Scott C. James

Transport of polydisperse colloids in a saturated fracture with spatially variable aperture

A particle tracking model is developed to simulate the transport of variably sized colloids in a fracture with a spatially variable aperture. The aperture of the fracture is treated as a lognormally distributed random variable. The spatial fluctuations of the aperture are described by an exponential autocovariance function. It is assumed that colloids can sorb onto the fracture walls but may not penetrate the rock matrix. Particle advection is governed by the local fracture velocity and diffusion by the Stokes-Einstein equation. Model simulations for various realizations of aperture fluctuations indicate that lognormal colloid size distributions exhibit greater spreading than monodisperse suspensions. Both sorption and spreading of the polydisperse colloids increase with increasing variance in the particle diameter. It is shown that the largest particles are preferentially transported through the fracture leading to early breakthrough while the smallest particles are preferentially sorbed. Increasing the variance of the aperture fluctuations leads to increased tailing for both monodisperse and variably sized colloid suspensions, while increasing the correlation length of the aperture fluctuations leads to increased spreading.

Effective velocity and effective dispersion coefficient for finite-sized particles flowing in a uniform fracture

In this work we derive expressions for the effective velocity and effective dispersion coefficient for finite-sized spherical particles with neutral buoyancy flowing within a water saturated fracture. We considered the miscible displacement of a fluid initially free of particles by another fluid containing particles of finite size in suspension within a fracture formed by two semi-infinite parallel plates. Particle spreading occurs due to the combined actions of molecular diffusion and the dispersive effect of the Poiseuille velocity profile. Unlike Taylor dispersion, here the finite size of the particles is taken into account. It is shown that because the finite size of a particle excludes it from the slowest moving portion of the velocity profile, the effective particle velocity is increased, while the overall particle dispersion is reduced. A similar derivation applied to particles flowing in uniform tubes yields analogous results. The effective velocity and dispersion coefficient derived in this work for particle transport in fractures with uniform aperture are unique and ideally suited for use in particle tracking models.

Transport of polydisperse colloid suspensions in a single fracture

The transport of variably sized colloids (polydisperse) in a fracture with uniform aperture is investigated by a particle-tracking model that treats colloids as discrete particles with unique transport properties while accounting for either matrix diffusion or irreversible colloid deposition. For the special case of a monodisperse colloid suspension the particle-tracking model is in perfect agreement with predictions based on an existing analytical solution. It is shown that lognormal colloid size distributions exhibit greater spreading than monodisperse suspensions. Increasing the fracture porosity of the solid matrix leads to higher matrix diffusion, which in turn delays particle breakthrough for both the monodisperse and variably sized colloid suspensions. The smallest particles of a distribution are more greatly affected by matrix diffusion whereas the largest particles are transported faster and further along a fracture. Both perfect sink and kinetic colloid deposition onto fracture surfaces are examined. Kinetic deposition accounts for colloid surface exclusion by either a linear or nonlinear blocking function. For both cases the smallest colloid particles tend to preferentially deposit onto the fracture wall. Both matrix diffusion and surface deposition tend to discretize colloid distributions according to particle size so that larger particles are least retarded and smaller particles are more slowly transported. Furthermore, it is shown that the rate of colloid deposition is inversely proportional to the fracture aperture.

Analytical solutions for monodisperse and polydisperse colloid transport in uniform fractures

Abstract Analytical solutions are derived describing the transport of suspensions of monodisperse as well as polydisperse colloid plumes of neutral buoyancy within a fracture with uniform aperture. Various initial and boundary conditions are considered. It is shown that both the finite colloid size and the characteristics of the colloid diameter distribution significantly affect the shape of colloid concentration breakthrough curves. Furthermore, increasing the standard deviation of the colloid diameter enhances colloid spreading and increases the number of attached colloids when colloid–wall interactions are taken into account. Excellent agreement between available experimental data and the analytical solution for the case of an instantaneous release of monodisperse colloids in a natural fracture is observed.

Simulating environmental changes due to marine hydrokinetic energy installations

Marine hydrokinetic (MHK) projects will extract energy from ocean currents and tides, thereby altering water velocities and currents in the sites waterway. These hydrodynamics changes can potentially affect the ecosystem, both near the MHK installation and in surrounding (i.e., far field) regions. In both marine and freshwater environments, devices will remove energy (momentum) from the system, potentially altering water quality and sediment dynamics. In estuaries, tidal ranges and residence times could change (either increasing or decreasing depending on system flow properties and where the effects are being measured). Effects will be proportional to the number and size of structures installed, with large MHK projects having the greatest potential effects and requiring the most in-depth analyses. This work implements modification to an existing flow, sediment dynamics, and water-quality code (SNL-EFDC) to qualify, quantify, and visualize the influence of MHK-device momentum/energy extraction at a representative site. New algorithms simulate changes to system fluid dynamics due to removal of momentum and reflect commensurate changes in turbulent kinetic energy and its dissipation rate. A generic model is developed to demonstrate corresponding changes to erosion, sediment dynamics, and water quality. Also, bed-slope effects on sediment erosion and bedload velocity are incorporated to better understand scour potential.

Transport of Neutrally Buoyant and Dense Variably Sized Colloids in a Two-Dimensional Fracture with Anisotropic Aperture

The transport of monodisperse as well as polydisperse colloid suspensions in a two-dimensional, water saturated fracture with spatially variable and anisotropic aperture is investigated with a particle tracking model. Both neutrally buoyant and dense colloid suspensions are considered. Although flow and transport in fractured subsurface formations have been studied extensively by numerous investigators, the transport of dense, polydisperse colloid suspensions in a fracture with spatially variable and anisotropic aperture has not been previously explored. Simulated snapshots and breakthrough curves of ensemble averages of several realizations of a log-normally distributed aperture field show that polydisperse colloids exhibit greater spreading than monodisperse colloids, and dense colloids show greater retardation than neutrally buoyant colloids. Moreover, it is demonstrated that aperture anisotropy oriented along the flow direction substantially increases colloid spreading; whereas, aperture anisotropy oriented transverse to the flow direction retards colloid movement.

Advances in sediment transport modelling

A detailed description of how recently-developed sediment dynamics formulations are incorporated into the United States Environmental Protection Agencys Environmental Fluid Dynamics Code is presented. The new approach is an extension of previous models and accounts for multiple sediment size classes, has a unified treatment of suspended load and bedload, and appropriately replicates bed armouring. The resulting flow, transport, and sediment dynamics model is an improvement to previous models because it may directly incorporate site-specific data, while maintaining a physically consistent, unified treatment of bedload and suspended load. Experimental data from a noncohesive sediment erosion experiment in a straight channel help validate the numerical model. In this simulation, unknown parameters representing the active layer thickness and the erosion rates of the two largest sediment size classes when they are newly deposited are identified from the available data.

An efficient particle tracking equation with specified spatial step for the solution of the diffusion equation

The traditional diffusive particle tracking equation provides an updated particle location as a function of its previous location and molecular diffusion coefficient while maintaining a constant time step. A smaller time step yields an increasingly accurate, yet more computationally demanding solution. Selection of this time step becomes an important consideration and, depending on the complexity of the problem, a single optimum value may not exist. The characteristics of the system under consideration may be such that a constant time step may yield solutions with insufficient accuracy in some portions of the domain and excess computation time for others. In this work, new particle tracking equations specifically designed for the solution of problems associated with diffusion processes in one, two, and three dimensions are presented. Instead of a constant time step, the proposed equations employ a constant spatial step. Using a traditional particle tracking algorithm, the travel time necessary for a particle with a diffusion coefficient inversely proportional to its diameter to achieve a pre-specified distance was determined. Because the size of a particle affects how it diffuses in a quiescent fluid, it is expected that two differently sized particles would require different travel times to move a given distance. The probability densities of travel times for plumes of monodisperse particles were consistently found to be log-normal in shape. The parameters describing this log-normal distribution, i.e., mean and standard deviation, are functions of the distance specified for travel and the diffusion coefficient of the particles. Thus, a random number selected from this distribution approximates the time required for a given particle to travel a specified distance. The new equations are straightforward and may be easily incorporated into appropriate particle tracking algorithms. In addition, the new particle tracking equations are as accurate and often more computationally efficient than the traditional particle tracking equation.

Electrostatic Spray Deposition of Copper–Indium Thin Films

Electrostatic spray deposition is an innovative coating technique that produces fine, uniform, self-dispersive (due to Coulombic repulsion), and highly wettable, atomized droplets. Copper–indium salts are dissolved in an alcohol-based solvent; this precursor is then electrostatically sprayed onto a moderately heated, molybdenum-coated substrate. Precursor flowrates range from 0.02 to 5 mL/h under applied voltages of 1–18 kV, yielding droplet sizes around a few hundred nanometers. Comparing scanning electron microscope images of the coated samples showed that the substrate temperature, applied voltage, and precursor flowrate were the primary parameters controlling coating quality. Also, the most stable electrostatic spray mode that reliably produced uniform and fine droplets was the cone-jet mode with a Taylor cone issuing from the nozzle.

Determining the random time step in a constant spatial step particle tracking algorithm

In some cases, the accuracy and efficiency of a particle tracking model may be greatly enhanced by determining the time for a particle to travel a specified distance rather than the distance traveled during some time interval. For instance, it may be desirable to know when a particle reaches a boundary or interface or a location where the system properties change. In this work, we derive an analytical expression in the form of a probability function describing the distribution of random times necessary for a particle to diffusively travel a specified distance. Upon substitution of the specified distance and a random number for the probability, the expression may be solved for the necessary time. Comparison of the results from this equation with an empirical expression determined by James and Chrysikopoulos (Chem. Eng. Sci. 56(23)(2001)6535) shows excellent agreement. Recommendations for implementing the analytical solution into particle tracking algorithms with or without a deterministic velocity component are included. This general equation is amenable to use in modeling both fractured and porous media systems.