Constrictivity is viewed to depend on the ratio of the diameter of the diffusing particle to the pore diameter. The value of constrictivity is always less than 1. The constrictivity is defined not for a single pore, but as the parameter of the entire pore space considered.
The resistance to transport in porous media increases because the viscosity of the fluid (which fills the pores) increases in the vicinity of the pore walls (Renkin effect;[1] see also electroviscous effects). This effect is important in very narrow pores and in pore narrowing their diameter to the same size as the diameter of the diffusing particles. Constrictivity must be distinguished from the effects of Knudsen diffusion. Knudsen diffusion occurs when the particle interacts with the pore walls more than it does with other particles due to the large free path and narrow pores. Constrictivity, on the other hand, depends on the influence of the pore walls on the fluid filling the pores.
There are a number of empirical formulas used to estimate the value of constrictivity.[1][2][3][4][5] For simple pore geometries, constrictivity can be inferred from the geometry of the porous media.[6][7][8] In practice, the constrictivity together with the porosity and tortuosity are often used in models as purely empirical parameters to establish the effective diffusivities in porous media.
Footnotes
1 2 Renkin, EM (1954): Filtration, diffusion and molecular sieving through porous cellulose membranes. J. Gen. Physiologist., 38: 225-243
↑ Beck, RE, Schultz, JS (1970): Hindered Diffusion in Microporous Membranes with known pore geometry. Science, 170: 1302-1305
↑ Satterfield, CN, Colton, CK (1973): Restricted diffusion in liquids within fine pores. AIChE J., 19: 628
↑ Chantong, A., Massoth, FE (1983): Restrictive diffusion in aluminas. AIChE J., 29 (5): 725-731
↑ Berg, CF (2012): Re-examining Archie's law: conductance description by tortuosity and constriction. PRE, 86 (4): 046314
↑ Petersen, EE (1958): Diffusion in a pore of varying cross section. AIChE J., 4 (3): 343-345
↑ Curie, JA (1960): Gaseous diffusion in porous media, Parts 1 and 2. Br. J. Appl. Phys., 11: 314-324
↑ Michaels, AS (1959): Diffusion in a pore of irregular cross section. AIChE J., 5: 270-271
Sources
P. Grathwohl: Diffusion in natural porous media: Contaminant transport, sorption/desorption and dissolution kinetics. Kluwer Academic Publishers, 1998, ISBN0-7923-8102-5
R. K. M. Thambynayagam: The Diffusion Handbook: Applied Solutions for Engineers. McGraw-Hill, 2011, ISBN978-0-07-175184-1
van Brakel, J., Heertjes, P. M. (1974): Analysis of diffusion in macroporous media in terms of a porosity, a tortuosity and a constrictivity factor. Int. J. Heat Mass Transfer, 17: 1093–1103
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.
The Knudsen number (Kn) is a dimensionless number defined as the ratio of the molecular mean free path length to a representative physical length scale. This length scale could be, for example, the radius of a body in a fluid. The number is named after Danish physicist Martin Knudsen (1871–1949).
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 materials science, a porous medium or a porous material is a material containing pores (voids). The skeletal portion of the material is often called the "matrix" or "frame". The pores are typically filled with a fluid. The skeletal material is usually a solid, but structures like foams are often also usefully analyzed using concept of porous media.
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:
In physics, Knudsen diffusion, named after Martin Knudsen, is a means of diffusion that occurs when the scale length of a system is comparable to or smaller than the mean free path of the particles involved. An example of this is in a long pore with a narrow diameter (2–50 nm) because molecules frequently collide with the pore wall. As another example, consider the diffusion of gas molecules through very small capillary pores. If the pore diameter is smaller than the mean free path of the diffusing gas molecules, and the density of the gas is low, the gas molecules collide with the pore walls more frequently than with each other, leading to Knudsen diffusion.
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.
Nanofiltration is a membrane filtration process that uses nanometer sized pores through which particles smaller than about 1–10 nanometers pass through the membrane. Nanofiltration membranes have pore sizes of about 1–10 nanometers, smaller than those used in microfiltration and ultrafiltration, but a slightly bigger than those in reverse osmosis. Membranes used are predominantly polymer thin films. It is used to soften, disinfect, and remove impurities from water, and to purify or separate chemicals such as pharmaceuticals.
Diffusivity, mass diffusivity or diffusion coefficient is usually written as the proportionality constant between the molar flux due to molecular diffusion and the negative value of the gradient in the concentration of the species. More accurately, the diffusion coefficient times the local concentration is the proportionality constant between the negative value of the mole fraction gradient and the molar flux. This distinction is especially significant in gaseous systems with strong temperature gradients. Diffusivity derives its definition from Fick's law and plays a role in numerous other equations of physical chemistry.
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.
In Petrophysics a Klinkenberg correction is a procedure for calibration of permeability data obtained from a minipermeameter device. A more accurate correction factor can be obtained using Knudsen correction. When using nitrogen gas for core plug measurements, the Klinkenberg correction is usually necessary due to the so-called Klinkenberg gas slippage effect. This takes place when the pore space approaches the mean free path of the gas
Diffusion is the net movement of anything generally from a region of higher concentration to a region of lower concentration. Diffusion is driven by a gradient in Gibbs free energy or chemical potential. It is possible to diffuse "uphill" from a region of lower concentration to a region of higher concentration, as in spinodal decomposition. Diffusion is a stochastic process due to the inherent randomness of the diffusing entity and can be used to model many real-life stochastic scenarios. Therefore, diffusion and the corresponding mathematical models are used in several fields beyond physics, such as statistics, probability theory, information theory, neural networks, finance, and marketing.
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.
Membrane technology encompasses the scientific processes used in the construction and application of membranes. Membranes are used to facilitate the transport or rejection of substances between mediums, and the mechanical separation of gas and liquid streams. In the simplest case, filtration is achieved when the pores of the membrane are smaller than the diameter of the undesired substance, such as a harmful microorganism. Membrane technology is commonly used in industries such as water treatment, chemical and metal processing, pharmaceuticals, biotechnology, the food industry, as well as the removal of environmental pollutants.
John A. Quinn was the Robert D. Bent Professor Emeritus of Chemical and Biomolecular Engineering at the University of Pennsylvania School of Engineering and Applied Science. He was a leader in the fields of mass transfer and membrane transport in synthetic membranes since the 1960s. In the early phase of his career at the University of Illinois, Quinn and his students devised simple, elegant experiments to elucidate the role of the interface in mass transfer between phases. In later work at Penn, he applied these insights to problems of engineering and biological significance involving chemical reaction and diffusion within and through both finely porous and reactive membranes. His chemical engineering science has informed matters as far afield as the separation of chiral pharmaceuticals and the behavior of cells at interfaces.
Microvasculature comprises the microvessels – venules and capillaries of the microcirculation, with a maximum average diameter of 0.3 millimeters. As the vessels decrease in size, they increase their surface-area-to-volume ratio. This allows surface properties to play a significant role in the function of the vessel.
Suresh Kumar Bhatia is an Indian-born chemical engineer and professor emeritus at the School of Chemical Engineering, University of Queensland. He is known for his studies on porous media and catalytic and non-catalytic solid fluid reactions. He was awarded an ARC Australian Professorial Fellowship (2010–15) and is an elected fellow of the Indian Academy of Sciences (1993), and the Australian Academy of Technological Sciences and Engineering (2010). In 1993, the Council of Scientific and Industrial Research, the Indian government's peak agency for scientific research, awarded him the Shanti Swarup Bhatnagar Prize for Science and Technology, one of the highest Indian science awards, for his contributions to the engineering sciences.
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.
This page is based on this Wikipedia article Text is available under the CC BY-SA 4.0 license; additional terms may apply. Images, videos and audio are available under their respective licenses.
