Force networks and elasticity in granular silos.

We have made experimental observations of the force networks within a two-dimensional granular silo similar to the classical system of Janssen. Models like that of Janssen predict that pressure within a silo saturates with depth as the result of vertical forces being redirected to the walls of the silo where they can then be carried by friction. We use photoelastic particles to obtain information not available in previous silo experiments --the internal force structure. We directly compare various predictions with the results obtained by averaging ensembles of experimentally obtained force networks. We identify several differences between the mean behavior in our system and that predicted by Janssen-like models: We find that the redirection parameter describing how the force network transfers vertical forces to the walls varies with depth. We find that changes in the preparation of the material can cause the pressure within the silo to either saturate or to continue building with depth. Most strikingly, we observe a nonlinear response to overloads applied to the top of the material in the silo. For larger overloads we observe the previously reported "giant overshoot" effect where overload pressure decays only after an initial increase (G. Ovarlez et al., Phys. Rev. E 67, 060302(R) (2003)). For smaller overloads we find that additional pressure propagates to great depth. Analysis of the differences between the inter-grain contact and force networks suggests that, for our system, when the load and the particle weight are comparable, particle elasticity acts to stabilize the force network, allowing deep propagation. For larger loads, the force network rearranges, resulting in the expected, Janssen-like behavior. Thus, a meso-scale network phenomenon results in an observable nonlinearity in the mean pressure profile.

Why do granular materials stiffen with shear rate? Test of novel stress-based statistics.

Recent experiments exhibit a rate dependence for granular shear such that the stress grows linearly in the logarithm of the shear rate, gamma. Assuming a generalized activated process mechanism, we show that these observations are consistent with a recent proposal for a stress-based statistical ensemble. By contrast, predictions for rate dependence using conventional energy-based statistical mechanics to describe activated processes, predicts a rate dependence of (ln(gamma))(1/2).

Logarithmic rate dependence of force networks in sheared granular materials.

Many models of slow, dense granular flows assume that the internal stresses are independent of the shearing rate. In contrast, logarithmic rate dependence is found in solid-on-solid friction, geological settings and elsewhere. Here we investigate the rate dependence of stress in a slowly sheared two-dimensional system of photoelastic disks, in which we are able to determine forces on the granular scale. We find that the mean (time-averaged) stress displays a logarithmic dependence on the shear rate for plastic (irreversible) deformations. However, there is no perceivable dependence on the driving rate for elastic (reversible) deformations, such as those that occur under moderate repetitive compression. Increasing the shearing rate leads to an increase in the strength of the force network and stress fluctuations. Qualitatively, this behaviour resembles the changes associated with an increase in density. Increases in the shearing rate also lead to qualitative changes in the distributions of stress build-up and relaxation events. If shearing is suddenly stopped, stress relaxations occur with a logarithmic functional form over long timescales. This slow collective relaxation of the stress network provides a mechanism for rate-dependent strengthening.

Aggregation and chimney formation during the solidification of ammonium chloride.

Experiments study large-scale pattern formation during the growth of ammonium chloride (NH4Cl) from solution in a thin (Hele-Shaw) geometry. In particular a solid-liquid mixture ("mushy layer") forms in which growing solid NH4Cl crystals form a solid network interspersed with liquid. There are different ways that the mushy layer can be formed, however. If the cell is heated from below and cooled from above, thermal convection generates large-scale recirculating flows that carry seed crystals from the upper (cold) boundary to the (warmer) side and bottom boundaries. Ballistic deposition of these seed crystals leads to aggregation patterns with significant voids (filled with liquid) with a wide range of length scales. If the cell is cooled from below with a warm environment, the solid NH4Cl grows dendritically without deposition, resulting in a compact mushy layer. Plume convection within this mushy layer produces one or two well-defined "chimneys." If the environment is cool (comparable to the liquidus temperature of the solution), the mushy layer forms by a combination of dendritic growth and ballistic deposition, resulting in a more permeable mushy layer and enhanced chimney formation. The effects of ballistic deposition are enhanced if the cell is tipped, in which case the voids reappear. Plume convection and chimney formation are dramatically enhanced in this case. Additional experiments are done in which fluid flows in the system are enhanced artificially to verify that enhancements in chimney formation are due primarily to the aggregation process, and not to the increases in fluid flows due to thermal and compositional convection.