LBE Flows in Disordered Media

2018 ◽  
Author(s):  
Sauro Succi
Keyword(s):  
Porous Media ◽  
Fluid Mechanics ◽  
Condensed Matter ◽  
Disordered Media ◽  
Environmental Sciences ◽  
Science And Engineering ◽  
Particle Trajectories ◽  
Irregular Geometries ◽  
Numerical Tool ◽  
Bounce Back

The study of transport phenomena in disordered media is a subject of wide interdisciplinary concern, with many applications in fluid mechanics, condensed matter, life and environmental sciences as well. Flows through grossly irregular (porous) media is a specific fluid mechanical application of great practical value in applied science and engineering. It is arguably also one of the applications of choice of the LBE methods. The dual field–particle character of LBE shines brightly here: the particle-like nature of LBE (populations move along straight particle trajectories) permits a transparent treatment of grossly irregular geometries in terms of elementary mechanical events, such as mirror and bounce-back reflections. These assets were quickly recognized by researchers in the field, and still make of LBE (and eventually LGCA) an excellent numerical tool for flows in porous media, as it shall be discussed in this Chapter.

scholarly journals Upscaled phase-field models for interfacial dynamics in strongly heterogeneous domains

2012 ◽  
Vol 468 (2147) ◽  
pp. 3705-3724 ◽  
Author(s):  
Markus Schmuck ◽  
Marc Pradas ◽  
Grigorios A. Pavliotis ◽  
Serafim Kalliadasis
Keyword(s):  
Porous Media ◽  
Free Energy ◽  
Phase Field ◽  
Single Channel ◽  
Confined Geometries ◽  
Science And Engineering ◽  
Hilliard Equation ◽  
Phase Field Models ◽  
Cahn Hilliard Equation ◽  
Double Well Potential

We derive a new, effective macroscopic Cahn–Hilliard equation whose homogeneous free energy is represented by fourth-order polynomials, which form the frequently applied double-well potential. This upscaling is done for perforated/strongly heterogeneous domains. To the best knowledge of the authors, this seems to be the first attempt of upscaling the Cahn–Hilliard equation in such domains. The new homogenized equation should have a broad range of applicability owing to the well-known versatility of phase-field models. The additionally introduced feature of systematically and reliably accounting for confined geometries by homogenization allows for new modelling and numerical perspectives in both science and engineering. Our results are applied to wetting dynamics in porous media and to a single channel with strongly heterogeneous walls.

Fractional vector calculus and fluid mechanics

2017 ◽  
Vol 26 (1-2) ◽  
pp. 43-54 ◽  
Author(s):  
Konstantinos A. Lazopoulos ◽  
Anastasios K. Lazopoulos
Keyword(s):  
Differential Geometry ◽  
Porous Media ◽  
Fluid Mechanics ◽  
Research Field ◽  
Flow In Porous Media ◽  
Navier Stokes ◽  
Basic Fluid ◽  
Vector Calculus ◽  
Fractional Differential ◽  
Fractional Continuum

AbstractBasic fluid mechanics equations are studied and revised under the prism of fractional continuum mechanics (FCM), a very promising research field that satisfies both experimental and theoretical demands. The geometry of the fractional differential has been clarified corrected and the geometry of the fractional tangent spaces of a manifold has been studied in Lazopoulos and Lazopoulos (Lazopoulos KA, Lazopoulos AK. Progr. Fract. Differ. Appl. 2016, 2, 85–104), providing the bases of the missing fractional differential geometry. Therefore, a lot can be contributed to fractional hydrodynamics: the basic fractional fluid equations (Navier Stokes, Euler and Bernoulli) are derived and fractional Darcy’s flow in porous media is studied.

Signature of coalescence during scalar mixing in heterogeneous flow fields

2020 ◽  
Author(s):  
Sabyasachi Sen ◽  
Prajwal Singh ◽  
Joris Heyman ◽  
Tanguy Le Borgne ◽  
Aditya Bandopadhyay
Keyword(s):  
Porous Media ◽  
Fluid Mechanics ◽  
Large Scale ◽  
Scalar Fields ◽  
Flow Fields ◽  
Scalar Mixing ◽  
Heterogeneous Flow ◽  
Strip Method ◽  
Mixing Rates ◽  
Flow Through

<p>Stretching of fluid elements by a heterogeneous flow field, such as the flow through a porous media or geophysical flows such as atmospheric or oceanic vortices, is known to enhance mixing rates of scalar fields[1]. While the mechanisms leading to the elongation of material lines are well understood, predicting mixing rates still remains a challenge particularly when there is a reconnection (or aggregation) between several parts of the mixing interface, leading, at large mixing time, to a so-called coalescence regime[1][2]. In this presentation, we numerically study this coalescence dynamics through scalar transport in two different flow fields, the Rankine vortex and Stokes flow through a periodic bead pack[3]. The former is typical of large-scale turbulent flows [4] whereas the second is generic of small-scale laminar flows in porous media [5]. Both flows show a net elongation of the mixing interfaces, although at very different rates. To solve the transport problem in these flows, we use a Lagrangian method (the diffusive strip method[6]). This method allows us to reconstruct, at high resolution, the scalar concentration fields and to compute the evolution of the distribution of concentrations levels, scalar dissipation rate and scalar power spectrum in time. The signature of coalescence is clearly observed in both flows and we assess the influence of coalescence on the difference in mixing behaviour for the two flows. We finally discuss how coalescence may affect the reaction kinetics of mixing-limited reactive flows. The analysis proposed sheds light on fundamental aspects of transport and mixing in earth surface and subsurface flows.</p><p>[1] Emmanuel Villermaux. Mixing versus stirring. Annual Review of Fluid Mechanics, 51:245–273, 2019.<br>[2] Tanguy Le Borgne, Marco Dentz, and Emmanuel Villermaux. The lamellar description of mixing in porous media. Journal of Fluid Mechanics, 770:458–498, 2015.<br>[3] Régis Turuban, David R Lester, Tanguy Le Borgne, and Yves Méheust. Space-group symmetries generate chaotic fluid advection in crystalline granular media. Physical review letters, 120(2):024501, 2018.<br>[4] RT Pierrehumbert. Large-scale horizontal mixing in planetary atmospheres. Physics of Fluids A: Fluid Dynamics, 3(5):1250–1260, 1991.<br>[5] Brian Berkowitz, Andrea Cortis, Marco Dentz, and Harvey Scher. Modeling non-fickian transport in geological formations as a continuous time random walk. Reviews of Geophysics, 44(2), 2006.<br>[6] Patrice Meunier and Emmanuel Villermaux. The diffusive strip method for scalar mixing in two dimensions. Journal of fluid mechanics, 662:134–172, 2010.</p>

The effect of order on dispersion in porous media

1989 ◽  
Vol 200 ◽  
pp. 173-188 ◽  
Author(s):  
Donald L. Koch ◽  
Raymond G. Cox ◽  
Howard Brenner ◽  
John F. Brady
Keyword(s):  
Porous Media ◽  
Velocity Field ◽  
Fluid Velocity ◽  
Fluid Motion ◽  
Grain Structure ◽  
Disordered Media ◽  
Molecular Diffusivity ◽  
Mechanical Dispersion ◽  
Spatial Periodicity ◽  
Flow Through

The effect of spatial periodicity in grain structure on the average transport properties resulting from flow through porous media are derived from the basic conservation equations. At high Péclet number, the mechanical dispersion that is induced by the stochastic fluid velocity field in disordered media and is independent of the molecular diffusivity is absent in periodic media where the velocity field is deterministic. Instead, the fluid motion enhances diffusion by an amount proportional to U2l2/D when the bulk flow is in certain directions (of which there are an infinite number), and to D otherwise. The non-mechanical dispersion mechanisms associated with the zero velocity of the fixed grains is qualitatively similar in ordered and disordered media.

Buoyancy-induced flow in porous media generated near a drilled oil well. Part 1. The accumulation of filtrate at a horizontal impermeable boundary

1993 ◽  
Vol 254 ◽  
pp. 283-311 ◽  
Author(s):  
E. B. Dussan V. ◽  
François M. Auzerais
Keyword(s):  
Porous Media ◽  
Fluid Mechanics ◽  
Drilling Fluid ◽  
Flow In Porous Media ◽  
Porous Solids ◽  
Oil Well ◽  
Great Success ◽  
Ct Scanner ◽  
X Ray ◽  
Impermeable Barrier

A substantial amount of drilling fluid can invade a permeable bed during the drilling of an oil well. The presence of this fluid, often referred to as filtrate, can greatly influence the performance of instruments lowered into the wellbore for the purpose of locating these permeable beds. The invaded filtrate can also substantially alter the physical properties of the porous rock. For these reasons, it is of great interest to known where the filtrate goes upon entering the bed. The objective of this study is to quantify the influence of the difference in density between the filtrate and the naturally occurring formation fluid on the shape of the filtrate front as the filtrate invades the formation. This type of phenomenon is often referred to as buoyancy or gravity segregation. In this study, Part 1, we determine the behaviour of the filtrate as it accumulates (and spreads out) at a horizontal impermeable barrier within the formation. This is a combined theoretical and experimental study in which an X-ray CT scanner is extensively used to determine the appropriateness and limitations of the simplifying assumptions used in the theory. In Part 2, the flow of the invading filtrate within the entire bed will be presented. The problem addressed in Part 1 may be viewed from the broader, more fundamental, perspective, as a well-defined model fluid mechanics problem for flow in porous media. One fundamental issue infrequently addressed concerns the consequence on the dynamics of the fluids of heterogeneities, always present to some degree, in consolidated porous solids. The X-ray CT scanner enables the assessment of the appropriateness of modelling such porous solids as spatially homogeneous, a very popular assumption. This study also addresses the limitation of the small-slope approximation when a fluid–fluid interface occurs in a porous solid, an approximation which has enjoyed great success in free-surface fluid mechanics problems when no porous media is present.

Permeability prediction of fibrous porous media by the lattice Boltzmann method with a fluid-structure boundary reconstruction scheme

2020 ◽  
pp. 152808372097891
Author(s):  
Suguru Ando ◽  
Masayuki Kaneda ◽  
Kazuhiko Suga
Keyword(s):  
Porous Media ◽  
Lattice Boltzmann Method ◽  
Lattice Boltzmann ◽  
Boundary Data ◽  
Fluid Structure ◽  
Nonwoven Fabrics ◽  
Correlation Models ◽  
Structure Boundary ◽  
Boltzmann Method ◽  
Bounce Back

The D3Q27 lattice Boltzmann method (LBM) combined with the fluid-structure boundary reconstruction (fsBR) scheme and the interpolated bounce back (IPBB) method is extensively evaluated to predict the permeability of nonwoven fibrous porous media. The fsBR-IPBB method transfers digitally defined step-like boundary data, e.g. the three-dimensional structure data obtained by the X-ray computed tomography, to continuous smooth boundary data via level-set functions. It leads to highly accurate calculations despite low lattice resolutions of thin fibers with circular cross-sectional shapes, compared to the conventional half-way bounce back (HWBB) method. The fsBR-IPBB method is first applied to predict the permeability of two different arrays of impermeable circular cylinders and verified by comparing the results with the data in the literature. We then validate the method referring to the numerically and experimentally obtained permeability of six types of nonwoven fabrics prepared by the industrial hydroentanglement process. Finally, the discussion on the applicability and the limitation of the macroscopic correlation models to estimate permeability of porous media is carried out. The results show that although the calculated permeability is in reasonable agreement with the measured one with an error of 8.1–16.3%, analytical or empirical correlation models fail to give the correct trend due to the highly inhomogeneous and anisotropic properties of hydroentangled nonwoven fabrics.

Influence of Different Joints on Moisture Transport in Building Walls - A Brief Review

2019 ◽  
Vol 22 ◽  
pp. 19-23
Author(s):  
A.S. Guimarães ◽  
J.M.P.Q. Delgado ◽  
V.P. de Freitas ◽  
A.C. Azevedo
Keyword(s):  
Porous Media ◽  
Moisture Transport ◽  
Building Envelope ◽  
Petroleum Engineering ◽  
Soil Science ◽  
Building Ceramic ◽  
Science And Engineering ◽  
Building Envelopes ◽  
Building Walls ◽  
Building Engineering

The phenomena of transport in porous media arises in many diverse fields of science and engineering, ranging from agricultural, biomedical, building, ceramic, chemical, and petroleum engineering to food and soil science. Several authors provide an extensive description of the problems involving porous media. For building engineering, obtaining a good understanding of moisture transport in building envelopes is becoming one of the most important tasks. In the last few decades, many studies investigating moisture transport in building envelopes have been published, which have helped to improve overall building envelope design. This work presents a brief review of these studies.

Fluid Mechanics of Longitudinal Contractions in the Small Intestine

1979 ◽  
Vol 101 (4) ◽  
pp. 284-288 ◽  
Author(s):  
J. G. Melville ◽  
N. Denli
Keyword(s):  
Reynolds Number ◽  
Small Intestine ◽  
Motor Activity ◽  
Fluid Mechanics ◽  
Low Reynolds Number ◽  
Retrograde Flow ◽  
Particle Trajectories ◽  
Low Reynolds

Longitudinal contractions in the duodenum are shown to exit experimentally. A low Reynolds number model of flows induced by propagating longitudinal contractions is presented for circular conduits. Particle trajectories and time lines are shown to elucidate the flowfields. Longitudinal motor activity is shown to have the capability of satisfying the mixing function of the small intestine and to be a possible contributor of retrograde flow.

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