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Velásquez-Parra A, Marone F, Griffa M, Jiménez-Martínez J. Chaotic Transport of Solutes in Unsaturated Porous Media. ENVIRONMENTAL SCIENCE & TECHNOLOGY 2024; 58:12643-12652. [PMID: 38970478 DOI: 10.1021/acs.est.4c02799] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 07/08/2024]
Abstract
Unsaturated porous media, characterized by the combined presence of several immiscible fluid phases in the pore space, are highly relevant systems in nature, because they control the fate of contaminants and the availability of nutrients in the subsoil. However, a full understanding of the mechanisms controlling solute mixing in such systems is still missing. In particular, the role of saturation in the development of chaotic solute mixing has remained unexplored. Using three-dimensional numerical simulations of flow and transport at the pore scale, built upon X-ray tomograms of a porous medium at different degrees of liquid (wetting)-phase saturation, we show the occurrence of chaotic dynamics in both the deformation of the solute plume, as characterized by computed chaos metrics (Lyapunov exponents), and the mixing of the injected solute. Our results show an enhancement of these chaotic dynamics at lower saturation and their occurrence even under diffusion-relevant conditions over the medium's length, also being strengthened by larger flow velocities. These findings highlight the dominant role of the pore-scale spatial heterogeneity of the system, enhanced by the presence of an immiscible phase (e.g., air), on the mixing efficiency. This represents a stepping stone for the assessment of mixing and reactions in unsaturated porous media.
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Affiliation(s)
- Andrés Velásquez-Parra
- Department of Water Resources and Drinking Water, Swiss Federal Institute of Aquatic Science and Technology (Eawag), 8600 Dübendorf, Switzerland
- Department of Civil, Environmental and Geomatic Engineering, ETH Zürich, 8092 Zürich, Switzerland
| | - Federica Marone
- Swiss Light Source, Paul Scherrer Institute, 5232 Villigen, Switzerland
| | - Michele Griffa
- Swiss Federal Laboratories for Materials Science and Technology (Empa), 8600 Dübendorf, Switzerland
| | - Joaquín Jiménez-Martínez
- Department of Water Resources and Drinking Water, Swiss Federal Institute of Aquatic Science and Technology (Eawag), 8600 Dübendorf, Switzerland
- Department of Civil, Environmental and Geomatic Engineering, ETH Zürich, 8092 Zürich, Switzerland
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Basilio Hazas M, Ziliotto F, Lee J, Rolle M, Chiogna G. Evolution of plume geometry, dilution and reactive mixing in porous media under highly transient flow fields at the surface water-groundwater interface. JOURNAL OF CONTAMINANT HYDROLOGY 2023; 258:104243. [PMID: 37696230 DOI: 10.1016/j.jconhyd.2023.104243] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/16/2023] [Revised: 08/11/2023] [Accepted: 09/02/2023] [Indexed: 09/13/2023]
Abstract
Highly transient boundary conditions affect mixing of dissolved solutes in groundwater. An example of these transient boundary conditions occurs at the surface water-groundwater interface, where the water level in rivers can change rapidly due to the operation of hydropower plants, leading to a regime known as hydropeaking. Inspired by this phenomenon, this work studies at laboratory scale the effects of fluctuating surface water bodies on solute transport in aquifers. We performed flow-through experiments at two different flow velocities and under steady and transient flow conditions where a conservative tracer was injected in the system and its concentration measured with optical imaging methods. The experimental results were quantitatively interpreted with numerical simulations implementing a non-linear velocity-dependent dispersive transport model. We estimated plume dilution by computing the dilution index and its evolution as well as two key geometrical metrics of the transient plumes: the perimeter and the area. We further investigated reactive mixing and mixing enhancement considering mixing-controlled bimolecular reactions using different critical mixing ratios. In general, highly transient boundary conditions lead to a larger area, perimeter and plume dilution and the results show greater relative enhancement for the scenarios with low groundwater flow velocity. A linear relationship was observed between the evolution of the area and the dilution index of the plumes for the transient flow scenarios investigated. Considering reactive transport and mixing-limited reactions at the surface water-groundwater interface, we identified different dilution and reaction dominated regimes, characterized, respectively, by increasing and decreasing plume entropies at different mixing ratios of the reactants. Furthermore, reactive mixing was enhanced by transient flows leading to a faster degradation of contaminant plumes compared to corresponding steady flow conditions.
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Affiliation(s)
- Mónica Basilio Hazas
- Chair of Hydrology and River Basin Management, Technical University of Munich, Munich, Germany
| | - Francesca Ziliotto
- Chair of Hydrology and River Basin Management, Technical University of Munich, Munich, Germany
| | - Jonghyun Lee
- Department of Civil and Environmental Engineering and Water Resources Research Center, University of Hawai'i at Mānoa, Honolulu, USA
| | - Massimo Rolle
- Department of Environmental and Resource Engineering, Technical University of Denmark, Lyngby, Denmark; Institute of Applied Geosciences, Technical University of Darmstadt, Darmstadt, Germany.
| | - Gabriele Chiogna
- Chair of Hydrology and River Basin Management, Technical University of Munich, Munich, Germany
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Aquino T, Le Borgne T, Heyman J. Fluid-Solid Reaction in Porous Media as a Chaotic Restart Process. PHYSICAL REVIEW LETTERS 2023; 130:264001. [PMID: 37450789 DOI: 10.1103/physrevlett.130.264001] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/23/2022] [Revised: 02/10/2023] [Accepted: 06/05/2023] [Indexed: 07/18/2023]
Abstract
Chemical and biological reactions at fluid-solid interfaces are central to a broad range of porous material applications and research. Pore-scale solute transport limitations can reduce reaction rates, with marked consequences for a wide spectrum of natural and engineered processes. Recent advances show that chaotic mixing occurs spontaneously in porous media, but its impact on surface reactions is unknown. We show that pore-scale chaotic mixing significantly increases reaction efficiency compared to nonchaotic flows. We find that reaction rates are well described in terms of diffusive first-passage times of reactants to the solid interface subjected to a stochastic restart process resulting from Lagrangian chaos. Under chaotic mixing, the shear layer at no-slip interfaces sets the restart rate and leads to a characteristic scaling of reaction efficiency with Péclet number, in excellent agreement with numerical simulations. Reaction rates are insensitive to the flow topology as long as flow is chaotic, suggesting the relevance of this process to a broad range of porous materials.
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Affiliation(s)
- Tomás Aquino
- Spanish National Research Council (IDAEA - CSIC), 08034 Barcelona, Spain
- Université de Rennes, CNRS, Géosciences Rennes, UMR 6118, 35000 Rennes, France
| | - Tanguy Le Borgne
- Université de Rennes, CNRS, Géosciences Rennes, UMR 6118, 35000 Rennes, France
| | - Joris Heyman
- Université de Rennes, CNRS, Géosciences Rennes, UMR 6118, 35000 Rennes, France
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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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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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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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7
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Taming Taylor-Aris dispersion through chaotic advection. J Chromatogr A 2022; 1673:463110. [DOI: 10.1016/j.chroma.2022.463110] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/31/2022] [Revised: 04/29/2022] [Accepted: 04/29/2022] [Indexed: 11/22/2022]
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Fluidic bacterial diodes rectify magnetotactic cell motility in porous environments. Nat Commun 2021; 12:5949. [PMID: 34642318 PMCID: PMC8511139 DOI: 10.1038/s41467-021-26235-6] [Citation(s) in RCA: 12] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/24/2021] [Accepted: 09/21/2021] [Indexed: 11/08/2022] Open
Abstract
Directed motility enables swimming microbes to navigate their environment for resources via chemo-, photo-, and magneto-taxis. However, directed motility competes with fluid flow in porous microbial habitats, affecting biofilm formation and disease transmission. Despite this broad importance, a microscopic understanding of how directed motility impacts the transport of microswimmers in flows through constricted pores remains unknown. Through microfluidic experiments, we show that individual magnetotactic bacteria directed upstream through pores display three distinct regimes, whereby cells swim upstream, become trapped within a pore, or are advected downstream. These transport regimes are reminiscent of the electrical conductivity of a diode and are accurately predicted by a comprehensive Langevin model. The diode-like behavior persists at the pore scale in geometries of higher dimension, where disorder impacts conductivity at the sample scale by extending the trapping regime over a broader range of flow speeds. This work has implications for our understanding of the survival strategies of magnetotactic bacteria in sediments and for developing their use in drug delivery applications in vascular networks.
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Matreux T, Le Vay K, Schmid A, Aikkila P, Belohlavek L, Çalışkanoğlu AZ, Salibi E, Kühnlein A, Springsklee C, Scheu B, Dingwell DB, Braun D, Mutschler H, Mast CB. Heat flows in rock cracks naturally optimize salt compositions for ribozymes. Nat Chem 2021; 13:1038-1045. [PMID: 34446924 DOI: 10.1038/s41557-021-00772-5] [Citation(s) in RCA: 11] [Impact Index Per Article: 3.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/28/2020] [Accepted: 07/13/2021] [Indexed: 11/09/2022]
Abstract
Catalytic nucleic acids, such as ribozymes, are central to a variety of origin-of-life scenarios. Typically, they require elevated magnesium concentrations for folding and activity, but their function can be inhibited by high concentrations of monovalent salts. Here we show that geologically plausible high-sodium, low-magnesium solutions derived from leaching basalt (rock and remelted glass) inhibit ribozyme catalysis, but that this activity can be rescued by selective magnesium up-concentration by heat flow across rock fissures. In contrast to up-concentration by dehydration or freezing, this system is so far from equilibrium that it can actively alter the Mg:Na salt ratio to an extent that enables key ribozyme activities, such as self-replication and RNA extension, in otherwise challenging solution conditions. The principle demonstrated here is applicable to a broad range of salt concentrations and compositions, and, as such, highly relevant to various origin-of-life scenarios.
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Affiliation(s)
- T Matreux
- Systems Biophysics, Ludwig Maximilians University Munich, Munich, Germany
| | - K Le Vay
- MPI für Biochemie, Biomimetische Systeme, Martinsried, Germany
| | - A Schmid
- Systems Biophysics, Ludwig Maximilians University Munich, Munich, Germany
| | - P Aikkila
- Systems Biophysics, Ludwig Maximilians University Munich, Munich, Germany
| | - L Belohlavek
- Earth and Environmental Sciences, Ludwig Maximilians University Munich, Munich, Germany
| | - A Z Çalışkanoğlu
- Earth and Environmental Sciences, Ludwig Maximilians University Munich, Munich, Germany
| | - E Salibi
- MPI für Biochemie, Biomimetische Systeme, Martinsried, Germany
| | - A Kühnlein
- Systems Biophysics, Ludwig Maximilians University Munich, Munich, Germany
| | - C Springsklee
- Earth and Environmental Sciences, Ludwig Maximilians University Munich, Munich, Germany
| | - B Scheu
- Earth and Environmental Sciences, Ludwig Maximilians University Munich, Munich, Germany
| | - D B Dingwell
- Earth and Environmental Sciences, Ludwig Maximilians University Munich, Munich, Germany
| | - D Braun
- Systems Biophysics, Ludwig Maximilians University Munich, Munich, Germany
| | | | - C B Mast
- Systems Biophysics, Ludwig Maximilians University Munich, Munich, Germany.
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Heyman J, Lester DR, Le Borgne T. Scalar Signatures of Chaotic Mixing in Porous Media. PHYSICAL REVIEW LETTERS 2021; 126:034505. [PMID: 33543984 DOI: 10.1103/physrevlett.126.034505] [Citation(s) in RCA: 6] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/04/2020] [Revised: 11/13/2020] [Accepted: 12/09/2020] [Indexed: 06/12/2023]
Abstract
Steady laminar flows through porous media spontaneously generate Lagrangian chaos at pore scale, with qualitative implications for a range of transport, reactive, and biological processes. The characterization and understanding of mixing dynamics in these opaque environments is an outstanding challenge. We address this issue by developing a novel technique based upon high-resolution imaging of the scalar signature produced by push-pull flows through porous media samples. Owing to the rapid decorrelation of particle trajectories in chaotic flows, the scalar image measured outside the porous material is representative of in situ mixing dynamics. We present a theoretical framework for estimation of the Lyapunov exponent based on extension of Lagrangian stretching theories to correlated aggregation. This method provides a full characterization of chaotic mixing dynamics in a large class of porous materials.
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Affiliation(s)
- J Heyman
- 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
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11
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Stretching and folding sustain microscale chemical gradients in porous media. Proc Natl Acad Sci U S A 2020; 117:13359-13365. [PMID: 32467164 DOI: 10.1073/pnas.2002858117] [Citation(s) in RCA: 20] [Impact Index Per Article: 5.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/18/2022] Open
Abstract
Fluid flow in porous media drives the transport, mixing, and reaction of molecules, particles, and microorganisms across a wide spectrum of natural and industrial processes. Current macroscopic models that average pore-scale fluctuations into an effective dispersion coefficient have shown significant limitations in the prediction of many important chemical and biological processes. Yet, it is unclear how three-dimensional flow in porous structures govern the microscale chemical gradients controlling these processes. Here, we obtain high-resolution experimental images of microscale mixing patterns in three-dimensional porous media and uncover an unexpected and general mixing mechanism that strongly enhances concentration gradients at pore-scale. Our experiments reveal that systematic stretching and folding of fluid elements are produced in the pore space by grain contacts, through a mechanism that leads to efficient microscale chaotic mixing. These insights form the basis for a general kinematic model linking chaotic-mixing rates in the fluid phase to the generic structural properties of granular matter. The model successfully predicts the resulting enhancement of pore-scale chemical gradients, which appear to be orders of magnitude larger than predicted by dispersive approaches. These findings offer perspectives for predicting and controlling the vast diversity of reactive transport processes in natural and synthetic porous materials, beyond the current dispersion paradigm.
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12
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13
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Arzani A, Shadden SC. Wall shear stress fixed points in cardiovascular fluid mechanics. J Biomech 2018; 73:145-152. [DOI: 10.1016/j.jbiomech.2018.03.034] [Citation(s) in RCA: 38] [Impact Index Per Article: 6.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/11/2018] [Revised: 03/09/2018] [Accepted: 03/21/2018] [Indexed: 12/13/2022]
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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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15
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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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Jin C, Langston PA, Pavlovskaya GE, Hall MR, Rigby SP. Statistics of highly heterogeneous flow fields confined to three-dimensional random porous media. Phys Rev E 2016; 93:013122. [PMID: 26871169 DOI: 10.1103/physreve.93.013122] [Citation(s) in RCA: 10] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/02/2015] [Indexed: 11/07/2022]
Abstract
We present a strong relationship between the microstructural characteristics of, and the fluid velocity fields confined to, three-dimensional random porous materials. The relationship is revealed through simultaneously extracting correlation functions R_{uu}(r) of the spatial (Eulerian) velocity fields and microstructural two-point correlation functions S_{2}(r) of the random porous heterogeneous materials. This demonstrates that the effective physical transport properties depend on the characteristics of complex pore structure owing to the relationship between R_{uu}(r) and S_{2}(r) revealed in this study. Further, the mean excess plot was used to investigate the right tail of the streamwise velocity component that was found to obey light-tail distributions. Based on the mean excess plot, a generalized Pareto distribution can be used to approximate the positive streamwise velocity distribution.
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Affiliation(s)
- C Jin
- Department of Chemical and Environmental Engineering, Faculty of Engineering, University of Nottingham, NG7 2RD, United Kingdom.,GeoEnergy Research Centre (GERC), University of Nottingham, NG7 2RD, United Kingdom.,British Geological Survey, Keyworth, Nottingham NG12 5GG, United Kingdom
| | - P A Langston
- Department of Chemical and Environmental Engineering, Faculty of Engineering, University of Nottingham, NG7 2RD, United Kingdom
| | - G E Pavlovskaya
- Sir Peter Mansfield Magnetic Resonance Centre, University of Nottingham, NG7 2RD, United Kingdom
| | - M R Hall
- GeoEnergy Research Centre (GERC), University of Nottingham, NG7 2RD, United Kingdom.,British Geological Survey, Keyworth, Nottingham NG12 5GG, United Kingdom
| | - S P Rigby
- Department of Chemical and Environmental Engineering, Faculty of Engineering, University of Nottingham, NG7 2RD, United Kingdom.,GeoEnergy Research Centre (GERC), University of Nottingham, NG7 2RD, United Kingdom.,British Geological Survey, Keyworth, Nottingham NG12 5GG, United Kingdom
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17
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Holzner M, Morales VL, Willmann M, Dentz M. Intermittent Lagrangian velocities and accelerations in three-dimensional porous medium flow. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2015; 92:013015. [PMID: 26274277 DOI: 10.1103/physreve.92.013015] [Citation(s) in RCA: 29] [Impact Index Per Article: 3.2] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/05/2014] [Indexed: 06/04/2023]
Abstract
Intermittency of Lagrangian velocity and acceleration is a key to understanding transport in complex systems ranging from fluid turbulence to flow in porous media. High-resolution optical particle tracking in a three-dimensional (3D) porous medium provides detailed 3D information on Lagrangian velocities and accelerations. We find sharp transitions close to pore throats, and low flow variability in the pore bodies, which gives rise to stretched exponential Lagrangian velocity and acceleration distributions characterized by a sharp peak at low velocity, superlinear evolution of particle dispersion, and double-peak behavior in the propagators. The velocity distribution is quantified in terms of pore geometry and flow connectivity, which forms the basis for a continuous-time random-walk model that sheds light on the observed Lagrangian flow and transport behaviors.
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Affiliation(s)
- M Holzner
- Institute of Environmental Engineering, ETH Zurich, Wolfgang-Pauli-Strasse 15, 8093 Zürich, Switzerland
| | - V L Morales
- SIMBIOS Centre, University of Abertay, Bell Street Dundee DD1 1HG, United Kingdom
| | - M Willmann
- Institute of Environmental Engineering, ETH Zurich, Wolfgang-Pauli-Strasse 15, 8093 Zurich, Switzerland
| | - M Dentz
- Spanish National Research Council (IDAEA-CSIC), c/Jordi Girona 18, 08034 Barcelona, Spain
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18
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Lester DR, Metcalfe G, Trefry MG. Anomalous transport and chaotic advection in homogeneous porous media. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2014; 90:063012. [PMID: 25615192 DOI: 10.1103/physreve.90.063012] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/10/2014] [Indexed: 06/04/2023]
Abstract
The topological complexity inherent to all porous media imparts persistent chaotic advection under steady flow conditions, which, in concert with the no-slip boundary condition, generates anomalous transport. We explore the impact of this mechanism upon longitudinal dispersion via a model random porous network and develop a continuous-time random walk that predicts both preasymptotic and asymptotic transport. In the absence of diffusion, the ergodicity of chaotic fluid orbits acts to suppress longitudinal dispersion from ballistic to superdiffusive transport, with asymptotic variance scaling as σ(L)(2)(t)∼t(2)/(ln t)(3). These results demonstrate that anomalous transport is inherent to homogeneous porous media and has significant implications for macrodispersion.
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Affiliation(s)
- D R Lester
- Mathematics, Informatics and Statistics, CSIRO, PO Box 56, Highett, Victoria 3190, Australia and School of Civil, Environmental and Chemical Engineering, Royal Melbourne Institute of Technology, Melbourne, Victoria 3001, Australia
| | - G Metcalfe
- Materials Science and Engineering, CSIRO, PO Box 56, Highett, Victoria 3190, Australia
| | - M G Trefry
- Land and Water, CSIRO, Private Bag 5, Wembley, Western Australia 6913, Australia and School of Earth and Environment, The University of Western Australia, 35 Stirling Highway, Crawley, Western Australia 6009, Australia
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19
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Engdahl NB, Benson DA, Bolster D. Predicting the enhancement of mixing-driven reactions in nonuniform flows using measures of flow topology. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2014; 90:051001. [PMID: 25493728 DOI: 10.1103/physreve.90.051001] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/07/2014] [Indexed: 06/04/2023]
Abstract
The ability for reactive constituents to mix is often the key limiting factor for the completion of reactions across a huge range of scales in a variety of media. In flowing systems, deformation and shear enhance mixing by bringing constituents into closer proximity, thus increasing reaction potential. Accurately quantifying this enhanced mixing is key to predicting reactions and typically is done by observing or simulating scalar transport. To eliminate this computationally expensive step, we use a Lagrangian stochastic framework to derive the enhancement to reaction potential by calculating the collocation probability of particle pairs in a heterogeneous flow field accounting for deformations. We relate the enhanced reaction potential to three well known flow topology metrics and demonstrate that it is best correlated to (and asymptotically linear with) one: the largest eigenvalue of the (right) Cauchy-Green tensor.
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Affiliation(s)
- Nicholas B Engdahl
- Department of Civil and Environmental Engineering, Washington State University, Pullman, Washington 99164, USA
| | - David A Benson
- Hydrologic Science and Engineering, Colorado School of Mines, Golden, Colorado 80401, USA
| | - Diogo Bolster
- Department of Civil and Environmental Engineering and Earth Sciences, University of Notre Dame, Notre Dame, Indiana 46556, USA
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