Computational sciences in the upstream oil and gas industry.

The predominant technical challenge of the upstream oil and gas industry has always been the fundamental uncertainty of the subsurface from which it produces hydrocarbon fluids. The subsurface can be detected remotely by, for example, seismic waves, or it can be penetrated and studied in the extremely limited vicinity of wells. Inevitably, a great deal of uncertainty remains.

Motion of packings of frictional grains.

Friction plays a key role in controlling the rheology of dense granular flows. Counting the number of constraints vs the number of variables indicates that critical coordination numbers Zc=3 (in D=2) and Zc=4 (in D=3) are special, in that states in which all contacts roll without frictional sliding are naively possible at and below these average coordination numbers. We construct an explicit example of such a state in D=2 based on a honeycomb lattice.

Avalanche dynamics on a rough inclined plane.

The avalanche behavior of gravitationally forced granular layers on a rough inclined plane is investigated experimentally for different materials and for a variety of grain shapes ranging from spherical beads to highly anisotropic particles with dendritic shape. We measure the front velocity, area, and height of many avalanches and correlate the motion with the area and height. We also measure the avalanche profiles for several example cases.

Velocity correlations in dense gravity-driven granular chute flow.

We report numerical results for velocity correlations in dense, gravity-driven granular flow down an inclined plane. For the grains on the surface layer, our results are consistent with experimental measurements reported by Pouliquen. We show that the correlation structure within planes parallel to the surface persists in the bulk.

Two scenarios for avalanche dynamics in inclined granular layers.

We report experimental measurements of avalanche behavior of thin granular layers on an inclined plane for low volume flow rate. The dynamical properties of avalanches were quantitatively and qualitatively different for smooth glass beads compared to irregular granular materials such as sand. Two scenarios for granular avalanches on an incline are identified, and a theoretical explanation for these different scenarios is developed based on a depth-averaged approach that takes into account the differing rheologies of the granular materials.

Ripening of porous media.

We address the surface-tension-driven dynamics of porous media in nearly saturated pore-space solutions. We linearize this dynamics in the reaction-limited regime near its fixed points--surfaces of constant mean curvature (CMC surfaces). We prove that the only stable interface for this dynamics is the plane and estimate the time scale for a CMC surface to become unstable.

Stability of monomer-dimer piles.

We present an experimental and theoretical study of piles consisting of monodisperse spherical grains mixed with a weight fraction nu(d) of dimer grains made by the rigid bonding of two such spherical grains. The maximum static angle of stability tantheta(c) of the pile increases from 0.45 to 1.

Analogies between granular jamming and the liquid-glass transition.

Based on large-scale, three-dimensional chute flow simulations of granular systems, we uncover strong analogies between the jamming of the grains and the liquid-glass transition. The angle of inclination theta in the former transition appears as an analog of temperature T in the latter. The transition is manifested in the development of a plateau in the contact normal force distribution P(f) at small forces, the splitting of the second peak in the pair-correlation function g(r), and increased fluctuations of the system energy.

Critical angle of wet sandpiles.

We measure the increase in the maximum stable angle of a sandpile, theta(c), with the volume fraction, phi of a liquid added to cause cohesion between the grains. For two different liquids, tan theta(c) does not apparently scale with the air-liquid surface tension at low phi, whereas it does at higher phi. This suggests that the liquid forms menisci at asperities on the surfaces of the grains before filling cohesive menisci at intergrain contact points.

Geometry of frictionless and frictional sphere packings.

We study static packings of frictionless and frictional spheres in three dimensions, obtained via molecular dynamics simulations, in which we vary particle hardness, friction coefficient, and coefficient of restitution. Although frictionless packings of hard spheres are always isostatic (with six contacts) regardless of construction history and restitution coefficient, frictional packings achieve a multitude of hyperstatic packings that depend on system parameters and construction history. Instead of immediately dropping to four, the coordination number reduces smoothly from z=6 as the friction coefficient mu between two particles is increased.

Branched growth with eta approximately 4 walkers.

Diffusion-limited aggregation has a natural generalization to the "eta models," in which eta random walkers must arrive at a point on the cluster surface in order for growth to occur. It has recently been proposed that in spatial dimensionality d=2, there is an upper critical eta(c)=4 above which the fractal dimensionality of the clusters is D=1. I compute the first-order correction to D for eta<4, obtaining D=1 + 1/2 (4-eta).

Granular flow down an inclined plane: Bagnold scaling and rheology.

We have performed a systematic, large-scale simulation study of granular media in two and three dimensions, investigating the rheology of cohesionless granular particles in inclined plane geometries, i.e., chute flows.

Electrorheological fluids.

Suspensions of polarizable particles in nonpolarizable solvents form fibrillated structures in strong electric fields. The resulting increase in viscosity of these "electrorheological" fluids can couple electrical to hydraulic components in a servomechanism. The physical properties of these fluids are unusual owing to the long-range, anisotropic nature of the interparticle forces.