Understanding diffusion-controlled bubble growth in porous media using experiments and simulations.

Nucleation and subsequent expansion of gas bubbles in porous media is relevant to many applications, including oil recovery, carbon storage, and boiling. We have built an experimental setup using microfluidic chips to study the dynamics of bubble growth in porous media. Visualization experiments of the growth of carbon dioxide bubbles in a supersaturated dodecane solution were conducted. We show that bubbles grow as dissolved gas molecules inside the oversaturated liquid diffuse to the gas-liquid interface. Bubbles expanding inside a porous medium displace the liquid phase until the cluster of the gas-filled pores becomes connected to the outlet at the critical gas saturation, which is used as a measure for the total liquid displacement. Our experiments uniquely focus on the growth of a single bubble and show that larger pressure drops lead to faster bubble growth while resulting in lower critical gas saturations. A nonlinear pore-network model is implemented to simulate bubble growth. We compare model predictions for bubble growth dynamics to our experimental results and present the need for further theoretical development to capture deviations from invasion-percolation when a large pressure drop is applied.

Quantifying Induced Polarization of Conductive Inclusions in Porous Media and Implications for Geophysical Measurements.

Induced polarization (IP) mapping has gained increasing attention in the past decades, as electrical induced polarization has been shown to provide interesting signatures for detecting the presence of geological materials such as clay, ore, pyrite, and potentially, hydrocarbons. However, efforts to relate complex conductivities associated with IP to intrinsic physical properties of the corresponding materials have been largely empirical. Here we present a quantitative interpretation of induced polarization signatures from brine-filled rock formations with conductive inclusions and show that new opportunities in geophysical exploration and characterization could arise. Initially tested with model systems with solid conductive inclusions, this theory is then extended and experimentally tested with nanoporous conductors that are shown to have a distinctive spectral IP response. Several of the tests were conducted with nano-porous sulfides (pyrite) produced by sulfate-reducing bacteria grown in the lab in the presence of a hydrocarbon source, as well as with field samples from sapropel formations. Our discoveries and fundamental understanding of the electrode polarization mechanism with solid and porous conductive inclusions suggest a rigorous new approach in geophysical exploration for mineral deposits. Moreover, we show how induced polarization of biologically generated mineral deposits can yield a new paradigm for basin scale hydrocarbon exploration.

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. The two-point velocity correlation function exhibits exponential decay for small to intermediate values of the separation between spheres. The correlation lengths identified by exponential fits to the data show nontrivial dependence on the averaging time Deltat used to determine grain velocities. We discuss the correlation length dependence on averaging time, incline angle, pile height, depth of the layer, system size, and grain stiffness and relate the results to other length scales associated with the rheology of the system. We find that correlation lengths are typically quite small, of the order of a particle diameter, and increase approximately logarithmically with a minimum pile height for which flow is possible, hstop, contrary to the theoretical expectation of a proportional relationship between the two length scales.

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. We also discuss the differences between dynamics in open and closed environments, pointing out the unlikelihood that CMC surfaces are ever realized in such environments on any time scale.

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. The static state also exhibits history dependence, akin to the quench-rate dependence of structural properties of glasses, due to the hyperstaticity of the contact network.

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.

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 1.1 and the grain packing fraction Phi decreases from 0.58 to 0.52 as nu(d) is increased from 0 to 1. The stability of these piles appears to be controlled by the grains sitting on the surface, which roll out of their local "traps" as the tilt angle is increased. We attribute the increase in tan theta(c)(nu(d)) to the enhanced stability of dimers on the surface, such that at higher tilt angles, there are sufficiently many stable surface traps available to accommodate the reduced density of monomers on the surface. A full characterization of the grain-scale roughness of the surface is required to quantitatively account for the changes in theta(c) with nu(d).