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Entropy
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Statistical Mechanics of Porous Media Flow
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Statistical Mechanics of Porous Media Flow

A special issue of Entropy (ISSN 1099-4300). This special issue belongs to the section "Statistical Physics".

Deadline for manuscript submissions: 15 September 2024 | Viewed by 2520

Special Issue Editors

Prof. Dr. Eirik Grude Flekkøy

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Guest Editor
Department of Physics, University of OSLO, Blindern, NO-0316 Oslo, Norway
Interests: condensed matter physics; computational physics; statistical physics; fluid; hydrodynamics; geophysics
Prof. Dr. Alex Hansen

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Guest Editor
PoreLab, Department of Physics, Norwegian University of Science and Technology, 7491 Trondheim, Norway
Interests: transport in porous media; multiphase flow in porous media; non-Newtonian fluid flow in porous media; statistical mechanics; fluid mechanics; nonequilibrium thermodynamics
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

Flow in porous media is driven process, and therefore a non-equilibrium one in the statistical mechanical sense. Yet, in many cases it has common features with equilibrium systems: For instance, the steady states in immiscible fluid flows continuously explore a large configuration space and gives rise to well-defined averages. This makes it possible to formulate a statistical mechanics starting from the pore-scale, rather than the molecular or atomic scale, at which the microstates in traditional statistical mechanics are described. Recently, this has been done using concepts from Shannons information theory.

Also, processes that gives rise to entropy production in the classical sense include mixing, viscous dissipation and the evolution of active matter populations.  Characterizing such entropy producing systems may yield Onsager reciprocity relations for the viscous cross-coupling between two immiscible fluids, or the symmetry of dispersion tensors.  Transport processes within porous media, such as the growth of bacterial cultures may yield analytical solutions based on the link between Langevin and Fokker-Planck equations. In this special issue we seek to give examples of these descriptions and thereby illustrate how the tool box provided by statistical physics may be applied to, and in some cases, enlarged, in order to expand the understanding of porous media flows. 

Prof. Dr. Eirik Grude Flekkøy
Prof. Dr. Alex Hansen
Guest Editors

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Entropy is an international peer-reviewed open access monthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 2600 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

  • thermodynamics of porous media
  • active matter in porous media
  • anomalous diffusion in porous media
  • fractal behavior of displacement structures in imiscible fluids

Published Papers (3 papers)

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Research

25 pages, 2452 KiB  
Article
Statistical Mechanics of Electrowetting
by Michel Y. Louge and Yujie Wang
Entropy 2024, 26(4), 276; https://doi.org/10.3390/e26040276 - 22 Mar 2024
Viewed by 564
Abstract
We derive the ab initio equilibrium statistical mechanics of the gas–liquid–solid contact angle on planar periodic, monodisperse, textured surfaces subject to electrowetting. To that end, we extend an earlier theory that predicts the advance or recession of the contact line amount to distinct [...] Read more.
We derive the ab initio equilibrium statistical mechanics of the gas–liquid–solid contact angle on planar periodic, monodisperse, textured surfaces subject to electrowetting. To that end, we extend an earlier theory that predicts the advance or recession of the contact line amount to distinct first-order phase transitions of the filling state in the ensemble of nearby surface cavities. Upon calculating the individual capacitance of a cavity subject to the influence of its near neighbors, we show how hysteresis, which is manifested by different advancing and receding contact angles, is affected by electrowetting. The analysis reveals nine distinct regimes characterizing contact angle behavior, three of which arise only when a voltage is applied to the conductive liquid drop. As the square voltage is progressively increased, the theory elucidates how the drop occasionally undergoes regime transitions triggering jumps in the contact angle, possibly changing its hysteresis, or saturating it at a value weakly dependent on further voltage growth. To illustrate these phenomena and validate the theory, we confront its predictions with four data sets. A benefit of the theory is that it forsakes trial and error when designing textured surfaces with specific contact angle behavior. Full article
(This article belongs to the Special Issue Statistical Mechanics of Porous Media Flow)
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8 pages, 886 KiB  
Article
Hyper-Ballistic Superdiffusion of Competing Microswimmers
by Kristian Stølevik Olsen, Alex Hansen and Eirik Grude Flekkøy
Entropy 2024, 26(3), 274; https://doi.org/10.3390/e26030274 - 21 Mar 2024
Viewed by 688
Abstract
Hyper-ballistic diffusion is shown to arise from a simple model of microswimmers moving through a porous media while competing for resources. By using a mean-field model where swimmers interact through the local concentration, we show that a non-linear Fokker–Planck equation arises. The solution [...] Read more.
Hyper-ballistic diffusion is shown to arise from a simple model of microswimmers moving through a porous media while competing for resources. By using a mean-field model where swimmers interact through the local concentration, we show that a non-linear Fokker–Planck equation arises. The solution exhibits hyper-ballistic superdiffusive motion, with a diffusion exponent of four. A microscopic simulation strategy is proposed, which shows excellent agreement with theoretical analysis. Full article
(This article belongs to the Special Issue Statistical Mechanics of Porous Media Flow)
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26 pages, 1069 KiB  
Article
A Unified Approach to Two-Dimensional Brinkman-Bénard Convection of Newtonian Liquids in Cylindrical and Rectangular Enclosures
by Pradeep G. Siddheshwar, Kanakapura M. Lakshmi and David Laroze
Entropy 2024, 26(1), 2; https://doi.org/10.3390/e26010002 - 19 Dec 2023
Viewed by 945
Abstract
A unified model for the analysis of two-dimensional Brinkman–Bénard/Rayleigh–Bénard/ Darcy–Bénard convection in cylindrical and rectangular enclosures (CE/RE) saturated by a Newtonian liquid is presented by adopting the local thermal non-equilibrium (LTNE) model [...] Read more.
A unified model for the analysis of two-dimensional Brinkman–Bénard/Rayleigh–Bénard/ Darcy–Bénard convection in cylindrical and rectangular enclosures (CE/RE) saturated by a Newtonian liquid is presented by adopting the local thermal non-equilibrium (LTNE) model for the heat transfer between fluid and solid phases. The actual thermophysical properties of water and porous media are used. The range of permissible values for all the parameters is calculated and used in the analysis. The result of the local thermal equilibrium (LTE) model is obtained as a particular case of the LTNE model through the use of asymptotic analyses. The critical value of the Rayleigh number at which the entropy generates in the system is reported in the study. The analytical expression for the number of Bénard cells formed in the system at the onset of convection as a function of the aspect ratio, So, and parameters appearing in the problem is obtained. For a given value of So it was found that in comparison with the case of LTE, more number of cells manifest in the case of LTNE. Likewise, smaller cells form in the DBC problem when compared with the corresponding problem of BBC. In the case of RBC, fewer cells form when compared to that in the case of BBC and DBC. The above findings are true in both CE and RE. In other words, the presence of a porous medium results in the production of less entropy in the system, or a more significant number of cells represents the case of less entropy production in the system. For small and finite So, the appearance of the first cell differs in the CE and RE problems. Full article
(This article belongs to the Special Issue Statistical Mechanics of Porous Media Flow)
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