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Allen G. Hunt - One of the best experts on this subject based on the ideXlab platform.
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Unsaturated hydraulic conductivity in porous media: Percolation Theory
Geoderma, 2012Co-Authors: Behzad Ghanbarian-alavijeh, Allen G. HuntAbstract:Abstract The unsaturated hydraulic conductivity is an important property of porous media whose estimation is still investigated. In this study, we developed a new unsaturated hydraulic conductivity model from applying Percolation Theory to the pore–solid fractal approach (PSF). In actual applications the pore size distribution was obtained from the soil water retention curve. Using 104 soil samples from the UNSODA data base, the new developed unsaturated hydraulic conductivity model was compared with the Mualem's approach combined with water retention models of van Genuchten and PSF. The calculated root mean square error (RMSE) for the new model developed in this study, vG-M and PSF-M models was 0.69, 0.91 and 0.83 cm day− 1, respectively. The results showed that Percolation Theory model estimated unsaturated hydraulic conductivity curve better than the vG-M and PSF-M models especially at high water contents.
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Percolation Theory: Topology and Structure
Percolation Theory for Flow in Porous Media, 2009Co-Authors: Allen G. Hunt, Robert P. EwingAbstract:The fundamental concepts of Percolation Theory are introduced in Chaps. 1 and 2. Chapter 1 includes descriptions of geometrical and topological variables, while the description of such properties as tortuosity and transport are deferred to Chap. 2. Chapter 1 has, generally speaking, two purposes: (1) to be a reference for material that will be applied later in the book, (2) to provide a means for a scientist to gain a working familiarity with Percolation Theory. The chapter is organized in such a way that those sections that provide essentially all of the expertise required for arbitrary applications of Percolation Theory to porous media problems can be read in early explorations, while those sections (1.11–1.15) that provide additional detail can be skipped. The role of universal scaling functions and the relevance of power-law behavior are discussed in terms of the understanding of the fractal structure of Percolation Theory. The chapter concludes with a discussion of the non-universality of the Percolation threshold and presentation of what general methods have been proposed to predict it.
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Percolation Theory for Flow in Porous Media
Lecture Notes in Physics, 2009Co-Authors: Robert P. Ewing, Allen G. HuntAbstract:This monograph presents, for the first time, a unified and comprehensive introduction to some of the basic transport properties of porous media, such as electrical and hydraulic conductivity, air permeability and diffusion. The treatment is based on critical path analysis and the scaling of transport properties which are individually described as functions of saturation. At the same time, the book supplies a tutorial on Percolation Theory for hydrologists, providing them with the tools for solving actual problems. In turn, a separate chapter serves to introduce physicists to some of the language and complications of groundwater hydrology necessary for successful modelling. End of chapter problems often indicate open questions, on which young researchers entering the field can readily start work on. This significantly revised and much expanded edition was made necessary by both the selling out of the first edition and the rapid progress in the field. At the same time the tutorial aspects of the first few chapters have been considerably improved and the number of models, experiments and range of medium properties considered have been increased. Topics discussed for the first time in detail in this edition are advanced topological aspects of Percolation Theory that serve as a basis for examining dispersion aspects in porous media. "The book is suitable for advanced graduate courses, with selected problems and questions appearing at the end of each chapter. [...] I think the book is an important work that will guide soil scientists, hydrologists, and physicists to gain a better qualitative and quantitative understanding of multitransport properties of soils." (Marcel G. Schaap, Soil Science Society of America Journal, May-June, 2006
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Percolation Theory for flow in porous media
2005Co-Authors: Allen G. HuntAbstract:Percolation Theory: Topology and Structure.- Properties Relevant for Transport and Transport Applications.- Porous Media Primer for Physicists.- Specific Examples of Critical Path Analysis.- Hydraulic and Electrical Conductivity: Conductivity Exponents and Critical Path Analysis.- Other Transport Properties of Porous Media.- Pressure–Saturation Curves and the Critical Volume Fraction for Percolation: Accessibility Function of Percolation Theory.- Applications of the Correlation Length: Scale Effects on Flow.- Applications of the Cluster Statistics.- Properties based on Tortuosity.- Effects of Multi-Scale Heterogeneity.
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Continuum Percolation Theory for Saturation Dependence of Air Permeability
Vadose Zone Journal, 2005Co-Authors: Allen G. HuntAbstract:Continuum Percolation Theory has recently been used to find the saturation, S , dependence of the hydraulic conductivity, K ( S ), of probabilistic fractal porous media. Analysis of K ( S ) in conjunction with solute diffusion revealed the presence of a critical volume fraction, θ t , for Percolation in natural porous media. For moisture contents within a few percent of θ t , K ( S ) depends on the moisture content as a power of θ − θ t . At higher moisture contents, K ( S ) is determined through critical path analysis, which uses continuum Percolation Theory to find the dependence of a bottleneck (flow-limiting) pore radius on S . The physics near θ t is thus dominated by connectivity and tortuosity issues, but far from θ t by the variations in the radius of a bottleneck pore. Here it is demonstrated that the bottleneck pore radius for air permeability, k a , does not change as a function of saturation. Using the same scaling for the air permeability in the vicinity of the Percolation of the air phase as proposed for the hydraulic conductivity in the vicinity of the Percolation of the water phase yields results for k a in accordance with experimental data.
Robert P. Ewing - One of the best experts on this subject based on the ideXlab platform.
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Percolation Theory: Topology and Structure
Percolation Theory for Flow in Porous Media, 2009Co-Authors: Allen G. Hunt, Robert P. EwingAbstract:The fundamental concepts of Percolation Theory are introduced in Chaps. 1 and 2. Chapter 1 includes descriptions of geometrical and topological variables, while the description of such properties as tortuosity and transport are deferred to Chap. 2. Chapter 1 has, generally speaking, two purposes: (1) to be a reference for material that will be applied later in the book, (2) to provide a means for a scientist to gain a working familiarity with Percolation Theory. The chapter is organized in such a way that those sections that provide essentially all of the expertise required for arbitrary applications of Percolation Theory to porous media problems can be read in early explorations, while those sections (1.11–1.15) that provide additional detail can be skipped. The role of universal scaling functions and the relevance of power-law behavior are discussed in terms of the understanding of the fractal structure of Percolation Theory. The chapter concludes with a discussion of the non-universality of the Percolation threshold and presentation of what general methods have been proposed to predict it.
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Percolation Theory for Flow in Porous Media
Lecture Notes in Physics, 2009Co-Authors: Robert P. Ewing, Allen G. HuntAbstract:This monograph presents, for the first time, a unified and comprehensive introduction to some of the basic transport properties of porous media, such as electrical and hydraulic conductivity, air permeability and diffusion. The treatment is based on critical path analysis and the scaling of transport properties which are individually described as functions of saturation. At the same time, the book supplies a tutorial on Percolation Theory for hydrologists, providing them with the tools for solving actual problems. In turn, a separate chapter serves to introduce physicists to some of the language and complications of groundwater hydrology necessary for successful modelling. End of chapter problems often indicate open questions, on which young researchers entering the field can readily start work on. This significantly revised and much expanded edition was made necessary by both the selling out of the first edition and the rapid progress in the field. At the same time the tutorial aspects of the first few chapters have been considerably improved and the number of models, experiments and range of medium properties considered have been increased. Topics discussed for the first time in detail in this edition are advanced topological aspects of Percolation Theory that serve as a basis for examining dispersion aspects in porous media. "The book is suitable for advanced graduate courses, with selected problems and questions appearing at the end of each chapter. [...] I think the book is an important work that will guide soil scientists, hydrologists, and physicists to gain a better qualitative and quantitative understanding of multitransport properties of soils." (Marcel G. Schaap, Soil Science Society of America Journal, May-June, 2006
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Assessment of the application of Percolation Theory to a water repellent soil
Soil Research, 2005Co-Authors: Tammo S. Steenhuis, Allen G. Hunt, J.-yves Parlange, Robert P. EwingAbstract:A few hydrophobic grains in otherwise hydrophilic sand render the soil hydrophobic and can completely alter the flow of water through unsaturated sands. In this paper we examine whether Percolation Theory can explain the phenomenon. Percolation Theory has been used to describe the dependence of large-scale flow phenomena on heterogeneities found at the pore scale and should, therefore, be able to explain the water flow behaviour in hydrophobic soil. We show that the Theory is valid, in general, for a hydrophilic soil into which a small but increasing fraction of highly hydrophobic grains is mixed. However, the application of Percolation Theory is limited by the complex interactions of matric potential and contact angle effects due to the introduction of hydrophobic particles.
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Percolation Theory and network modeling applications in soil physics
Surveys in Geophysics, 1998Co-Authors: Brian Berkowitz, Robert P. EwingAbstract:The application of Percolation Theory to porous media is closely tied to network models. A network model is a detailed model of a porous medium, generally incorporating pore-scale descriptions of the medium and the physics of pore-scale events. Network models and Percolation Theory are complementary: while network models have yielded insight into behavior at the pore scale, Percolation Theory has shed light, at the larger scale, on the nature and effects of randomness in porous media. This review discusses some basic aspects of Percolation Theory and its applications, and explores work that explicitly links Percolation Theory to porous media using network models. We then examine assumptions behind Percolation Theory and discuss how network models can be adapted to capture the physics of water, air and solute movement in soils. Finally, we look at some current work relating Percolation Theory and network models to soils.
Hans Leuenberger - One of the best experts on this subject based on the ideXlab platform.
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Percolation Theory and the Role of Maize Starch as a Disintegrant for a Low Water-Soluble Drug
Pharmaceutical development and technology, 2007Co-Authors: Go Kimura, Maxim Puchkov, Gabriele Betz, Hans LeuenbergerAbstract:The objective of the present work is to investigate the presence or absence of a critical concentration of maize starch according to the Percolation Theory for a truly ternary system with respect to a minimum disintegration time. The results of this study show that the application of Percolation Theory is not limited to the study of binary systems. In this work it is shown how it can be used to analyze the behavior of binary and ternary systems for caffeine and mefenamic acid formulations containing a starch-based disintegrant. The Percolation threshold pc can be described by the volumetric ratio of the disintegrant to the drug substance being equal to pc = 0.2 (v/v) in in which both components have similar average particle sizes. In addition, the behavior of the disintegration time in the neighborhood of the Percolation threshold can be mathematically modeled with the basic equation of the Percolation Theory yielding a critical exponent q = 0.28 ± 0.06.
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The application of Percolation Theory in powder technology
Advanced Powder Technology, 1999Co-Authors: Hans LeuenbergerAbstract:It is about 10 years ago since the author of this invited paper started to apply Percolation Theory in the field of (pharmaceutical) powder technology. Thus the invited paper summarizes 10 years of experience in the application of Percolation Theory. The goal of the paper is to share this experience and to stimulate a broader use of Percolation Theory. The application of Percolation Theory is a fast growing field in very different areas of science and technology. However, Percolation Theory has not yet reached as broad an application in the field of powder technology as it should deserve. For this purpose, within this article a strong emphasis is put on a condensed but still rigorous introduction to the concepts of Percolation Theory to facilitate a broader application in powder technology. In this respect it is important to get a deeper knowledge and understanding of the basic power law of Percolation Theory to describe a desired property X = S* (p - pc)q, where S* is the scaling factor, p is the (bond or site) occupation probability, pc is the Percolation threshold and q is the critical exponent, close to the Percolation threshold. A prerequisite is a geometrical or a physical phase transition at pc. An explicit statement about the nature of the Percolation threshold phenomenon should be part of the system and model analyzed. The question of the universal character of a critical exponent q, which depends only on the dimensionality d of a system, plays an important role as well as the concept of Percolation threshold pc, which reflects the microstructure of a system. Different examples illustrate the successful application of Percolation Theory in (pharmaceutical) powder technology, covering important unit operations such as the compression of powder and the dissolution of an active substance from a binary powder compact, etc. Percolation Theory provides key tools for a more rational design of pharmaceutical dosage forms and for the development of robust formulations. Thus the development time can be speeded up and time to market can be reduced. The examples presented show the range of application and possible limitations of Percolation Theory. An outlook is given for a broader application as well as for a possible fruitful application of Percolation Theory in nanoscience and nanotechnology.
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Percolation Theory and physics of compression
European Journal of Pharmaceutics and Biopharmaceutics, 1997Co-Authors: Hans Leuenberger, Lotti IneichenAbstract:Abstract The concept of Percolation Theory is an excellent tool to elucidate the physics of compression. Earlier findings taking into account the Percolation Theory indicated that the formation of a tablet can be subdivided into a two-stage process with a ‘weak-bond’ Percolation effect at a lower Percolation threshold pc corresponding to the relative tapped density ϱr and a ‘strong-bond/site’ Percolation effect at an upper Percolation threshold p c ∗ , i.e. at a relative density ϱ r ∗ , where brittle fracture and/or plastic flow starts to play an important role for the formation of a stable compact. The new findings which are now presented indicate that the uniaxial compression can be interpreted as a 2-dimensional Percolation process where the stress is transmitted by the contact points of the particles. Thus the modified Young's elasticity modulus of the compact can be described by the fundamental equation of Percolation Theory with a critical exponent q = 1.3 (which is the conductivity exponent) and with a lower Percolation threshold of the relative tapped density ϱr. If the same equation is applied for the tensile strength, high values of the critical exponent result, indicating that a still unknown fractal dimension seems to play a key role.
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study of the release mechanism of carteolol inert matrix tablets on the basis of Percolation Theory
International Journal of Pharmaceutics, 1994Co-Authors: Isidoro Caraballo, M A Holgado, M Fernandezarevalo, A M Rabasco, Hans LeuenbergerAbstract:Abstract In the present paper, Percolation Theory has been applied to the study of the release mechanism obtained from controlled release tablets of carteolol hydrochloride. These dosage systems had already been studied on the basis of ‘classical’ theories. The new approach to this study has allowed us to obtain more complete information about the release behaviour of these inert matrix systems. The results obtained in this study demonstrate that Percolation Theory can provide useful parameters that can be considered as important tools for the proper design of these controlled release dosage forms.
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Application of Percolation Theory and Fractal Geometry to Tablet Compaction
Drug Development and Industrial Pharmacy, 1992Co-Authors: Hans Leuenberger, R. Leu, J. D. BonnyAbstract:AbstractPercolation Theory1 and fractal geogetry2 represent novel powerful concepts which cover a wide range of applications in pharmaceutical technology3. Both concepts provide new insights into the physics of tablet compaction and the properties of compacts4-11. The paper reviews and summarizes the most recent findings in the application of Percolation Theory and fractal geometry to tablet compaction which include four sections i.e. 1) short introduction to Percolation Theory and fractal qeometrv, 2) the formation of a tablet4, 7, 10, 3) tablet properties such as deformation hardness, tensile strength10 and 4) drug dissolution from a matrix type controlled release system3, 9, 11.
J. C. Phillips - One of the best experts on this subject based on the ideXlab platform.
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Quantum Percolation Theory and high-temperature superconductivity
Philosophical Transactions of the Royal Society of London. Series A: Physical and Engineering Sciences, 1991Co-Authors: J. C. PhillipsAbstract:An overall view of the methodology of quantum Percolation Theory as applied to high-temperature superconductivity clarifies the differences in its approach compared to others. Several crucial predictions have been confirmed by experiment, including the percolative nature of the superconductive transition itself.
Klaus Regenauer-lieb - One of the best experts on this subject based on the ideXlab platform.
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Application of Percolation Theory to microtomography of rocks
Earth-Science Reviews, 2021Co-Authors: Jie Liu, Klaus Regenauer-liebAbstract:Abstract Percolation Theory has made significant breakthroughs in the understanding of physical processes through identification of an infinite connected cluster. It allows the definition of critical material parameters such as Percolation threshold, critical exponents, crossover length and fractal dimension and has evolved from a purely mathematical approach to an applied field of study. In geosciences, the most popular application of Percolation Theory is the analysis of fluid flow in porous media. The capability to image the 3D structure of such porous networks through Computed Tomography (CT) opens new avenues for the concise application of Percolation Theory. Here we summarize digital rock techniques developed to derive rock properties and the critical Percolation parameter from CT-scans and compare the results to the mathematical ideal structures and laboratory experiments. We demonstrate that a near ideal synthetic rock, which has been designed to reproduce a homogenous sample for geophysical experiments, portrays significantly different Percolation properties to their mathematical counterparts. Furthermore, we present a variety of rock specimens with different microstructures and report stronger departures to the mathematical ideal structures. The generation of derivative models of the digital rock and their Percolation analysis allows the identification of the Percolation threshold, crossover length and critical exponent of correlation length. The technique is demonstrated in application for upscaling permeability, elastic moduli and yield stress. Three independent techniques for the identification of a Representative Volume Element (RVE) are presented: stochastic analysis, thermodynamic averaging and crossover length. A worked example for a dynamic environment is presented in a transect across a deformation zone, where several RVE subsamples are analyzed in terms of their Percolation properties. A clear trend from a 2-D dominated to a 3-D network in the deformation center allowed unprecedented insights into the microphysical dynamic processes that established the Percolation network. Examples for the newly emerging trend of time-lapse imaging (so-called 4-D tomography) are also discussed. The provided techniques and concepts thus open a new era in digital rock physics.
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Application of Percolation Theory to microtomography of structured media: Percolation threshold, critical exponents, and upscaling.
Physical Review E, 2011Co-Authors: Jie Liu, Klaus Regenauer-liebAbstract:Percolation Theory provides a tool for linking microstructure and macroscopic material properties. In this paper, Percolation Theory is applied to the analysis of microtomographic images for the purpose of deriving scaling laws for upscaling of properties. We have tested the acquisition of quantities such as Percolation threshold, crossover length, fractal dimension, and critical exponent of correlation length from microtomography. By inflating or deflating the target phase and Percolation analysis, we can get a critical model and an estimation of the Percolation threshold. The crossover length is determined from the critical model by numerical simulation. The fractal dimension can be obtained either from the critical model or from the relative size distribution of clusters. Local probabilities of Percolation are used to extract the critical exponent of the correlation length. For near-isotropic samples such as sandstone and bread, the approach works very well. For strongly anisotropic samples, such as highly deformed rock (mylonite) and a tree branch, the Percolation threshold and fractal dimension can be assessed with accuracy. However, the uncertainty of the correlation length makes it difficult to accurately extract its critical exponents. Therefore, this aspect of Percolation Theory cannot be reliably used for upscaling properties of strongly anisotropic media. Other methods of upscaling have to be used for such media.