SOME BOUNDS ON THE BULK CONDUCTIVITY OF A TWO-PHASE MEDIUM: A COMPARISON BETWEEN PERIODIC AND RANDOM STRUCTURE

1992 ◽  
Vol 02 (03) ◽  
pp. 283-294 ◽  
Author(s):  
ANDREA GAVIOLI
Keyword(s):  
Positive Constant ◽  
Percolation Theory ◽  
Effective Conductivity ◽  
Three Dimensional ◽  
Random Structure ◽  
Bulk Conductivity ◽  
Two Phase ◽  
Phase Medium

We prove that the effective conductivity of a three-dimensional medium with a periodic chessboard structure does not exceed [Formula: see text] where α and β are the values of the conductivity in the cells of the chessboard, and A is a positive constant; then we show how the corresponding “random” structure behaves in a quite different way, according to recent results in percolation theory.

scholarly journals Growth model for large branched three-dimensional hydraulic crack system in gas or oil shale

2016 ◽  
Vol 374 (2078) ◽  
pp. 20150418 ◽  
Author(s):  
Viet T. Chau ◽  
Zdeněk P. Bažant ◽  
Yewang Su
Keyword(s):  
Solid Phase ◽  
Three Dimensional ◽  
Cohesive Crack ◽  
Rock Joints ◽  
Recent Analysis ◽  
Band Model ◽  
Two Phase ◽  
Strength Limit ◽  
Crack Wall ◽  
Phase Medium

Recent analysis of gas outflow histories at wellheads shows that the hydraulic crack spacing must be of the order of 0.1 m (rather than 1 m or 10 m). Consequently, the existing models, limited to one or several cracks, are unrealistic. The reality is 10 5 –10 6 almost vertical hydraulic cracks per fracking stage. Here, we study the growth of two intersecting near-orthogonal systems of parallel hydraulic cracks spaced at 0.1 m, preferably following pre-existing rock joints. One key idea is that, to model lateral cracks branching from a primary crack wall, crack pressurization, by viscous Poiseuille-type flow, of compressible (proppant-laden) frac water must be complemented with the pressurization of a sufficient volume of micropores and microcracks by Darcy-type water diffusion into the shale, to generate tension along existing crack walls, overcoming the strength limit of the cohesive-crack or crack-band model. A second key idea is that enforcing the equilibrium of stresses in cracks, pores and water, with the generation of tension in the solid phase, requires a new three-phase medium concept, which is transitional between Biot’s two-phase medium and Terzaghi’s effective stress and introduces the loading of the solid by pressure gradients of diffusing pore water. A computer program, combining finite elements for deformation and fracture with volume elements for water flow, is developed to validate the new model. This article is part of the themed issue ‘Energy and the subsurface’.

ON THE PROBLEM OF HEAT CONDUCTION FOR RANDOM DISPERSIONS OF SPHERES ALLOWED TO OVERLAP

1992 ◽  
Vol 02 (03) ◽  
pp. 249-269 ◽  
Author(s):  
KONSTANTIN Z. MARKOV ◽  
CHRISTO I. CHRISTOV
Keyword(s):  
Correlation Functions ◽  
Unit Volume ◽  
Effective Conductivity ◽  
Heat Propagation ◽  
Two Phase ◽  
Statistical Solution ◽  
Spherical Inclusions ◽  
Phase Medium ◽  
Factorial Series ◽  
The Mean

We consider a random two-phase medium which represents a matrix containing an array of allowed to overlap spherical inclusions with random radii. A statistical theory of transport phenomena in the medium, on the example of heat propagation, is constructed by means of the functional (Volterra-Wiener) series approach. The functional series for the temperature is rendered virial in the sense that its truncation after the p-tuple term yields results for all multipoint correlation functions of the temperature field that are asymptotically correct to the order np, where n is the mean number of spheres per unit volume. The case p=2 is considered in detail and the needed kernels of the factorial series are found to the order n2. In this way not only the effective conductivity, but also the full statistical solution, i.e., all needed correlation functions, can be expressed in a closed form, correct to the said order.

Elastic strain energy and forces on point defects in a two-phase medium

1986 ◽  
Vol 1 (1) ◽  
pp. 193-201 ◽  
Author(s):  
K. Jagannadham ◽  
J. Narayan
Keyword(s):  
Point Source ◽  
Point Defects ◽  
Elastic Strain ◽  
Strain Energy ◽  
Three Dimensional ◽  
Elastic Strain Energy ◽  
Second Phase ◽  
Two Phase ◽  
Phase Medium ◽  
Important Field

Elastic strain energy and forces on point defects in a two-phase medium with a planar interface are analyzed employing the surface dislocation analysis developed earlier for three-dimensional distortions. The important field components, namely, the tractions and the displacements arising due to the point source at the interface, are determined. Furthermore, the field components at the interface are used to determine the elastic strain energy associated with the point source in the two-phase medium and the elastic force exerted by the second phase on the point defect. The significance of these results to the force acting on a vacancy or an interstitial at the interface is emphasized.

scholarly journals AGN Dusty Tori as a Clumpy Two-Phase Medium: the 10 μm Silicate Feature

2011 ◽  
Vol 20 (3) ◽  
Author(s):  
Marko Stalevski ◽  
Jacopo Fritz ◽  
Maarten Baes ◽  
Theodoros Nakos ◽  
Luka Č. Popović
Keyword(s):  
Three Dimensional ◽  
Galactic Nuclei ◽  
Infrared Emission ◽  
Spectral Energy ◽  
Two Phase ◽  
Random Arrangement ◽  
Wide Range ◽  
Phase Medium ◽  
Silicate Feature ◽  
Dust Distribution

AbstractWe investigated the emission of active galactic nuclei dusty tori in the infrared domain, with a focus on the 10 μm silicate feature. We modeled the dusty torus as a clumpy two-phase medium with high-density clumps and a low-density medium filling the space between the clumps. We used a three-dimensional radiative transfer code to obtain spectral energy distributions and images of tori at different wavelengths. We calculated a grid of models for different parameters and analyzed the influence of these parameters on the shape of the mid-infrared emission. A corresponding set of clumps-only models and models with a smooth dust distribution is calculated for comparison. We found that the dust distribution, the optical depth and a random arrangement of clumps in the innermost region, all have an impact on the shape and strength of the silicate feature. The 10 μm silicate feature can be suppressed for some parameters, but models with smooth dust distribution are also able to produce a wide range of the silicate feature strength.

SYNTHESIS OF HYDROGEN IN ACOUSTOPLASMA DISCHARGE IN A LIQUID-PHASE STREAM

2019 ◽  
pp. 42-48 ◽  
Author(s):  
N. A. Bulychev
Keyword(s):  
Liquid Phase ◽  
Organic Compounds ◽  
Electrode Materials ◽  
Solid Phase ◽  
Plasma Discharge ◽  
Raw Material ◽  
Two Phase ◽  
Reduced Pressure ◽  
External Power Source ◽  
Phase Medium

In this paper, the plasma discharge in a high-pressure fluid stream in order to produce gaseous hydrogen was studied. Methods and equipment have been developed for the excitation of a plasma discharge in a stream of liquid medium. The fluid flow under excessive pressure is directed to a hydrodynamic emitter located at the reactor inlet where a supersonic two-phase vapor-liquid flow under reduced pressure is formed in the liquid due to the pressure drop and decrease in the flow enthalpy. Electrodes are located in the reactor where an electric field is created using an external power source (the strength of the field exceeds the breakdown threshold of this two-phase medium) leading to theinitiation of a low-temperature glow quasi-stationary plasma discharge.A theoretical estimation of the parameters of this type of discharge has been carried out. It is shown that the lowtemperature plasma initiated under the flow conditions of a liquid-phase medium in the discharge gap between the electrodes can effectively decompose the hydrogen-containing molecules of organic compounds in a liquid with the formation of gaseous products where the content of hydrogen is more than 90%. In the process simulation, theoretical calculations of the voltage and discharge current were also made which are in good agreement with the experimental data. The reaction unit used in the experiments was of a volume of 50 ml and reaction capacity appeared to be about 1.5 liters of hydrogen per minute when using a mixture of oxygen-containing organic compounds as a raw material. During their decomposition in plasma, solid-phase products are also formed in insignificant amounts: carbon nanoparticles and oxide nanoparticles of discharge electrode materials.

Some 1-substitution derivatives of 4-aryl-2,3-dihalogeno-1-naphthols

1984 ◽  
Vol 49 (1) ◽  
pp. 110-121 ◽  
Author(s):  
Jiří Křepelka ◽  
Drahuše Vlčková ◽  
Milan Mělka
Keyword(s):  
Thionyl Chloride ◽  
Oxirane Ring ◽  
Secondary Amines ◽  
Two Phase ◽  
Lytic Effect ◽  
Primary And Secondary Amines ◽  
Phase Medium ◽  
Chloro Derivatives ◽  
Derivatives Of

Alkylation of derivatives of 4-aryl-1-naphthols (I-V) by 2,3-epoxypropyl chloride in methanolic sodium hydroxide gave epoxy derivatives VI, VIII, IX, XI and XII, apart from products of cleavage of the oxirane ring, VII and X. Analogous alkylation of compounds I, IV and V by 2-(N,N-diethylamino)ethyl chloride hydrochloride in a two-phase medium afforded basic ethers XIII to XV. The cleavage of the oxirane ring in compound VI by the action of primary and secondary amines, piperidine and substituted piperazines led to compounds XVI-XXIV. Reaction of thionyl chloride with compounds XXI, XXII and XXIV gave chloro derivatives XXV-XXVII.Exposure of compound XXII to 4-methylbenzenesulfonyl chloride produced compound XXVIII, retaining the secondary alcoholic group. In an antineoplastic screening in vivo none of the compounds prepared had an appreciable activity. Compound XVII, being an analogue of propranolol, was used in the test of isoproterenolic tachycardia, and showed a beta-lytic effect comparable with that of propranol.

scholarly journals Three-Dimensional Analysis of the In Vivo Motion of Implantable Cardioverter Defibrillator Leads

2021 ◽  
Author(s):  
Tamas Szili-Torok ◽  
Jens Rump ◽  
Torsten Luther ◽  
Sing-Chien Yap
Keyword(s):  
Three Dimensional ◽  
Second Phase ◽  
Two Phase ◽  
Maximum Curvature ◽  
Phase Study ◽  
Absolute Curvature ◽  
Icd Leads ◽  
Lead Testing ◽  
Design And Testing

Abstract Better understanding of the lead curvature, movement and their spatial distribution may be beneficial in developing lead testing methods, guiding implantations and improving life expectancy of implanted leads. Objective The aim of this two-phase study was to develop and test a novel biplane cine-fluoroscopy-based method to evaluate input parameters for bending stress in leads based on their in vivo 3D motion using precisely determined spatial distributions of lead curvatures. Potential tensile, compressive or torque forces were not subjects of this study. Methods A method to measure lead curvature and curvature evolution was initially tested in a phantom study. In the second phase using this model 51 patients with implanted ICD leads were included. A biplane cine-fluoroscopy recording of the intracardiac region of the lead was performed. The lead centerline and its motion were reconstructed in 3D and used to define lead curvature and curvature changes. The maximum absolute curvature Cmax during a cardiac cycle, the maximum curvature amplitude Camp and the maximum curvature Cmax@amp at the location of Camp were calculated. These parameters can be used to characterize fatigue stress in a lead under cyclical bending. Results The medians of Camp and Cmax@amp were 0.18 cm−1 and 0.42 cm−1, respectively. The median location of Cmax was in the atrium whereas the median location of Camp occurred close to where the transit through the tricuspid valve can be assumed. Increased curvatures were found for higher slack grades. Conclusion Our results suggest that reconstruction of 3D ICD lead motion is feasible using biplane cine-fluoroscopy. Lead curvatures can be computed with high accuracy and the results can be implemented to improve lead design and testing.

scholarly journals Thermocapillary effects in two-phase medium and applications to metal-silicate separation

2021 ◽  
pp. 106640
Author(s):  
Yanick Ricard ◽  
Stéphane Labrosse ◽  
Hidenori Terasaki ◽  
David Bercovici
Keyword(s):  
Two Phase ◽  
Metal Silicate ◽  
Phase Medium
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