A geometric construction of traveling waves in a bioremediation.

Bioremediation is a promising technique for cleaning contaminated soil. We study an idealized bioremediation model involving a substrate (contaminant to be removed), electron acceptor (added nutrient), and microorganisms in a one-dimensional soil column. Using geometric singular perturbation theory, we construct traveling waves (TW) corresponding to motion of a biologically active zone, in which the microorganisms consume both substrate and acceptor. For certain values of the parameters, the traveling waves exist on a three-dimensional slow manifold within the five-dimensional phase space. We prove persistence of the slow manifold under perturbation by controlling the nonlinearity via a change of coordinates, and we construct the wave in the transverse intersection of appropriate stable and unstable manifolds in this slow manifold. We study how the TW depends on the half saturation constants and other parameters and investigate numerically a bifurcation in which the TW loses stability to a periodic wav

From Individual to Collective Behavior of Unicellular Organisms: Recent Results and Open Problems

The collective movements of unicellular organisms such as bacteria or amoeboid (crawling) cells are often modeled by partial differential equations (PDEs) that describe the time evolution of cell density. In particular, chemotaxis equations have been used to model the movement towards various kinds of extracellular cues. Well-developed analytical and numerical methods for analyzing the time-dependent and time-independent properties of solutions make this approach attractive. However, these models are often based on phenomenological descriptions of cell fluxes with no direct correspondence to individual cell processes such signal transduction and cell movement. This leads to the question of how to justify these macroscopic PDEs from microscopic descriptions of cells, and how to relate the macroscopic quantities in these PDEs to individual-level parameters. Here we summarize recent progress on this question in the context of bacterial and amoeboid chemotaxis, and formulate several open problems

Statistical Analysis of a Semilinear Hyperbolic System Advected by a White in Time Random Velocity Field

We study a system of semilinear hyperbolic equations passively advected by smooth white noise in time random velocity fields. Such a system arises in modeling non-premixed isothermal turbulent flames under single-step kinetics of fuel and oxidizer. We derive closed equations for one-point and multi-point probability distribution functions (PDFs) and closed form analytical formulas for the one point PDF function, as well as the two-point PDF function under homogeneity and isotropy. Exact solution formulas allows us to analyze the ensemble averaged fuel/oxidizer concentrations and the motion of their level curves. We recover the empirical formulas of combustion in the thin reaction zone limit and show that these approximate formulas can either underestimate or overestimate average concentrations when reaction zone is not tending to zero. We show that the averaged reaction rate slows down locally in space due to random advection induced diffusion; and that the level curves of ensemble averaged concentration undergo diffusion about mean locations.Comment: 18 page

Transport of nonlinearly biodegradable contaminants in aquifers

This thesis deals with the transport behavior of nonlinearly biodegradable contaminants in aquifers. Such transport occurs during in situ bioremediation which is based on the injection of an electron acceptor or electron donor. The main interests in this thesis are the mutual influences of underlying processes, i.e. transport, adsorption and biodegradation, and their influence on in situ bioremediation performance. To gain insight in these influences, the processes in a homogeneous aquifer are studied. Subsequently, the effect of physical heterogeneity of an aquifer on the displacement of the biodegradable contaminant is examined.Considering a homogeneous aquifer, numerical simulations are performed to ascertain the effect of transport, adsorption and biodegradation on the displacement of the contaminant and of the electron acceptor or electron donor. In the initial phase, the developed numerical results are successfully described by first order degradation. In the final phase, the numerical results show a traveling wave behavior; the developed concentration fronts have constant front shapes and 'travel' with a constant velocity through the aquifer. This behavior is due to the balance between the steepening effect of nonlinear biodegradation and the spreading effect of dispersion. Because of this traveling wave behavior, semi-analytical solutions have been derived that satisfactorily approximate the numerical results. These semi-analytical solutions are used to assess the performance of the in situ bioremediation. If in situ bioremediation is applied to a polluted site, the electron acceptor injection concentration and the injection velocity will be the only manipulative properties. By varying these two properties, the in situ bioremediation performance can be influenced and optimized.To study a physical heterogeneous aquifer, the hydraulic conductivity is considered spatially variable and it is assumed to be a random space function. The effect of physical heterogeneity is determined using a Lagrangian stochastic approach. Results show that incorporation of physical heterogeneity leads to a spreading of the breakthrough curve of both the contaminant and the electron acceptor or electron donor. In case of a large degree of heterogeneity, i.e. a strongly heterogeneous aquifer, it is the heterogeneity which determines the shape of the breakthrough curve and not the dispersion or nonlinear biodegradation.</p

Lattice-Boltzmann Modeling of Bacterial Chemotaxis in the Subsurface

The Lattice Boltzmann method (LBM) has been widely used because it is well-suited to model flow and transport in the complex geometries that are typical for subsurface porous media. Bacterial chemotaxis enables motile bacteria to move preferably toward chemoattractants that may be contaminants in the subsurface. This microbial phenomenon provides a valuable mechanism to enhance in situ bioremediation. Therefore, we developed Lattice Boltzmann (LB) models to study bacterial chemotaxis in the subsurface. A multiple-relaxation-time (MRT) LB model was developed to study the formation and migration of traveling bacterial waves caused by chemotaxis (chemotactic waves) in the absence of bacterial growth and decay. This model was validated by comparing simulations with experiments in which the chemotactic bacteria entered a tube filled with substrate due to chemotaxis. Simulations were performed to evaluate the effects of substrate diffusion, initial bacterial concentration, and hydrodynamic dispersion on the formation, shape, and propagation of such chemotactic waves. Wave formation requires a sufficiently high initial number of bacteria and a small substrate diffusion coefficient. Uniform flow does not affect the waves while shear flow does. Bacterial waves move both upstream and downstream when the flow velocity is small. However, the waves disappear once the velocity becomes large due to hydrodynamic dispersion. Generally waves can only be observed if the dimensionless ratio between a particularly defined coefficient, chemotactic sensitivity coefficient, and the effective diffusion coefficient of the bacteria exceeds a critical value, that is, when the biased movement due to chemotaxis overcomes the diffusion-like movement due to the random motility and hydrodynamic dispersion. Another two-relaxation-time (TRT) LB model was also introduced to simulate bacterial chemotaxis and other reactive transport. The TRT LB model can eliminate numerical diffusion by including a velocity correction term. One-dimensional solute transport with initial Gaussian and top hat distributions were investigated to evaluate the accuracy and stability of the TRT models with and without the velocity correction. The TRT model with the correction demonstrated better numerical accuracy and stability than that without the correction. When the velocity is small, the numerical diffusion can be neglected, and the TRT model without the correction attained very similar simulation results as the TRT model with the correction. However, it is necessary for the TRT model to include the velocity correction when the velocity is large. Since bacterial survival is a significant factor for contaminant remediation at contaminated sites, we studied the coupled effects of chemotaxis and growth on bacterial migration and contaminant remediation. The impacts of initial electron acceptor concentration on different bacteria and substrate systems were examined. The simulations showed that bacteria could form a growth/decay/motility wave due to a dynamic equilibrium between bacterial growth, decay and random motility, even though the bacteria perform no chemotaxis. We derived an analytical solution to estimate this growth/decay/motility wave speed. The initial electron acceptor concentration was shown to significantly affect the bacterial movement and substrate removal. The impact of chemotaxis on bacterial migration is determined by comparison of the chemotactic wave speed with the growth/decay/motility wave speed. When chemotaxis is too weak to allow for the formation of a chemotactic wave or its wave speed is less than half of the growth/decay/motility wave speed, it hardly enhances the bacterial propagation. However, chemotaxis significantly improves bacterial propagation once its wave speed exceeds the growth/decay/motility wave speed. The bacterial survival plays a crucial role in determining the efficiency of contaminant removal. If there is no growth, the traveling wave will move with a decreasing speed and finally terminates. Although chemotaxis has been widely observed to be able to improve contaminant degradation in laboratories, it is rarely reported to enhance bioremediation at field sites. We discuss this discrepancy based on our simulation findings and suggest operable measures to take advantage of chemotaxis in in situ bioremediation

Ultrasonic enhanced soil washing

Soil washing is an ex-situ process employing chemical and physical extraction and separation techniques to remove a broad range of organic, inorganic, and radioactive contaminants from soils. This research investigates the enhanced soil washing of a high level Polycyclic Aromatic Hydrocarbons (PAHs) contaminated coal tar soil by the application of ultrasound energy coupled with surfactant (soap) emulsions and attempts to optimize pollutant removal from contaminated soils. The non-ionic surfactant, octyl-phenyl-ethoxylate, was used as the surfactant. Using bench-scale experiments, the magnitude of the ultrasonic enhancement was evaluated by changing the process parameters, such as ultrasonic power density, Dwell (extractor residence time), surfactant concentration, solvent ratio (liquid/soil w/w ratio), pH, and temperature. Experimental results show that the ultrasonic power density was the main contributing factor for the removal of PAHs. In general, the enhancement of removal efficiency due to ultrasound reached up to 40% to 60% when compared with that without ultrasound. The optimum condition with ultrasound was obtained at a solvent ratio of 25 with 750 Watts power density, 30 minutes dwell time, and 1% concentration of surfactant solution. The removal efficiency can be further improved by increasing the pH of the surfactant solution

Stochastic forward and inverse groundwater flow and solute transport modeling

Keywords: calibration, inverse modeling, stochastic modeling, nonlinear biodegradation, stochastic-convective, advective-dispersive, travel time, network design, non-Gaussian distribution, multimodal distribution, representers This thesis offers three new approaches that contribute to the ability of groundwater modelers to better account for heterogeneity in physically-based, fully distributed groundwater models. In both forward and inverse settings, this thesis tackles major issues with respect to handling heterogeneity and uncertainty in various situations, and thus extends the ability to correctly and/or effectively deal with heterogeneity to these particular situations. The first method presented in the thesis uses the recently developed advective-dispersive streamtube approach in combination with a one-dimensional traveling wave solution for nonlinear bioreactive transport, to study the interplay between physical heterogeneity, local-scale dispersion and nonlinear biodegradation and gain insight in the long-term asymptotic behavior of solute fronts, in order to deduce (the validity of) upscaling equations. Using the method in synthetic small-scale numerical experiments, it is shown that asymptotic front shapes are neither Fickian nor constant, which raises questions about the current practice of upscaling bioreactive transport. The second method presented in the thesis enhances the management of heterogeneity by extending inverse theory (specifically, the representer-based inverse method) to determinations of groundwater age/travel time. A first-order methodology is proposed to include groundwater age or tracer arrival time determinations in measurement network design. Using the method, it is shown that, in the applied synthetic numerical example, an age estimation network outperforms equally sized head measurement networks and conductivity measurement networks, even if the age estimations are highly uncertain. The study thus suggests a high potential of travel time/groundwater age data to constrain groundwater models. Finally, the thesis extends the applicability of inverse methods to multimodal parameter distributions. Multimodal distributions arise when multiple statistical populations exist within one parameter field, each having different means and/or variances of the parameter of concern. No inverse methods exist that can calibrate multimodal parameter distributions while preserving the geostatistical properties of the various statistical populations. The thesis proposes a method that resolves the difficulties existing inverse methods have with the multimodal distribution. The method is successfully applied to both synthetic and real-world cases. </p

Vector Winter 2016

Vector is the student engineering magazine on campus. Published by the Student Engineering Council, Vector is completely written, managed, and designed by students for students. With issues dating back to 1971, the magazine has a long-standing tradition of serving as the voice for engineering students at The University of Texas at Austin. The Vector staff publishes two issues per semester. For more information regarding the Vector magazine, please contact us at vector@ sec.engr.utexas.eduCockrell School of EngineeringCockrell School of Engineerin

Numerical Simulations of Gravity-Driven Fingering in Unsaturated Porous Media Using a Non-Equilibrium Model

This is a computational study of gravity-driven fingering instabilities in unsaturated porous media. The governing equations and corresponding numerical scheme are based on the work of Nieber et al. [Ch. 23 in Soil Water Repellency, eds. C. J. Ritsema and L. W. Dekker, Elsevier, 2003] in which non-monotonic saturation profiles are obtained by supplementing the Richards equation with a non-equilibrium capillary pressure-saturation relationship, as well as including hysteretic effects. The first part of the study takes an extensive look at the sensitivity of the finger solutions to certain key parameters in the model such as capillary shape parameter, initial saturation, and capillary relaxation coefficient. The second part is a comparison to published experimental results that demonstrates the ability of the model to capture realistic fingering behaviour