Porous medium

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Open-cell ceramic Porousceramic.jpg
Open-cell ceramic

In materials science, a porous medium or a porous material is a material containing pores (voids). [1] The skeletal portion of the material is often called the "matrix" or "frame". The pores are typically filled with a fluid (liquid or gas). The skeletal material is usually a solid, but structures like foams are often also usefully analyzed using concept of porous media.

Contents

A porous medium is most often characterised by its porosity. Other properties of the medium (e.g. permeability, tensile strength, electrical conductivity, tortuosity) can sometimes be derived from the respective properties of its constituents (solid matrix and fluid) and the media porosity and pores structure, but such a derivation is usually complex. Even the concept of porosity is only straightforward for a poroelastic medium.

Often both the solid matrix and the pore network (also known as the pore space) are continuous, so as to form two interpenetrating continua such as in a sponge. However, there is also a concept of closed porosity and effective porosity, i.e. the pore space accessible to flow.

Many natural substances such as rocks and soil (e.g. aquifers, petroleum reservoirs), zeolites, biological tissues (e.g. bones, wood, cork), and man made materials such as cements and ceramics can be considered as porous media. Many of their important properties can only be rationalized by considering them to be porous media.

The concept of porous media is used in many areas of applied science and engineering: filtration, mechanics (acoustics, geomechanics, soil mechanics, rock mechanics), engineering (petroleum engineering, bioremediation, construction engineering), geosciences (hydrogeology, petroleum geology, geophysics), biology and biophysics, material science. Two important current fields of application for porous materials are energy conversion and energy storage, where porous materials are essential for superpacitors, (photo-)catalysis, [2] fuel cells, [3] and batteries.

Microscopic and macroscopic

At the microscopic and macroscopic levels, porous media can be classified. At the microscopic scale, the structure is represented statistically by the distribution of pore sizes, the degree of pore interconnection and orientation, the proportion of dead pores, etc. [4] The macroscopic technique makes use of bulk properties that have been averaged at scales far bigger than pore size. [4] [5]

Depending on the goal, these two techniques are frequently employed since they are complimentary. It is obvious that the microscopic description is required to comprehend surface phenomena like the adsorption of macromolecules from polymer solutions and the blocking of pores, whereas the macroscopic approach is frequently quite sufficient for process design where fluid flow, heat, and mass transfer are of highest concern. and the molecular dimensions are significantly smaller than pore size of the porous system. [4] [6]

Fluid flow through porous media

Fluid flow through porous media Aquifere Darcy permeabilite.jpg
Fluid flow through porous media

Fluid flow through porous media is a subject of common interest and has emerged a separate field of study. The study of more general behaviour of porous media involving deformation of the solid frame is called poromechanics.

The theory of porous flows has applications in inkjet printing [7] and nuclear waste disposal [8] technologies, among others.

Numerous factors influence fluid flow in porous media, and its fundamental function is to expend energy and create fluid via the wellbore. In flow mechanics via porous medium, the connection between energy and flow rate becomes the most significant issue. The most fundamental law that characterizes this connection is Darcy's law [9] , particularly applicable to fine-porous media. In contrast, Forchheimer's law finds utility in the context of coarse-porous media [10] .

Pore structure models

A representation of the void phase that exists inside porous materials using a set or network of pores. It serves as a structural foundation for the prediction of transport parameters and is employed in the context of pore structure characterisation. [11]

There are many idealized models of pore structures. They can be broadly divided into three categories:

Porous materials often have a fractal-like structure, having a pore surface area that seems to grow indefinitely when viewed with progressively increasing resolution. [12] Mathematically, this is described by assigning the pore surface a Hausdorff dimension greater than 2. [13] Experimental methods for the investigation of pore structures include confocal microscopy [14] and x-ray tomography. [15] Porous materials have found some applications in many engineering fields including automotive sectors. [16]

Laws for porous materials

One of the Laws for porous materials is the generalized Murray's law. The generalized Murray's law is based on optimizing mass transfer by minimizing transport resistance in pores with a given volume, and can be applicable for optimizing mass transfer involving mass variations and chemical reactions involving flow processes, molecule or ion diffusion. [17]

For connecting a parent pipe with radius of r0 to many children pipes with radius of ri , the formula of generalized Murray's law is: , where the X is the ratio of mass variation during mass transfer in the parent pore, the exponent α is dependent on the type of the transfer. For laminar flow α =3; for turbulent flow α =7/3; for molecule or ionic diffusion α =2; etc.

See also

Related Research Articles

In fluid mechanics, the Rayleigh number (Ra, after Lord Rayleigh) for a fluid is a dimensionless number associated with buoyancy-driven flow, also known as free (or natural) convection. It characterises the fluid's flow regime: a value in a certain lower range denotes laminar flow; a value in a higher range, turbulent flow. Below a certain critical value, there is no fluid motion and heat transfer is by conduction rather than convection. For most engineering purposes, the Rayleigh number is large, somewhere around 106 to 108.

<span class="mw-page-title-main">Sintering</span> Process of forming and bonding material by heat or pressure

Sintering or frittage is the process of compacting and forming a solid mass of material by pressure or heat without melting it to the point of liquefaction. Sintering happens as part of a manufacturing process used with metals, ceramics, plastics, and other materials. The nanoparticles in the sintered material diffuse across the boundaries of the particles, fusing the particles together and creating a solid piece.

<span class="mw-page-title-main">Hydrogeology</span> Study of the distribution and movement of groundwater

Hydrogeology is the area of geology that deals with the distribution and movement of groundwater in the soil and rocks of the Earth's crust. The terms groundwater hydrology, geohydrology, and hydrogeology are often used interchangeably.

Permeability in fluid mechanics and the Earth sciences is a measure of the ability of a porous material to allow fluids to pass through it.

Darcy's law is an equation that describes the flow of a fluid through a porous medium. The law was formulated by Henry Darcy based on results of experiments on the flow of water through beds of sand, forming the basis of hydrogeology, a branch of earth sciences. It is analogous to Ohm's law in electrostatics, linearly relating the volume flow rate of the fluid to the hydraulic head difference via the hydraulic conductivity. In fact, the Darcy's law is a special case of the Stokes equation for the momentum flux, in turn deriving from the momentum Navier-Stokes equation.

<span class="mw-page-title-main">Metal foam</span> Porous material made from a metal

In materials science, a metal foam is a material or structure consisting of a solid metal with gas-filled pores comprising a large portion of the volume. The pores can be sealed or interconnected. The defining characteristic of metal foams is a high porosity: typically only 5–25% of the volume is the base metal. The strength of the material is due to the square–cube law.

Poromechanics is a branch of physics and specifically continuum mechanics and acoustics that studies the behaviour of fluid-saturated porous media. A porous medium or a porous material is a solid referred to as matrix) permeated by an interconnected network of pores (voids) filled with a fluid. Usually both solid matrix and the pore network, or pore space, are assumed to be continuous, so as to form two interpenetrating continua such as in a sponge. Natural substances including rocks, soils, biological tissues including heart and cancellous bone, and man-made materials such as foams and ceramics can be considered as porous media. Porous media whose solid matrix is elastic and the fluid is viscous are called poroelastic. A poroelastic medium is characterised by its porosity, permeability as well as the properties of its constituents. The distribution of pores across multiple scales as well as the pressure of the fluid with which they are filled give rise to distinct elastic behaviour of the bulk.

Poroelasticity is a field in materials science and mechanics that studies the interaction between fluid flow, pressure and bulk solid deformation within a linear porous medium and it is an extension of elasticity and porous medium flow. The deformation of the medium influences the flow of the fluid and vice versa. The theory was proposed by Maurice Anthony Biot as a theoretical extension of soil consolidation models developed to calculate the settlement of structures placed on fluid-saturated porous soils. The theory of poroelasticity has been widely applied in geomechanics, hydrology, biomechanics, tissue mechanics, cell mechanics, and micromechanics.

In physics and engineering, permeation is the penetration of a permeate through a solid. It is directly related to the concentration gradient of the permeate, a material's intrinsic permeability, and the materials' mass diffusivity. Permeation is modeled by equations such as Fick's laws of diffusion, and can be measured using tools such as a minipermeameter.

In petrophysics, Archie's law relates the in-situ electrical conductivity (C) of a porous rock to its porosity and fluid saturation of the pores:

<span class="mw-page-title-main">Tortuosity</span> Parameter for diffusion and fluid flow in porous media

Tortuosity is widely used as a critical parameter to predict transport properties of porous media, such as rocks and soils. But unlike other standard microstructural properties, the concept of tortuosity is vague with multiple definitions and various evaluation methods introduced in different contexts. Hydraulic, electrical, diffusional, and thermal tortuosities are defined to describe different transport processes in porous media, while geometrical tortuosity is introduced to characterize the morphological property of porous microstructures.

In petroleum engineering, the Leverett J-function is a dimensionless function of water saturation describing the capillary pressure,

Terzaghi's Principle states that when stress is applied to a porous material, it is opposed by the fluid pressure filling the pores in the material.

Porosity or void fraction is a measure of the void spaces in a material, and is a fraction of the volume of voids over the total volume, between 0 and 1, or as a percentage between 0% and 100%. Strictly speaking, some tests measure the "accessible void", the total amount of void space accessible from the surface.

Nuclear magnetic resonance (NMR) in porous materials covers the application of using NMR as a tool to study the structure of porous media and various processes occurring in them. This technique allows the determination of characteristics such as the porosity and pore size distribution, the permeability, the water saturation, the wettability, etc.

In fluid mechanics, fluid flow through porous media is the manner in which fluids behave when flowing through a porous medium, for example sponge or wood, or when filtering water using sand or another porous material. As commonly observed, some fluid flows through the media while some mass of the fluid is stored in the pores present in the media.

<span class="mw-page-title-main">Morris Muskat</span> American petroleum engineer

Morris Muskat was an American petroleum engineer. Muskat refined Darcy's equation for single phase flow, and this change made it suitable for the petroleum industry. Based on experimental results worked out by his colleagues, Muskat and Milan W. Meres also generalized Darcy's law to cover multiphase flow of water, oil and gas in the porous medium of a petroleum reservoir. The generalized flow equation provides the analytical foundation for reservoir engineering that exists to this day.

Titanium foams exhibit high specific strength, high energy absorption, excellent corrosion resistance and biocompatibility. These materials are ideally suited for applications within the aerospace industry. An inherent resistance to corrosion allows the foam to be a desirable candidate for various filtering applications. Further, titanium's physiological inertness makes its porous form a promising candidate for biomedical implantation devices. The largest advantage in fabricating titanium foams is that the mechanical and functional properties can be adjusted through manufacturing manipulations that vary porosity and cell morphology. The high appeal of titanium foams is directly correlated to a multi-industry demand for advancement in this technology.

<span class="mw-page-title-main">Fault zone hydrogeology</span>

Fault zone hydrogeology is the study of how brittlely deformed rocks alter fluid flows in different lithological settings, such as clastic, igneous and carbonate rocks. Fluid movements, that can be quantified as permeability, can be facilitated or impeded due to the existence of a fault zone. This is because different mechanisms that deform rocks can alter porosity and permeability within a fault zone. Fluids involved in a fault system generally are groundwater and hydrocarbons.

<span class="mw-page-title-main">Pore structure</span>

Pore structure is a common term employed to characterize the porosity, pore size, pore size distribution, and pore morphology of a porous medium. Pores are the openings in the surfaces impermeable porous matrix which gases, liquids, or even foreign microscopic particles can inhabit them. The pore structure and fluid flow in porous media are intimately related.

References

  1. ↑ Su, Bao-Lian; Sanchez, Clément; Yang, Xiao-Yu, eds. (2011). Hierarchically Structured Porous Materials: From Nanoscience to Catalysis, Separation, Optics, Energy, and Life Science - Wiley Online Library. doi:10.1002/9783527639588. ISBN   9783527639588.
  2. ↑ Madanu, Thomas L.; Mouchet, Sébastien R.; Deparis, Olivier; Liu, Jing; Li, Yu; Su, Bao-Lian (2023). "Tuning and transferring slow photons from TiO2 photonic crystals to BiVO4 nanoparticles for unprecedented visible light photocatalysis". Journal of Colloid and Interface Science. 634: 290–299. doi:10.1016/j.jcis.2022.12.033.
  3. ↑ Zhang, Tao; Asefa, Tewodros (2020). Gitis, Vitaly; Rothenberg, Gadi (eds.). Handbook of Porous Materials. Singapore: WORLD SCIENTIFIC. doi:10.1142/11909. ISBN   978-981-12-2322-8.
  4. 1 2 3 Chhabra, R. P.; Richardson, J. F. (1 January 2008). "Chapter 5 - Particulate systems". Non-Newtonian Flow and Applied Rheology (Second Edition). Butterworth-Heinemann: 249–315. doi:10.1016/b978-0-7506-8532-0.00005-6. ISBN   9780750685320.
  5. ↑ "3 - Dye transport in fluid systems". Modelling, Simulation and Control of the Dyeing Process. Woodhead Publishing: 54–81. 1 January 2014. doi:10.1533/9780857097583.54. ISBN   9780857091338.
  6. ↑ Fu, Jinlong; Thomas, Hywel R.; Li, Chenfeng (January 2021). "Tortuosity of porous media: Image analysis and physical simulation" (PDF). Earth-Science Reviews. 212: 103439. doi:10.1016/j.earscirev.2020.103439. S2CID   229386129.
  7. ↑ Stephen D. Hoath, "Fundamentals of Inkjet Printing - The Science of Inkjet and Droplets", Wiley VCH 2016
  8. ↑ Martinez M.J., McTigue D.F. (1996) Modeling in Nuclear Waste Isolation: Approximate Solutions for Flow in Unsaturated Porous Media. In: Wheeler M.F. (eds) Environmental Studies. The IMA Volumes in Mathematics and its Applications, vol 79. Springer, New York, NY
  9. ↑ "Basic theory". Fluid Flow in Porous Media: 47–67. November 2020. doi:10.1142/9789811219535_0002. ISBN   978-981-12-1952-8.
  10. ↑ Mohammadizadeh, SeyedMehdi; Moghaddam, Mehdi Azhdary; Talebbeydokhti, Naser (2021). "Analysis of Flow in Porous Media using Combined Pressurized-Free surface Network". journal of Porous Media. Begel House Inc.: 1–15. doi:10.1615/JPorMedia.2021025407.
  11. ↑ Burganos, Vasilis (2015). "Pore Model". Encyclopedia of Membranes. Springer: 1–2. doi:10.1007/978-3-642-40872-4_1055-2. ISBN   978-3-642-40872-4.
  12. ↑ Dutta, Tapati (2003). "Fractal pore structure of sedimentary rocks: Simulation by ballistic deposition". Journal of Geophysical Research: Solid Earth. 108 (B2): 2062. Bibcode:2003JGRB..108.2062D. doi: 10.1029/2001JB000523 .
  13. ↑ Crawford, J.W. (1994). "The relationship between structure and the hydraulic conductivity of soil". European Journal of Soil Science. 45 (4): 493–502. doi:10.1111/j.1365-2389.1994.tb00535.x.
  14. ↑ M. K. Head, H. S. Wong, N. R. Buenfeld, "Characterisation of 'Hadley’ Grains by Confocal Microscopy", Cement & Concrete Research (2006), 36 (8) 1483 -1489
  15. ↑ Peng, Sheng; Hu, Qinhong; Dultz, Stefan; Zhang, Ming (2012). "Using X-ray computed tomography in pore structure characterization for a Berea sandstone: Resolution effect". Journal of Hydrology. 472–473: 254–261. Bibcode:2012JHyd..472..254P. doi:10.1016/j.jhydrol.2012.09.034.
  16. ↑ Ravanbod, Mohammad (2023). "Porous Liner Coated Inlet Duct: A Novel Approach to Attenuate Automotive Turbocharger Inlet Flow-Induced Sound Propagation". Engineering Research Express. 5 (1): 015047. doi: 10.1088/2631-8695/acbfa4 .
  17. ↑ Zheng, Xianfeng; Shen, Guofang; Wang, Chao; Li, Yu; Dunphy, Darren; Hasan, Tawfique; Brinker, C. Jeffrey; Su, Bao-Lian (2017-04-06). "Bio-inspired Murray materials for mass transfer and activity". Nature Communications. 8: 14921. Bibcode:2017NatCo...814921Z. doi:10.1038/ncomms14921. ISSN   2041-1723. PMC   5384213 . PMID   28382972.

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