of the tower can be used as a quick diagnostic tool to characterize the rheology of a granular suspension. [J. Chopin and A. Kudrolli, Phys. Rev. Lett. 107, 208304 (2011)]   

Dynamics of failure in cohesive granular packings

We explore the grain-scale interactions that precede large-scale deformations and mark the onset of mechanical failure in two-dimensional disordered granular packings. The two-dimensionality of the system allows for direct observation of all particle dynamics during the compression of a pillar. The grains are cohesive, with an attraction governed by tunable capillary forces induced through an interstitial fluid. For our analysis, we focus on the evolution of local rearrangements into shear bands within the pillar, quantifying the structural differences within the packing due to the presence of cohesion. We observe that cohesion results in greater spatial heterogeneity within the packing during compression. We also compare the compression of ordered and disordered packings.   

Cohesive granular aggregates under punching: theory and experiments

When poured into a container, cohesive granular materials form low-density, open granular aggregates. If put under compression, these aggregates densify by particle rearrangement. We seek experimental evidence that particle rearrangement occurs in the form of a phase transition between two configurational phases of the aggregate (G.\ Gioia, A.\ M.\ Cuiti\~no, S.\ Zheng, and T.\ Uribe, PRL {\bf 88}, 204302, 2002). We use a simple model to show that when an open granular aggregate with two configurational phases is penetrated by a punch that lacks a characteristic length scale, the functional relation between the punching force and the penetration of the punch depends solely on the dimensionality of the punch: for a two-dimensional, wedge-shaped punch the force--penetration curve is linear whereas for a three-dimensional, conical punch the force--penetration curve is quadratic. To test these predictions we carry out experiments with open granular aggregates of a fine powder. The experimental measurements are in accord with the theoretical predictions.   

Discrete Particle Dynamics Simulations of Adhesive Systems with Thermostatting

Aggregation/coagulation/flocculation processes are ubiquitous in modern industry from fields as diverse as waste water treatment, the food industry, algae biofuel production, and materials processing where control of the size and morphology of aggregates is paramount to the application of interest. Population balance models have historically been used with success in predicting aggregation kinetics and size distributions for these processes. However, even the most robust population balance schemes can lack an exact description of the underlying physical processes governing attractive or adhesive particulate matter suspended in a background medium, including finite aggregate strength and yield stress, restructuring length and time scales, and response to hydrodynamic forces. In order to elucidate these phenomena, We develop and use a JKR type model for simulating adhesive particulate matter in a background medium varying from dilute gas to liquid. We evaluate the time and length scales for restructuring/fragmentation that result from this model as a function of aggregate size and fractal dimension. We additionally introduce a method for pairwise thermostatting of the adhesive potential and discuss the applicability of this model to various adhesive systems.   

Normal Mode Spectrum of Finite Sized Granular Systems: The Effects of Fluid Viscosity at the Grain Contacts

We investigate the effects of adsorbed films on the attenuative properties of loose granular media occupying a finite sized rigid container, which is open on the top. We measure the effective mass, $\tilde{M}(\omega)$, of loose tungsten particles prepared under two different sets of conditions: 1) We lightly coat tungsten grains with a fixed volume fraction of silicone oil (PDMS), where the liquid viscosity is varied for individual realizations. 2) In the other set of experiments we vary the humidity. On a theoretical level we are able to decompose the effective mass into a sum over the contributions from each of the normal modes of the granular medium. Our results indicate that increasing either the PDMS viscosity or the humidity, as the case may be, does markedly increase the damping rate of each normal mode relevant to our measurements. However, there is appreciable damping even in the absence of any macroscopic film. With a notable exception in the case of the highest humidity in the humidity controlled experiments, all the relevant modes are weakly damped in the sense of a microscopic theory based on damped contact forces between rigid particles.   

Influence of liquid bridges on the macroscopic properties of granular assemblies

We present the results of two experimental studies concerning the compaction dynamics of cohesive granular materials. In the first study, the cohesion between neighboring grains is induced by capillary bridges in a wet granular material. The cohesiveness is tuned using different liquids having specific surface tension values. The second study concerns initially dry granular materials surrounded by a well controlled air humidity. Then, the cohesion inside the packing is controlled through the relative humidity which influence both triboelectric and capilary effects. For both cases, the evolution of the parameters extracted from the compaction curves (the compaction characteristic time $\tau$, the initial and final packing fractions) have been analyzed as a function of the cohesiveness. A model, based on free volume kinetic equations and the presence of a capillary energy barrier, is able to reproduce quantitatively the experimental results (Phys. Rev. Lett. 105, 048001 (2010)).   

Wetting and packing effects on evaporation out of a porous medium

Evaporation through granular media involves complex fluid transport and exhibits two regimes: (1) a capillary-supported regime maintaining hydraulic continuity to the surface and vapor exchange with the atmosphere followed by (2) a diffusion-limited regime through the medium. A well-defined intermediate partially saturated zone (PSZ) has already been observed in the past. It is evidently seen from our experimental investigations using a 2D model soil of glass beads. The PSZ is the region identified above the interface formed by the drying front, which separates the PSZ from the fully-saturated wet region. This intermediate zone is filled with a dynamic mixture of vapor and liquid. The existence of this zone is of significant importance as it sets the kinetics of the evaporation process. Here we will present how wetting and packing effects influence the size of this partially saturated zone and we will show how a simple model based on geometrical considerations can explain our observations.   

A coupled deformation-diffusion theory for fluid-saturated porous solids

Fluid-saturated porous materials are important in several familiar applications, such as the response of soils in geomechanics, food processing, pharmaceuticals, and the biomechanics of living bone tissue. An appropriate constitutive theory describing the coupling of the mechanical behavior of the porous solid with the transport of the fluid is a crucial ingredient towards understanding the material behavior in these varied applications. In this work, we formulate and numerically implement in a finite-element framework a large-deformation theory for coupled deformation-diffusion in isotropic, fluid-saturated porous solids. The theory synthesizes the classical Biot theory of linear poroelasticity and the more-recent Coussy theory of poroplasticity in a large deformation framework. In this talk, we highlight several salient features of our theory and discuss representative examples of the application of our numerical simulation capability to problems of consolidation as well as deformation localization in granular materials.   

Water Retention of Sandy Soil with Hydrogel Particle Additives under Steady Rain

We probe the water retention behavior of a dry model sandy soil with hydrogel particle additives under a steady rain using a self-built raindrop impingement set-up. The 0.4mm dry hydrogel particles are sent into a dry model sandy soil, 1mm glass beads, in different methods and a steady rain is created to irrigate the soil packing. The mass of the retained water in the packing is measured as a function of rain time. The influences of packing height, gel concentration, and gel location are examined respectively. For the model sandy soil alone, the packing height has little effect on the results. Rain water wets a shallow top region and flows out through a narrow path in the packing. With hydrogel particles uniformly mixed into the top region of a model sandy soil packing, the retained water increases as the gel number ratio increases or when the hydrogel particles are concentrated into the wet top region. A better way is to place hydrogel particles in a layer at certain depths under soil surface. The wet gel layers formed during the rain not only lock water inside but also clog the water path and force rain water to wet other dry soil regions. The clogging efficiency is determined by the wet gel layer number and the soil confinement.   

Period tripling causes rotating spirals in agitated wet granular matter

Pattern formation of a thin layer of vertically agitated wet granular matter is investigated experimentally. Due to the strong cohesion arising from the capillary bridges formed between adjacent particles, agitated wet granular matter exhibits a different scenario as its dry counter-part. Rotating spirals with three arms, which correspond to the kinks between regions with different colliding phases, are the dominating pattern. This preferred number of arms corresponds to period tripling of the agitated granular layer, unlike predominantly subharmonic Faraday crispations in dry granular matter. The chirality of the spatiotemporal pattern corresponds to the rotation direction of the spirals. Understanding this well traceable instability could pave a way for testifying elaborate theories on dense flow of wet granular matter.   

The melting of an ice blok assembly

The melting of an assembly of ice blocks under an unidirectional controlled load was investigated. The volume occupied by the ice blocks and the volume of ice were simultaneously measured. While the ice volume continuously decreases, sudden breakdown of the total volume was observed suggesting large reorganization of the whole assembly. The waiting-times between two successive collapses and the magnitudes of the collapse have been correlated. The pile structure was studied using a x-ray tomography before and after a collapse. The arch network re-organization is responsible for the melting dynamics as the pile becomes more and more ordered during the melting.