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Salek MM, Carrara F, Zhou J, Stocker R, Jimenez‐Martinez J. Multiscale Porosity Microfluidics to Study Bacterial Transport in Heterogeneous Chemical Landscapes. ADVANCED SCIENCE (WEINHEIM, BADEN-WURTTEMBERG, GERMANY) 2024; 11:e2310121. [PMID: 38445967 PMCID: PMC11132056 DOI: 10.1002/advs.202310121] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/22/2023] [Indexed: 03/07/2024]
Abstract
Microfluidic models are proving to be powerful systems to study fundamental processes in porous media, due to their ability to replicate topologically complex environments while allowing detailed, quantitative observations at the pore scale. Yet, while porous media such as living tissues, geological substrates, or industrial systems typically display a porosity that spans multiple scales, most microfluidic models to date are limited to a single porosity or a small range of pore sizes. Here, a novel microfluidic system with multiscale porosity is presented. By embedding polyacrylamide (PAAm) hydrogel structures through in-situ photopolymerization in a landscape of microfabricated polydimethylsiloxane (PDMS) pillars with varying spacing, micromodels with porosity spanning several orders of magnitude, from nanometers to millimeters are created. Experiments conducted at different porosity patterns demonstrate the potential of this approach to characterize fundamental and ubiquitous biological and geochemical transport processes in porous media. Accounting for multiscale porosity allows studies of the resulting heterogeneous fluid flow and concentration fields of transported chemicals, as well as the biological behaviors associated with this heterogeneity, such as bacterial chemotaxis. This approach brings laboratory studies of transport in porous media a step closer to their natural counterparts in the environment, industry, and medicine.
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Affiliation(s)
- M. Mehdi Salek
- Department of Biological Engineering, School of EngineeringMassachusetts Institute of TechnologyCambridgeMAUSA
- Department of CivilEnvironmental and Geomatic EngineeringInstitute of Environmental EngineeringETH ZurichZurichSwitzerland
| | - Francesco Carrara
- Department of CivilEnvironmental and Geomatic EngineeringInstitute of Environmental EngineeringETH ZurichZurichSwitzerland
| | - Jiande Zhou
- Department of CivilEnvironmental and Geomatic EngineeringInstitute of Environmental EngineeringETH ZurichZurichSwitzerland
- Microsystems LaboratoryInstitute of MicroengineeringSchool of EngineeringEPFLLausanneSwitzerland
| | - Roman Stocker
- Department of CivilEnvironmental and Geomatic EngineeringInstitute of Environmental EngineeringETH ZurichZurichSwitzerland
| | - Joaquin Jimenez‐Martinez
- Department of CivilEnvironmental and Geomatic EngineeringInstitute of Environmental EngineeringETH ZurichZurichSwitzerland
- Department of Water Resources and Drinking WaterEawagDubendorfSwitzerland
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2
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Bultreys T, Ellman S, Schlepütz CM, Boone MN, Pakkaner GK, Wang S, Borji M, Van Offenwert S, Moazami Goudarzi N, Goethals W, Winardhi CW, Cnudde V. 4D microvelocimetry reveals multiphase flow field perturbations in porous media. Proc Natl Acad Sci U S A 2024; 121:e2316723121. [PMID: 38478686 PMCID: PMC10962996 DOI: 10.1073/pnas.2316723121] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/26/2023] [Accepted: 02/04/2024] [Indexed: 03/27/2024] Open
Abstract
Many environmental and industrial processes depend on how fluids displace each other in porous materials. However, the flow dynamics that govern this process are still poorly understood, hampered by the lack of methods to measure flows in optically opaque, microscopic geometries. We introduce a 4D microvelocimetry method based on high-resolution X-ray computed tomography with fast imaging rates (up to 4 Hz). We use this to measure flow fields during unsteady-state drainage, injecting a viscous fluid into rock and filter samples. This provides experimental insight into the nonequilibrium energy dynamics of this process. We show that fluid displacements convert surface energy into kinetic energy. The latter corresponds to velocity perturbations in the pore-scale flow field behind the invading fluid front, reaching local velocities more than 40 times faster than the constant pump rate. The characteristic length scale of these perturbations exceeds the characteristic pore size by more than an order of magnitude. These flow field observations suggest that nonlocal dynamic effects may be long-ranged even at low capillary numbers, impacting the local viscous-capillary force balance and the representative elementary volume. Furthermore, the velocity perturbations can enhance unsaturated dispersive mixing and colloid transport and yet, are not accounted for in current models. Overall, this work shows that 4D X-ray velocimetry opens the way to solve long-standing fundamental questions regarding flow and transport in porous materials, underlying models of, e.g., groundwater pollution remediation and subsurface storage of CO2 and hydrogen.
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Affiliation(s)
- Tom Bultreys
- Ghent University Centre for X-ray Tomography (UGCT), Ghent University, Ghent9000, Belgium
- Department of Geology, Ghent University, Ghent9000, Belgium
| | - Sharon Ellman
- Ghent University Centre for X-ray Tomography (UGCT), Ghent University, Ghent9000, Belgium
- Department of Geology, Ghent University, Ghent9000, Belgium
| | | | - Matthieu N. Boone
- Ghent University Centre for X-ray Tomography (UGCT), Ghent University, Ghent9000, Belgium
- Department of Physics and Astronomy, Ghent University, Ghent9000, Belgium
| | - Gülce Kalyoncu Pakkaner
- Ghent University Centre for X-ray Tomography (UGCT), Ghent University, Ghent9000, Belgium
- Department of Geology, Ghent University, Ghent9000, Belgium
| | - Shan Wang
- Ghent University Centre for X-ray Tomography (UGCT), Ghent University, Ghent9000, Belgium
- Department of Geology, Ghent University, Ghent9000, Belgium
| | - Mostafa Borji
- Ghent University Centre for X-ray Tomography (UGCT), Ghent University, Ghent9000, Belgium
- Department of Geology, Ghent University, Ghent9000, Belgium
| | - Stefanie Van Offenwert
- Ghent University Centre for X-ray Tomography (UGCT), Ghent University, Ghent9000, Belgium
- Department of Geology, Ghent University, Ghent9000, Belgium
| | - Niloofar Moazami Goudarzi
- Ghent University Centre for X-ray Tomography (UGCT), Ghent University, Ghent9000, Belgium
- Department of Physics and Astronomy, Ghent University, Ghent9000, Belgium
| | - Wannes Goethals
- Ghent University Centre for X-ray Tomography (UGCT), Ghent University, Ghent9000, Belgium
- Department of Physics and Astronomy, Ghent University, Ghent9000, Belgium
| | - Chandra Widyananda Winardhi
- Ghent University Centre for X-ray Tomography (UGCT), Ghent University, Ghent9000, Belgium
- Department of Geology, Ghent University, Ghent9000, Belgium
| | - Veerle Cnudde
- Ghent University Centre for X-ray Tomography (UGCT), Ghent University, Ghent9000, Belgium
- Department of Geology, Ghent University, Ghent9000, Belgium
- Department of Earth Sciences, Utrecht University, CB Utrecht3584, The Netherlands
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3
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Nguyen VT, Pham NH, Papavassiliou DV. Prediction of the aggregation rate of nanoparticles in porous media in the diffusion-controlled regime. Sci Rep 2024; 14:1916. [PMID: 38253573 PMCID: PMC10803321 DOI: 10.1038/s41598-023-50643-x] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/01/2023] [Accepted: 12/22/2023] [Indexed: 01/24/2024] Open
Abstract
The fate and aggregation of nanoparticles (NPs) in the subsurface are important due to potentially harmful impacts on the environment and human health. This study aims to investigate the effects of flow velocity, particle size, and particle concentration on the aggregation rate of NPs in a diffusion-limited regime and build an equation to predict the aggregation rate when NPs move in the pore space between randomly packed spheres (including mono-disperse, bi-disperse, and tri-disperse spheres). The flow of 0.2 M potassium chloride (KCl) through the random sphere packings was simulated by the lattice Boltzmann method (LBM). The movement and aggregation of cerium oxide (CeO2) particles were then examined by using a Lagrangian particle tracking method based on a force balance approach. This method relied on Newton's second law of motion and took the interaction forces among particles into account. The aggregation rate of NPs was found to depend linearly on time, and the slope of the line was a power function of the particle concentration, the Reynolds (Re) and Schmidt (Sc) numbers. The exponent for the Sc number was triple that of the Re number, which was evidence that the random movement of NPs has a much stronger effect on the rate of diffusion-controlled aggregation than the convection.
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Affiliation(s)
- Vi T Nguyen
- School of Sustainable Chemical, Biological and Materials Engineering, The University of Oklahoma, Norman, OK, 73019, USA
| | - Ngoc H Pham
- School of Sustainable Chemical, Biological and Materials Engineering, The University of Oklahoma, Norman, OK, 73019, USA
| | - Dimitrios V Papavassiliou
- School of Sustainable Chemical, Biological and Materials Engineering, The University of Oklahoma, Norman, OK, 73019, USA.
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4
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Markale I, Carrel M, Kurz DL, Morales VL, Holzner M, Jiménez-Martínez J. Internal Biofilm Heterogeneities Enhance Solute Mixing and Chemical Reactions in Porous Media. ENVIRONMENTAL SCIENCE & TECHNOLOGY 2023; 57:8065-8074. [PMID: 37205794 DOI: 10.1021/acs.est.2c09082] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/21/2023]
Abstract
Bacterial biofilms can form in porous media that are of interest in industrial applications ranging from medical implants to biofilters as well as in environmental applications such as in situ groundwater remediation, where they can be critical locations for biogeochemical reactions. The presence of biofilms modifies porous media topology and hydrodynamics by clogging pores and consequently solutes transport and reactions kinetics. The interplay between highly heterogeneous flow fields found in porous media and microbial behavior, including biofilm growth, results in a spatially heterogeneous biofilm distribution in the porous media as well as internal heterogeneity across the thickness of the biofilm. Our study leverages highly resolved three-dimensional X-ray computed microtomography images of bacterial biofilms in a tubular reactor to numerically compute pore-scale fluid flow and solute transport by considering multiple equivalent stochastically generated internal permeability fields for the biofilm. We show that the internal heterogeneous permeability mainly impacts intermediate velocities when compared with homogeneous biofilm permeability. While the equivalent internal permeability fields of the biofilm do not impact fluid-fluid mixing, they significantly control a fast reaction. For biologically driven reactions such as nutrient or contaminant uptake by the biofilm, its internal permeability field controls the efficiency of the process. This study highlights the importance of considering the internal heterogeneity of biofilms to better predict reactivity in industrial and environmental bioclogged porous systems.
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Affiliation(s)
- Ishaan Markale
- Eawag, Swiss Federal Institute of Aquatic Science and Technology, 8600 Dübendorf, Switzerland
- Department of Civil, Environmental and Geomatic Engineering, ETH Zürich, 8093 Zürich, Switzerland
| | | | - Dorothee L Kurz
- Eawag, Swiss Federal Institute of Aquatic Science and Technology, 8600 Dübendorf, Switzerland
- Department of Civil, Environmental and Geomatic Engineering, ETH Zürich, 8093 Zürich, Switzerland
| | - Verónica L Morales
- Department of Civil and Environmental Engineering, University of California Davis, Davis, California 95616-5270, United States
| | - Markus Holzner
- Eawag, Swiss Federal Institute of Aquatic Science and Technology, 8600 Dübendorf, Switzerland
- WSL, Swiss Federal Institute of Forest, Snow and Landscape Research, 8903 Birmensdorf, Switzerland
| | - Joaquín Jiménez-Martínez
- Eawag, Swiss Federal Institute of Aquatic Science and Technology, 8600 Dübendorf, Switzerland
- Department of Civil, Environmental and Geomatic Engineering, ETH Zürich, 8093 Zürich, Switzerland
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5
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Kurz DL, Secchi E, Stocker R, Jimenez-Martinez J. Morphogenesis of Biofilms in Porous Media and Control on Hydrodynamics. ENVIRONMENTAL SCIENCE & TECHNOLOGY 2023; 57:5666-5677. [PMID: 36976631 DOI: 10.1021/acs.est.2c08890] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/18/2023]
Abstract
The functioning of natural and engineered porous media, like soils and filters, depends in many cases on the interplay between biochemical processes and hydrodynamics. In such complex environments, microorganisms often form surface-attached communities known as biofilms. Biofilms can take the shape of clusters, which alter the distribution of fluid flow velocities within the porous medium, subsequently influencing biofilm growth. Despite numerous experimental and numerical efforts, the control of the biofilm clustering process and the resulting heterogeneity in biofilm permeability is not well understood, limiting our predictive abilities for biofilm-porous medium systems. Here, we use a quasi-2D experimental model of a porous medium to characterize biofilm growth dynamics for different pore sizes and flow rates. We present a method to obtain the time-resolved biofilm permeability field from experimental images and use the obtained permeability field to compute the flow field through a numerical model. We observe a biofilm cluster size distribution characterized by a spectrum slope evolving in time between -2 and -1, a fundamental measure that can be used to create spatio-temporal distributions of biofilm clusters for upscaled models. We find a previously undescribed biofilm permeability distribution, which can be used to stochastically generate permeability fields within biofilms. An increase in velocity variance for a decrease in physical heterogeneity shows that the bioclogged porous medium behaves differently than expected from studies on heterogeneity in abiotic porous media.
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Affiliation(s)
- Dorothee L Kurz
- Department of Civil, Environmental and Geomatic Engineering, Institute of Environmental Engineering, ETH Zurich, Laura-Hezner-Weg 7, 8093 Zurich, Switzerland
- Department Water Resources and Drinking Water, Eawag, Swiss Federal Institute of Aquatic Science and Technology, 8600 Dübendorf, Switzerland
| | - Eleonora Secchi
- Department of Civil, Environmental and Geomatic Engineering, Institute of Environmental Engineering, ETH Zurich, Laura-Hezner-Weg 7, 8093 Zurich, Switzerland
| | - Roman Stocker
- Department of Civil, Environmental and Geomatic Engineering, Institute of Environmental Engineering, ETH Zurich, Laura-Hezner-Weg 7, 8093 Zurich, Switzerland
| | - Joaquin Jimenez-Martinez
- Department of Civil, Environmental and Geomatic Engineering, Institute of Environmental Engineering, ETH Zurich, Laura-Hezner-Weg 7, 8093 Zurich, Switzerland
- Department Water Resources and Drinking Water, Eawag, Swiss Federal Institute of Aquatic Science and Technology, 8600 Dübendorf, Switzerland
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6
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Mixing Controlled Adsorption at the Liquid-Solid Interfaces in Unsaturated Porous Media. Transp Porous Media 2023; 146:159-175. [PMID: 36685618 PMCID: PMC9849304 DOI: 10.1007/s11242-022-01747-x] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/16/2021] [Accepted: 01/13/2022] [Indexed: 01/25/2023]
Abstract
The unsaturated zone, located between the soil surface and the phreatic level, plays an important role in defining the fate of any substance entering the subsoil. In addition to the processes of flow and transport taking place in the liquid phase, surface reactions such as adsorption to the solid phase may occur and increase the residence time of the substance entering the system. In this study, we aim to understand the pore-scale mechanisms that control adsorption in unsaturated systems. We combine 2D pore-scale experimental images with numerical simulations to analyze flow, transport, and adsorption under different liquid saturation degrees. We demonstrate the role of mixing on adsorption at the liquid-solid interfaces by analyzing the deformation in time of a pulse-injected surfactant. We also analyze the impact of the isotherm functional shape and the inclusion of the liquid-gas interfaces as adsorption sites on this surface reaction. The enhancement of mixing as saturation decreases is accompanied by a reduction in the amount of adsorbed mass, located mainly along preferential flow paths, where the solute is primarily transported. For the same isotherm, a nonlinear behavior of adsorption as a function of liquid saturation has been observed. This is explained by the nonlinear variation of the volume fraction of liquid behaving as preferential path or stagnation zone as liquid saturation decreases, despite the linear decrease in the surface area of solids accessible for adsorption. Supplementary Information The online version contains supplementary material available at 10.1007/s11242-022-01747-x.
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7
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Mixing in Porous Media: Concepts and Approaches Across Scales. Transp Porous Media 2022. [DOI: 10.1007/s11242-022-01852-x] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/17/2022]
Abstract
AbstractThis review provides an overview of concepts and approaches for the quantification of passive, non-reactive solute mixing in steady uniform porous media flows across scales. Mixing in porous media is the result of the interaction of spatial velocity fluctuations and diffusion or local-scale dispersion, which may lead to the homogenization of an initially segregated system. Velocity fluctuations are induced by spatial medium heterogeneities at the pore, Darcy or regional scales. Thus, mixing in porous media is a multiscale process, which depends on the medium structure and flow conditions. In the first part of the review, we discuss the interrelated processes of stirring, dispersion and mixing, and review approaches to quantify them that apply across scales. This implies concepts of hydrodynamic dispersion, approaches to quantify mixing state and mixing dynamics in terms of concentration statistics, and approaches to quantify the mechanisms of mixing. We review the characterization of stirring in terms of fluid deformation and folding and its relation with hydrodynamic dispersion. The integration of these dynamics to quantify the mechanisms of mixing is discussed in terms of lamellar mixing models. In the second part of this review, we discuss these concepts and approaches for the characterization of mixing in Poiseuille flow, and in porous media flows at the pore, Darcy and regional scales. Due to the fundamental nature of the mechanisms and processes of mixing, the concepts and approaches discussed in this review underpin the quantitative analysis of mixing phenomena in porous media flow systems in general.
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8
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Ranzinger F, Horn H, Wagner M. Imaging of particle deposition and resulting flow field during flocculation filtration within a granulated activated carbon filter. Sep Purif Technol 2022. [DOI: 10.1016/j.seppur.2022.121033] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/18/2022]
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9
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A Primer on the Dynamical Systems Approach to Transport in Porous Media. Transp Porous Media 2022. [DOI: 10.1007/s11242-022-01811-6] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/26/2022]
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10
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Nguyen VT, Papavassiliou DV. Velocity Magnitude Distribution for Flow in Porous Media. Ind Eng Chem Res 2021. [DOI: 10.1021/acs.iecr.1c02474] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- Vi T. Nguyen
- School of Chemical Biological and Materials Engineering, The University of Oklahoma, Norman, Oklahoma 73019, United States
| | - Dimitrios V. Papavassiliou
- School of Chemical Biological and Materials Engineering, The University of Oklahoma, Norman, Oklahoma 73019, United States
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11
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Flow Path Resistance in Heterogeneous Porous Media Recast into a Graph-Theory Problem. Transp Porous Media 2021. [DOI: 10.1007/s11242-021-01671-6] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/20/2022]
Abstract
Abstract
This work aims to describe the spatial distribution of flow from characteristics of the underlying pore structure in heterogeneous porous media. Thousands of two-dimensional samples of polydispersed granular media are used to (1) obtain the velocity field via direct numerical simulations, and (2) conceptualize the pore network as a graph in each sample. Analysis of the flow field allows us to distinguish preferential from stagnant flow regions and to quantify how channelized the flow is. Then, the graph’s edges are weighted by geometric attributes of their corresponding pores to find the path of minimum resistance of each sample. Overlap between the preferential flow paths and the predicted minimum resistance path determines the accuracy in individual samples. An evolutionary algorithm is employed to determine the “fittest” weighting scheme (here, the channel’s arc length to pore throat ratio) that maximizes accuracy across the entire dataset while minimizing over-parameterization. Finally, the structural similarity of neighboring edges is analyzed to explain the spatial arrangement of preferential flow within the pore network. We find that connected edges within the preferential flow subnetwork are highly similar, while those within the stagnant flow subnetwork are dissimilar. The contrast in similarity between these regions increases with flow channelization, explaining the structural constraints to local flow. The proposed framework may be used for fast characterization of porous media heterogeneity relative to computationally expensive direct numerical simulations.
Article Highlights
A quantitative assessment of flow channeling is proposed that distinguishes pore-scale flow fields into preferential and stagnant flow regions.
Geometry and topology of the pore network are used to predict the spatial distribution of fast flow paths from structural data alone.
Local disorder of pore networks provides structural constraints for flow separation into preferential v stagnant regions and informs on their velocity contrast.
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12
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Mueller EV, Gallagher MR, Skowronski N, Hadden RM. Approaches to Modeling Bed Drag in Pine Forest Litter for Wildland Fire Applications. Transp Porous Media 2021. [DOI: 10.1007/s11242-021-01637-8] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Abstract
AbstractModeling flow in vegetative fuel beds is a key component in any detailed physics-based tool for simulating wildland fire dynamics. Current approaches for drag modeling, particularly those employed in multiphase computational fluid dynamics (CFD) models, tend to take a relatively simple form and have been applied to a wide range of fuel structures. The suitability of these approaches has not been rigorously tested for conditions which may be encountered in a wildland fire context. Here, we focus on beds of Pinus rigida needle litter and undertake a two-part study to quantify the drag and evaluate the capabilities of a multiphase large eddy simulation CFD model, the NIST Fire Dynamics Simulator. In the first part, bed drag was measured in a wind tunnel under a range of conditions. The results were fit to a Forchheimer model, and the bed permeability was quantified. A traditional approach employed in the multiphase formulation was compared to the parameterized Forchheimer equation and was found to over-predict the drag by a factor of 1.2–2.5. In the second part, the development of a velocity profile above and within a discrete fuel layer was measured. Using the Forchheimer equation obtained in the first part of the study, the CFD model was able to replicate a qualitatively consistent velocity profile development. Within the fuel bed, the model appeared to under-predict the velocity magnitudes, which may be the result of unresolved pore-scale flow dynamics.
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13
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Puyguiraud A, Gouze P, Dentz M. Pore-Scale Mixing and the Evolution of Hydrodynamic Dispersion in Porous Media. PHYSICAL REVIEW LETTERS 2021; 126:164501. [PMID: 33961446 DOI: 10.1103/physrevlett.126.164501] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/10/2020] [Revised: 02/09/2021] [Accepted: 03/24/2021] [Indexed: 06/12/2023]
Abstract
We study the interplay of pore-scale mixing and network-scale advection through heterogeneous porous media, and its role for the evolution and asymptotic behavior of hydrodynamic dispersion. In a Lagrangian framework, we identify three fundamental mechanisms of pore-scale mixing that determine large scale particle motion, namely, the smoothing of intrapore velocity contrasts, the increase of the tortuosity of particle paths, and the setting of a maximum time for particle transitions. Based on these mechanisms, we derive a theory that predicts anomalous and normal hydrodynamic dispersion in terms of the characteristic pore length, Eulerian velocity distribution, and Péclet number.
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Affiliation(s)
- Alexandre Puyguiraud
- Spanish National Research Council (IDAEA-CSIC), 08034, Barcelona, Spain and Geoscience Montpellier, CNRS, Université de Montpellier, 34090, Montpellier, France
| | - Philippe Gouze
- Spanish National Research Council (IDAEA-CSIC), 08034, Barcelona, Spain and Geoscience Montpellier, CNRS, Université de Montpellier, 34090, Montpellier, France
| | - Marco Dentz
- Spanish National Research Council (IDAEA-CSIC), 08034, Barcelona, Spain and Geoscience Montpellier, CNRS, Université de Montpellier, 34090, Montpellier, France
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14
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Espeso MB, Corada-Fernández C, García-Delgado M, Candela L, González-Mazo E, Lara-Martín PA, Jiménez-Martínez J. Structural control of the non-ionic surfactant alcohol ethoxylates (AEOs) on transport in natural soils. ENVIRONMENTAL POLLUTION (BARKING, ESSEX : 1987) 2021; 269:116021. [PMID: 33221085 DOI: 10.1016/j.envpol.2020.116021] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/31/2020] [Revised: 09/13/2020] [Accepted: 11/05/2020] [Indexed: 06/11/2023]
Abstract
Surfactants, after use, enter the environment through diffuse and point sources such as irrigation with treated and non-treated waste water and urban and industrial wastewater discharges. For the group of non-ionic synthetic surfactant alcohol ethoxylates (AEOs), most of the available information is restricted to the levels and fate in aquatic systems, whereas current knowledge of their behavior in soils is very limited. Here we characterize the behavior of different homologs (C12-C18) and ethoxymers (EO3, EO6, and EO8) of the AEOs through batch experiments and under unsaturated flow conditions during infiltration experiments. Experiments used two different agricultural soils from a region irrigated with reclaimed water (Guadalete River basin, SW Spain). In parallel, water flow and chemical transport were modelled using the HYDRUS-1D software package, calibrated using the infiltration experimental data. Estimates of water flow and reactive transport of all surfactants were in good agreement between infiltration experiments and simulations. The sorption process followed a Freundlich isotherm for most of the target compounds. A systematic comparison between sorption data obtained from batch and infiltration experiments revealed that the sorption coefficient (Kd) was generally lower in infiltration experiments, performed under environmental flow conditions, than in batch experiments in the absence of flow, whereas the exponent (β) did not show significant differences. For the low clay and organic carbon content of the soils used, no clear dependence of Kd on them was observed. Our work thus highlights the need to use reactive transport parameterization inferred under realistic conditions to assess the risk associated with alcohol ethoxylates in subsurface environments.
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Affiliation(s)
- M Botella Espeso
- Department of Civil, Environmental and Geomatic Engineering, ETH Zurich, 8093, Zürich, Switzerland
| | - C Corada-Fernández
- Department of Physical Chemistry, Faculty of Marine and Environmental Sciences, University of Cadiz, Campus of International Excellence of the Sea (CEI•MAR), Río San Pedro, Puerto Real, Cádiz, 11510, Spain
| | - M García-Delgado
- Department of Physical Chemistry, Faculty of Marine and Environmental Sciences, University of Cadiz, Campus of International Excellence of the Sea (CEI•MAR), Río San Pedro, Puerto Real, Cádiz, 11510, Spain
| | - L Candela
- IMDEA Water, Avenida Punto Com 2, Parque Científico Tecnológico Universidad de Alcalá, Alcalá de Henares, 28805, Madrid, Spain
| | - E González-Mazo
- Department of Physical Chemistry, Faculty of Marine and Environmental Sciences, University of Cadiz, Campus of International Excellence of the Sea (CEI•MAR), Río San Pedro, Puerto Real, Cádiz, 11510, Spain
| | - P A Lara-Martín
- Department of Physical Chemistry, Faculty of Marine and Environmental Sciences, University of Cadiz, Campus of International Excellence of the Sea (CEI•MAR), Río San Pedro, Puerto Real, Cádiz, 11510, Spain
| | - J Jiménez-Martínez
- Department of Civil, Environmental and Geomatic Engineering, ETH Zurich, 8093, Zürich, Switzerland; Department of Water Resources and Drinking Water, Eawag, 8600, Dübendorf, Switzerland.
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15
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Sherman T, Engdahl NB, Porta G, Bolster D. A review of spatial Markov models for predicting pre-asymptotic and anomalous transport in porous and fractured media. JOURNAL OF CONTAMINANT HYDROLOGY 2021; 236:103734. [PMID: 33221038 DOI: 10.1016/j.jconhyd.2020.103734] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/16/2020] [Revised: 10/02/2020] [Accepted: 10/19/2020] [Indexed: 06/11/2023]
Abstract
Heterogeneity across a broad range of scales in geologic porous media often manifests in observations of non-Fickian or anomalous transport. While traditional anomalous transport models can successfully make predictions in certain geological systems, increasing evidence suggests that assumptions relating to independent and identically distributed increments constrain where and when they can be reliably applied. A relatively novel model, the Spatial Markov model (SMM), relaxes the assumption of independence. The SMM belongs to the family of correlated continuous time random walks and has shown promise across a wide range of transport problems relevant to natural porous media. It has been successfully used to model conservative as well as more recently reactive transport in highly complex flows ranging from pore scales to much larger scales of interest in geology and subsurface hydrology. In this review paper we summarize its original development and provide a comprehensive review of its advances and applications as well as lay out a vision for its future development.
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Affiliation(s)
- Thomas Sherman
- Civil and Environmental Engineering and Earth Sciences, University of Notre Dame, South Bend, IN, USA
| | - Nicholas B Engdahl
- Department of Civil and Environmental Engineering, Washington State University, Pullman, WA, USA
| | - Giovanni Porta
- Dipartimento di Ingegneria Civile ed Ambientale, Politecnico di Milano, Piazza L. Da Vinci, 32, 20133 Milano, Italy
| | - Diogo Bolster
- Civil and Environmental Engineering and Earth Sciences, University of Notre Dame, South Bend, IN, USA.
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16
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Eberhard U, Seybold HJ, Secchi E, Jiménez-Martínez J, Rühs PA, Ofner A, Andrade JS, Holzner M. Mapping the local viscosity of non-Newtonian fluids flowing through disordered porous structures. Sci Rep 2020; 10:11733. [PMID: 32678140 PMCID: PMC7366636 DOI: 10.1038/s41598-020-68545-7] [Citation(s) in RCA: 14] [Impact Index Per Article: 3.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/05/2019] [Accepted: 06/15/2020] [Indexed: 11/11/2022] Open
Abstract
Flow of non-Newtonian fluids through topologically complex structures is ubiquitous in most biological, industrial and environmental settings. The interplay between local hydrodynamics and the fluid’s constitutive law determines the distribution of flow paths. Consequently the spatial heterogeneity of the viscous resistance controls mass and solute transport from the micron to the meter scale. Examples range from oil recovery and groundwater engineering to drug delivery, filters and catalysts. Here we present a new methodology to map the spatial variation of the local viscosity of a non-Newtonian fluid flowing through a complex pore geometry. We use high resolution image velocimetry to determine local shear rates. Knowing the local shear rate in combination with a separate measurement of the fluid’s constitutive law allows to quantitatively map the local viscosity at the pore scale. Our experimental results—which closely match with three-dimensional numerical simulations—demonstrate that the exponential decay of the longitudinal velocity distributions, previously observed for Newtonian fluids, is a function of the spatial heterogeneity of the local viscosity. This work sheds light on the relationship between hydraulic properties and the viscosity at the pore scale, which is of fundamental importance for predicting transport properties, mixing, and chemical reactions in many porous systems.
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Affiliation(s)
- U Eberhard
- Department of Civil, Environmental and Geomatic Engineering, ETH Zurich, 8093, Zurich, Switzerland. .,Swiss Federal Institute for Forest, Snow and Landscape Research, WSL, 8903, Birmensdorf, Switzerland.
| | - H J Seybold
- Department of Environmental Systems Science, ETH Zurich, 8092, Zurich, Switzerland
| | - E Secchi
- Department of Civil, Environmental and Geomatic Engineering, ETH Zurich, 8093, Zurich, Switzerland
| | - J Jiménez-Martínez
- Department of Civil, Environmental and Geomatic Engineering, ETH Zurich, 8093, Zurich, Switzerland.,Swiss Federal Institute of Aquatic Science and Technology, EAWAG, 8600, Dübendorf, Switzerland
| | - P A Rühs
- Department of Materials, ETH Zurich, 8093, Zurich, Switzerland
| | - A Ofner
- Department of Materials, ETH Zurich, 8093, Zurich, Switzerland
| | - J S Andrade
- Departamento de Física, Universidade Federal do Ceará, 60451-970, Fortaleza, Ceará, Brazil
| | - M Holzner
- Department of Civil, Environmental and Geomatic Engineering, ETH Zurich, 8093, Zurich, Switzerland.,Swiss Federal Institute of Aquatic Science and Technology, EAWAG, 8600, Dübendorf, Switzerland.,Swiss Federal Institute for Forest, Snow and Landscape Research, WSL, 8903, Birmensdorf, Switzerland
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17
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Zhang C, Suekane T, Minokawa K, Hu Y, Patmonoaji A. Solute transport in porous media studied by lattice Boltzmann simulations at pore scale and x-ray tomography experiments. Phys Rev E 2020; 100:063110. [PMID: 31962407 DOI: 10.1103/physreve.100.063110] [Citation(s) in RCA: 10] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/19/2019] [Indexed: 11/07/2022]
Abstract
With the aid of nondestructive microfocus x-ray computed tomography (CT), we performed three-dimensional (3D) tracer dispersion experiments on randomly unconsolidated packed beds. Plumes of nonreactive sodium iodide solution were point injected into a sodium chloride solvent as a tracer for the evaluation of the dispersion process. The asymptotic dispersion coefficient was obtainable within the experimental scale and was summarized over Péclet numbers from 11.7 to ∼860. Then, the lattice Boltzmann method and moment propagation method were used to elucidate the mechanisms embedded in the dispersion phenomenon. The methods were rigorously verified against the classical Taylor dispersion problem and extended to simulate fluid flow and tracer dispersion in high-resolution 3D digital porous structures from CT. The method of moments, Lagrangian velocity correction function, and dilution index were thoroughly analyzed to evaluate the dispersion behaviors. Numerical simulations revealed ballistic and superdiffusive regimes at the transient times, whereas asymptotic dispersion behaviors appear at longer characteristic times. Besides, the observed transient times unanimously persist over convective length scales of around 12 particles transversely and 16 particles longitudinally. The estimated dispersion coefficients from simulation are in consistence with the experimental result. Furthermore, the simulation also enabled the identification of regimes, including diffusive, power law, and mechanical dispersion. Thus, the proposed experimental and computational schemes are of practical means to study dispersion behaviors by direct pore scale imaging and modeling.
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Affiliation(s)
- Chunwei Zhang
- Department of Mechanical Engineering, Tokyo Institute of Technology, 2-12-1-I6-33 Ookayama, Meguro-ku, Tokyo 152-8550, Japan
| | - Tetsuya Suekane
- Department of Mechanical Engineering, Tokyo Institute of Technology, 2-12-1-I6-33 Ookayama, Meguro-ku, Tokyo 152-8550, Japan
| | - Kosuke Minokawa
- Department of Mechanical Engineering, Tokyo Institute of Technology, 2-12-1-I6-33 Ookayama, Meguro-ku, Tokyo 152-8550, Japan
| | - Yingxue Hu
- Department of Mechanical Engineering, Tokyo Institute of Technology, 2-12-1-I6-33 Ookayama, Meguro-ku, Tokyo 152-8550, Japan
| | - Anindityo Patmonoaji
- Department of Mechanical Engineering, Tokyo Institute of Technology, 2-12-1-I6-33 Ookayama, Meguro-ku, Tokyo 152-8550, Japan
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18
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19
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20
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High-Resolution Temporo-Ensemble PIV to Resolve Pore-Scale Flow in 3D-Printed Fractured Porous Media. Transp Porous Media 2018. [DOI: 10.1007/s11242-018-1174-3] [Citation(s) in RCA: 14] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/28/2022]
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21
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Comolli A, Dentz M. Impact of diffusive motion on anomalous dispersion in structured disordered media: From correlated Lévy flights to continuous time random walks. Phys Rev E 2018; 97:052146. [PMID: 29906927 DOI: 10.1103/physreve.97.052146] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/20/2018] [Indexed: 11/07/2022]
Abstract
We elucidate the impact of diffusive motion on the nature of anomalous dispersion in layered and fibrous disordered media. We consider two types of disorder characterized by quenched random velocities and quenched random retardation properties. Purely advective particle motion is ballistic in both disorder models. This changes dramatically in the presence of transverse diffusion, which leads to dimension-dependent disorder sampling. For d≤3 dimensions, heavy-tailed velocity distributions render large-scale particle motion a correlated Lévy flight, while transport in the quenched random retardation model behaves as a biased continuous time random walk with correlated time increments.
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Affiliation(s)
- Alessandro Comolli
- Spanish National Research Council (IDAEA-CSIC), 08034 Barcelona, Spain.,Department of Civil and Environmental Engineering, Technical University of Catalonia (UPC), 08034 Barcelona, Spain.,Associated Unit: Hydrogeology Group (UPC-CSIC), 08034 Barcelona, Spain
| | - Marco Dentz
- Spanish National Research Council (IDAEA-CSIC), 08034 Barcelona, Spain.,Associated Unit: Hydrogeology Group (UPC-CSIC), 08034 Barcelona, Spain
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22
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Li S, Liu M, Hanaor D, Gan Y. Dynamics of Viscous Entrapped Saturated Zones in Partially Wetted Porous Media. Transp Porous Media 2018. [DOI: 10.1007/s11242-018-1113-3] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/28/2022]
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23
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Carrel M, Morales VL, Dentz M, Derlon N, Morgenroth E, Holzner M. Pore-Scale Hydrodynamics in a Progressively Bioclogged Three-Dimensional Porous Medium: 3-D Particle Tracking Experiments and Stochastic Transport Modeling. WATER RESOURCES RESEARCH 2018; 54:2183-2198. [PMID: 29780184 PMCID: PMC5947749 DOI: 10.1002/2017wr021726] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/17/2017] [Accepted: 02/25/2018] [Indexed: 05/30/2023]
Abstract
Biofilms are ubiquitous bacterial communities that grow in various porous media including soils, trickling, and sand filters. In these environments, they play a central role in services ranging from degradation of pollutants to water purification. Biofilms dynamically change the pore structure of the medium through selective clogging of pores, a process known as bioclogging. This affects how solutes are transported and spread through the porous matrix, but the temporal changes to transport behavior during bioclogging are not well understood. To address this uncertainty, we experimentally study the hydrodynamic changes of a transparent 3-D porous medium as it experiences progressive bioclogging. Statistical analyses of the system's hydrodynamics at four time points of bioclogging (0, 24, 36, and 48 h in the exponential growth phase) reveal exponential increases in both average and variance of the flow velocity, as well as its correlation length. Measurements for spreading, as mean-squared displacements, are found to be non-Fickian and more intensely superdiffusive with progressive bioclogging, indicating the formation of preferential flow pathways and stagnation zones. A gamma distribution describes well the Lagrangian velocity distributions and provides parameters that quantify changes to the flow, which evolves from a parallel pore arrangement under unclogged conditions, toward a more serial arrangement with increasing clogging. Exponentially evolving hydrodynamic metrics agree with an exponential bacterial growth phase and are used to parameterize a correlated continuous time random walk model with a stochastic velocity relaxation. The model accurately reproduces transport observations and can be used to resolve transport behavior at intermediate time points within the exponential growth phase considered.
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Affiliation(s)
- M. Carrel
- Institute of Environmental Engineering, Department of Civil, Environmental and Geomatic EngineeringETH ZurichZurichSwitzerland
| | - V. L. Morales
- Institute of Environmental Engineering, Department of Civil, Environmental and Geomatic EngineeringETH ZurichZurichSwitzerland
- Department of Civil and Environmental EngineeringUniversity of California, DavisDavisCAUSA
| | - M. Dentz
- Spanish National Research Council (IDAEA‐CSIC)BarcelonaSpain
| | - N. Derlon
- Institute of Environmental Engineering, Department of Civil, Environmental and Geomatic EngineeringETH ZurichZurichSwitzerland
- EAWAGDübendorfSwitzerland
| | - E. Morgenroth
- Institute of Environmental Engineering, Department of Civil, Environmental and Geomatic EngineeringETH ZurichZurichSwitzerland
- EAWAGDübendorfSwitzerland
| | - M. Holzner
- Institute of Environmental Engineering, Department of Civil, Environmental and Geomatic EngineeringETH ZurichZurichSwitzerland
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24
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Turuban R, Lester DR, Le Borgne T, Méheust Y. Space-Group Symmetries Generate Chaotic Fluid Advection in Crystalline Granular Media. PHYSICAL REVIEW LETTERS 2018; 120:024501. [PMID: 29376725 DOI: 10.1103/physrevlett.120.024501] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/12/2017] [Indexed: 06/07/2023]
Abstract
The classical connection between symmetry breaking and the onset of chaos in dynamical systems harks back to the seminal theory of Noether [Transp. Theory Statist. Phys. 1, 186 (1918)10.1080/00411457108231446]. We study the Lagrangian kinematics of steady 3D Stokes flow through simple cubic and body-centered cubic (bcc) crystalline lattices of close-packed spheres, and uncover an important exception. While breaking of point-group symmetries is a necessary condition for chaotic mixing in both lattices, a further space-group (glide) symmetry of the bcc lattice generates a transition from globally regular to globally chaotic dynamics. This finding provides new insights into chaotic mixing in porous media and has significant implications for understanding the impact of symmetries upon generic dynamical systems.
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Affiliation(s)
- R Turuban
- Geosciences Rennes, UMR 6118, Université de Rennes 1, CNRS, 35042 Rennes, France
| | - D R Lester
- School of Engineering, RMIT University, 3000 Melbourne, Australia
| | - T Le Borgne
- Geosciences Rennes, UMR 6118, Université de Rennes 1, CNRS, 35042 Rennes, France
| | - Y Méheust
- Geosciences Rennes, UMR 6118, Université de Rennes 1, CNRS, 35042 Rennes, France
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25
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Carrel M, Beltran MA, Morales VL, Derlon N, Morgenroth E, Kaufmann R, Holzner M. Biofilm imaging in porous media by laboratory X-Ray tomography: Combining a non-destructive contrast agent with propagation-based phase-contrast imaging tools. PLoS One 2017; 12:e0180374. [PMID: 28732010 PMCID: PMC5521744 DOI: 10.1371/journal.pone.0180374] [Citation(s) in RCA: 21] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/01/2016] [Accepted: 06/14/2017] [Indexed: 11/21/2022] Open
Abstract
X-ray tomography is a powerful tool giving access to the morphology of biofilms, in 3D porous media, at the mesoscale. Due to the high water content of biofilms, the attenuation coefficient of biofilms and water are very close, hindering the distinction between biofilms and water without the use of contrast agents. Until now, the use of contrast agents such as barium sulfate, silver-coated micro-particles or 1-chloronaphtalene added to the liquid phase allowed imaging the biofilm 3D morphology. However, these contrast agents are not passive and potentially interact with the biofilm when injected into the sample. Here, we use a natural inorganic compound, namely iron sulfate, as a contrast agent progressively bounded in dilute or colloidal form into the EPS matrix during biofilm growth. By combining a very long source-to-detector distance on a X-ray laboratory source with a Lorentzian filter implemented prior to tomographic reconstruction, we substantially increase the contrast between the biofilm and the surrounding liquid, which allows revealing the 3D biofilm morphology. A comparison of this new method with the method proposed by Davit et al (Davit et al., 2011), which uses barium sulfate as a contrast agent to mark the liquid phase was performed. Quantitative evaluations between the methods revealed substantial differences for the volumetric fractions obtained from both methods. Namely, contrast agent—biofilm interactions (e.g. biofilm detachment) occurring during barium sulfate injection caused a reduction of the biofilm volumetric fraction of more than 50% and displacement of biofilm patches elsewhere in the column. Two key advantages of the newly proposed method are that passive addition of iron sulfate maintains the integrity of the biofilm prior to imaging, and that the biofilm itself is marked by the contrast agent, rather than the liquid phase as in other available methods. The iron sulfate method presented can be applied to understand biofilm development and bioclogging mechanisms in porous materials and the obtained biofilm morphology could be an ideal basis for 3D numerical calculations of hydrodynamic conditions to investigate biofilm-flow coupling.
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Affiliation(s)
- Maxence Carrel
- Institute of Environmental Engineering, ETH Zürich, Stefano Franscini-Platz 5, 8093 Zurich, Switzerland
| | - Mario A. Beltran
- Swiss Federal Laboratories for Materials Science and Technology (EMPA), Dübendorf, Switzerland
| | - Verónica L. Morales
- Institute of Environmental Engineering, ETH Zürich, Stefano Franscini-Platz 5, 8093 Zurich, Switzerland
- Department of Civil and Environmental Engineering, University of California Davis, Davis, California, United States of America
| | - Nicolas Derlon
- Institute of Environmental Engineering, ETH Zürich, Stefano Franscini-Platz 5, 8093 Zurich, Switzerland
- Swiss Federal Institute of Aquatic Science and Technology (EAWAG), Dübendorf, Switzerland
| | - Eberhard Morgenroth
- Institute of Environmental Engineering, ETH Zürich, Stefano Franscini-Platz 5, 8093 Zurich, Switzerland
- Swiss Federal Institute of Aquatic Science and Technology (EAWAG), Dübendorf, Switzerland
| | - Rolf Kaufmann
- Swiss Federal Laboratories for Materials Science and Technology (EMPA), Dübendorf, Switzerland
| | - Markus Holzner
- Institute of Environmental Engineering, ETH Zürich, Stefano Franscini-Platz 5, 8093 Zurich, Switzerland
- * E-mail:
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26
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Fouxon I, Holzner M. Solvable continuous-time random walk model of the motion of tracer particles through porous media. Phys Rev E 2016; 94:022132. [PMID: 27627271 DOI: 10.1103/physreve.94.022132] [Citation(s) in RCA: 12] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/13/2016] [Indexed: 11/07/2022]
Abstract
We consider the continuous-time random walk (CTRW) model of tracer motion in porous medium flows based on the experimentally determined distributions of pore velocity and pore size reported by Holzner et al. [M. Holzner et al., Phys. Rev. E 92, 013015 (2015)PLEEE81539-375510.1103/PhysRevE.92.013015]. The particle's passing through one channel is modeled as one step of the walk. The step (channel) length is random and the walker's velocity at consecutive steps of the walk is conserved with finite probability, mimicking that at the turning point there could be no abrupt change of velocity. We provide the Laplace transform of the characteristic function of the walker's position and reductions for different cases of independence of the CTRW's step duration τ, length l, and velocity v. We solve our model with independent l and v. The model incorporates different forms of the tail of the probability density of small velocities that vary with the model parameter α. Depending on that parameter, all types of anomalous diffusion can hold, from super- to subdiffusion. In a finite interval of α, ballistic behavior with logarithmic corrections holds, which was observed in a previously introduced CTRW model with independent l and τ. Universality of tracer diffusion in the porous medium is considered.
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Affiliation(s)
- Itzhak Fouxon
- Institute of Environmental Engineering, ETH Zurich, 15 Wolfgang-Pauli-Strasse, 8093 Zurich, Switzerland.,Institute of Mechanical Science, Vilnius Gediminas Technical University, 28 J. Basanaviiaus Street, 03224 Vilnius, Lithuania
| | - Markus Holzner
- Institute of Environmental Engineering, ETH Zurich, 15 Wolfgang-Pauli-Strasse, 8093 Zurich, Switzerland
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27
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Comolli A, Hidalgo JJ, Moussey C, Dentz M. Non-Fickian Transport Under Heterogeneous Advection and Mobile-Immobile Mass Transfer. Transp Porous Media 2016. [DOI: 10.1007/s11242-016-0727-6] [Citation(s) in RCA: 19] [Impact Index Per Article: 2.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
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28
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Noetinger B, Roubinet D, Russian A, Le Borgne T, Delay F, Dentz M, de Dreuzy JR, Gouze P. Random Walk Methods for Modeling Hydrodynamic Transport in Porous and Fractured Media from Pore to Reservoir Scale. Transp Porous Media 2016. [DOI: 10.1007/s11242-016-0693-z] [Citation(s) in RCA: 64] [Impact Index Per Article: 8.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/21/2022]
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29
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Matyka M, Gołembiewski J, Koza Z. Power-exponential velocity distributions in disordered porous media. Phys Rev E 2016; 93:013110. [PMID: 26871158 DOI: 10.1103/physreve.93.013110] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/21/2015] [Indexed: 06/05/2023]
Abstract
Velocity distribution functions link the micro- and macro-level theories of fluid flow through porous media. Here we study them for the fluid absolute velocity and its longitudinal and lateral components relative to the macroscopic flow direction in a model of a random porous medium. We claim that all distributions follow the power-exponential law controlled by an exponent γ and a shift parameter u_{0} and examine how these parameters depend on the porosity. We find that γ has a universal value 1/2 at the percolation threshold and grows with the porosity, but never exceeds 2.
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Affiliation(s)
- Maciej Matyka
- Faculty of Physics and Astronomy, University of Wrocław, 50-204 Wrocław, Poland
| | | | - Zbigniew Koza
- Faculty of Physics and Astronomy, University of Wrocław, 50-204 Wrocław, Poland
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