Harlan W. Stockman

Applicability of the Reynolds Equation for modeling fluid flow between rough surfaces

Predictions of the Reynolds equation for flow between rough-walled surfaces have been compared to a more exact calculation of Navier-Stokes flow based on a lattice-gas automaton method. Two-dimensional channels were constructed with an idealized sinusoidal roughness on each wall. Flow in the channels was studied by both methods for various amplitude to wavelength ratios of the roughness, surface separations, relative alignment or phase of the sinusoids, and Reynolds numbers. The Reynolds equation overestimates fluid velocity as the surfaces are placed together or the amplitude of the roughness increases relative to its wavelength.

A lattice‐gas and lattice Boltzmann study of mixing at continuous fracture Junctions: Importance of boundary conditions

The lattice-gas automata and lattice Boltzmann (BGK) methods were used to estimate the mixing of fluid streams at a continuous fracture junction, for Peclet number (Pe) from 0 to 1547. Agreement with experimental results is good, particularly at Pe ≤ 25. At low Pe, a large fracture length/width is needed to obtain accurate mixing ratios (Mr). For a 90° intersection of two fractures with equal widths and flow rates, Mr approaches 0.5 (complete mixing) at Pe ≈ 1. At the highest Pe studied, Mr=0.022, in contrast with the streamline routing prediction Mr=0.

Mixing at fracture intersections: Influence of channel geometry and the Reynolds and Peclet Numbers

The 3D lattice Boltzmann (LB) method was used to model mixing at three types of continuous fracture intersections: planar, fluted (containing parallel grooves), and rough-walled. Peclet number (Pe) varied from 3 to 400, and Reynolds number (Re) varied from 0.5 to 100. In both planar- and rough-walled intersections, the mixing ratio (Mr) decreases with increasing Pe, though the decrease is less dramatic for the rough-walled geometry. In planar-walled intersections, the Mr decreases with increasing Re; however, the fluted and rough-walled intersections show the opposite trend. Overall, the impact of inertial effects is slight for Re ≤ 10. The effects of channel length are also small; the calculated Mr varies little for LB simulations with length/width ≥ 1.

A lattice gas study of retardation and dispersion in fractures: Assessment of errors from desorption kinetics and buoyancy

Lattice gas automata (LGA) were used to estimate errors in transport coefficients, as measured in laboratory experiments with Peclet numbers from 0 to 27.6 (defined relative to channel width), Damkohler numbers from 0.18 to ∞, Grashof numbers of 0 or 75, and length/width up to 180. Low Damkohler numbers yield long, low-amplitude elution tails, which contain much of the total solute. As a consequence, at Da ≈ 0.18 and KD = 8, the solute peak travels at the same speed as the carrier fluid, yielding an apparent KD ≈ 0 after five characteristic diffusion times. Such conditions correspond, for example, to a meter-long path through a 0.5-cm-wide, gas-filled fracture. Buoyancyenhanced dispersion, found in experiments with horizontal tubes, is confirmed by the LGA analysis; however, a different mechanism is suggested for the enhancement in horizontal fractures. Both kinetic and buoyancy errors can be greatly reduced, or experiments made much smaller, if the first and second moments of a tracer pulse can be measured as functions of time.

A lattice-gas study of dispersion in alveolated channels

Abstract Axial dispersion in alveolated channels was studied via lattice-gas automata (LGA), for both slug and step-change inlet conditions. There was good agreement between the effective diffusion coefficient ( D ∗ ) calculated by the LGA method, and the D ∗ predicted by the ‘stagnant pocket’ formalism developed by Aris, Turner, and Tsuda et al. The enhancement of D ∗ was dependent on the ratio of alveolar volume to central channel volume and the Peclet number. For Pe ≥ 5, D ∗ was substantially greater than the Taylor-Aris prediction for flow between parallel flat plates. For Pe D ∗ was less than the molecular diffusion coefficient, D m . In the absence of buoyancy, inlet conditions (pulse vs step-change) had little effect on the calculated D ∗ (≤ 3%). The effect of buoyancy, however, depends on the inlet condition; for an LGA corresponding to 1 mol% SF 6 tracer gas in air, D ∗ was increased up to 20% for the step-change, and decreased up to 6% for the slug.

Long-Term Modeling of Plutonium Solubility at a Desert Disposal Site, Including CO2 Diffusion, Cellulose Decay, and Chelation

The solubility of plutonium was estimated for waste buried at the Greater Confinement Disposal site in Nevada. The EQ3/6 thermochemical database was modified to include recent data on Pu complex formation, and the solubilities of two critical phases (probertite (CaNaB5O9·5H2O), added as a backfill material; and Ca sac-charate) were determined by experiment. Reaction path runs were used to model effects of cellulose degradation, including complexation of actinides by organic acids and carbonate, decay of the complexing agents, and the buildup and diffusive loss of CO2 through the permeable alluvium. For most waste interaction scenarios, long-term (≈103 years) concentrations of Pu in pore waters are ≤10−7 molal and are dominated by carbonate complexes, although organic complexes could dominate in the first ≈103 years. In unusual circumstances, carbonation of buried lithium could produce very high Pu solubilities; however, even in such a system, a slight lowering of the effective redox potential dramatically...