Permeability of mixed soft and hard granular material: hydrogels as drainage modifiers

We measure the flow of water through mixed packings of glass spheres and soft swellable hydrogel grains, at constant sample volume. Permeability values are obtained at constant sample volume and at porosities smaller than random close packing, for different glass bead diameters $D$ and for variable gel grain diameter $d$, as controlled by the salinity of the water. The gel content is also varied. We find that the permeability decays exponentially in $n(D/d)^b$ where $n=N_{gel}/N_{glass}$ is the gel to glass bead number ratio and $b$ is approximately 3. Therefore, flow properties are determined by the volume fraction of gel beads. A simple model based on the porosity of overlapping spheres is used to account for these observations

Effect of hydrogel particle additives on water-accessible pore structure of sandy soils: A custom pressure plate apparatus and capillary bundle model

To probe the effects of hydrogel particle additives on the water-accessible pore structure of sandy soils, we introduce a custom pressure plate method in which the volume of water expelled from a wet granular packing is measured as a function of applied pressure. Using a capillary bundle model, we show that the differential change in retained water per pressure increment is directly related to the cumulative cross-sectional area distribution $f(r)$ of the water-accessible pores with radii less than $r$. This is validated by measurements of water expelled from a model sandy soil composed of 2 mm diameter glass beads. In particular, the expelled water is found to depend dramatically on sample height and that analysis using the capillary bundle model gives the same pore size distribution for all samples. The distribution is found to be approximately log-normal, and the total cross-sectional area fraction of the accessible pore space is found to be $f_0=0.34$. We then report on how the pore distribution and total water-accessible area fraction are affected by superabsorbent hydrogel particle additives, uniformly mixed into a fixed-height sample at varying concentrations. Under both fixed volume and free swelling conditions, the total area fraction of water-accessible pore space in a packing decreases exponentially as the gel concentration increases. The size distribution of the pores is significantly modified by the swollen hydrogel particles, such that large pores are clogged while small pores are formed

Relaxing in foam

We investigate the mechanical response of an aqueous foam, and its relation to the microscopic rearrangement dynamics of the bubble-packing structure. At rest, even though the foam is coarsening, the rheology is demonstrated to be linear. Under flow, shear-induced rearrangements compete with coarsening-induced rearrangements. The macroscopic consequences are captured by a novel rheological method in which a step-strain is superposed on an otherwise steady flow

The partition of energy for air-fluidized grains

The dynamics of one and two identical spheres rolling in a nearly-levitating upflow of air obey the Langevin Equation and the Fluctuation-Dissipation Relation [Ojha et al. Nature 427, 521 (2004) and Phys. Rev. E 71, 01631 (2005)]. To probe the range of validity of this statistical mechanical description, we perturb the original experiments in four ways. First, we break the circular symmetry of the confining potential by using a stadium-shaped trap, and find that the velocity distributions remain circularly symmetric. Second, we fluidize multiple spheres of different density, and find that all have the same effective temperature. Third, we fluidize two spheres of different size, and find that the thermal analogy progressively fails according to the size ratio. Fourth, we fluidize individual grains of aspherical shape, and find that the applicability of statistical mechanics depends on whether or not the grain chatters along its length, in the direction of airflow.Comment: experimen

The Hindered Settling Function at Low Re Has Two Branches

We analyze hindered settling speed versus volume fraction $\phi$ for dispersions of monodisperse spherical particles sedimenting under gravity, using data from 15 different studies drawn from the literature, as well as 12 measurements of our own. We discuss and analyze the results in terms of popular empirical forms for the hindered settling function, and compare to the known limiting behaviors. A significant finding is that the data fall onto two distinct branches, both of which are well-described by a hindered settling function of the Richardson-Zaki form $H(\phi)=(1-\phi)^n$ but with different exponents: $n=5.6\pm0.1$ for Brownian systems with P\'eclet number ${\rm Pe}<{\rm Pe}_c$, and $n=4.48\pm0.04$ for non-Brownian systems with ${\rm Pe}>{\rm Pe}_c$. The crossover P\'eclet number is ${\rm Pe}_c\approx10^8$, which is surprisingly large.Comment: Supplementary material available on reques

Characterization of the Drag Force in an Air-Moderated Granular Bed

We measure the torque acting on a rod rotated perpendicular to its axis in a granular bed, through which an upflow of gas is utilized to tune the hydrostatic loading between grains. At low rotation rates the torque is independent of speed, but scales quadratically with rod-length and linearly with depth; the proportionality approaches zero linearly as the upflow of gas is increased towards a critical value above which the grains are fluidized. At high rotation rates the torque exhibits quadratic rate- dependence and scales as the rod's length to the 4th power. The torque has no dependence on either depth or airflow at these higher rates. A model used to describe the stopping force experienced by a projectile impacting a granular bed can be shown to predict these behaviors for our system's geometry, indicating that the same mechanics dictate both steady-state and transient drag forces in granular systems, regardless of geometry or material properties of the grains.Comment: 14 pages, 5 figure