Three-dimensional Network Model Research Articles

Integration Method of Three-dimensional Complex Tunnel Network Model

In recent years, Digital Mine has been an important research direction in the field of geology and mineral resources. In particular, three-dimensional network modeling of mine tunnel with its spatial analysis is an important research perspective. It is significant research direction on theoretical study of digital mine, mineral resources exploration, mining decision-making management, mine production and mine safety etc. In order to seamlessly integrate the models of simple tunnel and intersected complicate tunnel, directed double nodes approach and midpoint interpolation approach were proposed; In order to solve the problem that the two corresponding half-tunnels will crack at sharp turning, the uniform height approach on section arch was proposed. Using Windows XP as the platform, MS Visual C++6.0 as development tools and OpenGL graphics package as the graphic processing display tools, the experimental system of three-dimensional tunnel network model was designed and developed. Using real mining data, the experimental system was tested. It is shown that the proposed method is the practical and effective.

Three-dimensional network model of carbon containing only sp2-carbon bonds and boron nitride analogues

We design two network models of carbon and boron nitride crystalline networks, namely, the honeycomb and triangular foams. The triangular carbon foam is a unique 3D network model of carbon which contains only sp(2)-carbon bonds. Also, it has large internal surface area per unit volume and bulk modulus.

Three-Dimensional Micromechanical Finite-Element Network Model for Elastic Damage Behavior of Idealized Stone-Based Composite Materials

This paper presents a three-dimensional (3D) micromechanical finite-element (FE) network model for predicting elastic damage behavior of the idealized stone-based materials. Stone-based composite materials have multiphase structures: an aggregate (or stone) skeleton, a binding medium, fillers, and air voids. Numerical simulation of the micromechanical behavior of the idealized stone-based materials was accomplished by using a microframe element network model that incorporated the mechanical load transfer between adjacent particles. The elastic stiffness matrix of this special element was obtained from an approximate elastic stress-strain analysis of straight cement between particle pairs. A damage-coupled microframe element was then formulated with bilinear damage laws, including elastic and softening behavior based on the equivalent fracture release energy. Indirect tension and compression simulations were conducted with developed FE models on the idealized digital samples of the stone-based materials. These simulations predicted the internal microdamage distribution and global fracture behavior of these samples, which qualitatively agree with the laboratory observations. The results indicate that the developed FE models have the capability to predict the typical loading-related damage behavior observed from the stone-based materials.

Three-dimensional random network model for thermal conductivity in particulate materials

This paper describes a three-dimensional random network model to evaluate the thermal conductivity of particulate materials. The model is applied to numerical assemblies of poly-dispersed spheres generated using the discrete element method (DEM). The grain size distribution of Ottawa 20–30 sand is modeled using a logistic function in the DEM assemblies to closely reproduce the gradation of physical specimens. The packing density and inter-particle contact areas controlled by confining stress are explored as variables to underscore the effects of micro- and macro-scales on the effective thermal conductivity in particulate materials. It is assumed that skeletal structure of 3D granular system consists of the web of particle bodies interconnected by thermal resistor at contacts. The inter-particle contact condition (e.g., the degree of particle separation or overlap) and the particle radii determine the thermal conductance between adjacent particles. The Gauss–Seidel method allows evaluation of the evolution of temperature variation in the linear system. Laboratory measurements of thermal conductivity of Ottawa 20–30 sand corroborate the calculated results using the proposed network model. The model is extended to explore the evolution of thermal conduction depending on the nucleation habits of secondary solid phase as an anomalous material in the pore space. The proposed network model highlights that the coordination number, packing density and the inter-particle contact condition are integrated together to dominate the heat transfer characteristics in particulate materials, and allows fundamental understanding of particle-scale mechanism in macro-scale manifestation.

Determination of oxygen effective diffusivity in porous gas diffusion layer using a three-dimensional pore network model

In proton exchange membrane fuel cell (PEMFC) models, oxygen effective diffusivity is the most important parameter to characterize the oxygen transport in the gas diffusion layer (GDL). However, its determination is a challenge due to its complex dependency on GDL structure. In the present study, a three-dimensional network consisting of spherical pores and cylindrical throats is developed and used to investigate the effects of GDL structural parameters on oxygen effective diffusivity under the condition with/without water invasion process. Oxygen transport in the throat is described by Fick's law and water invasion process in the network is simulated using the invasion percolation with trapping algorithm. The simulation results reveal that oxygen effective diffusivity is slightly affected by network size but increases with decreasing the network heterogeneity and with increasing the pore connectivity. Impacts of network anisotropy on oxygen transport are also investigated in this paper. The anisotropic network is constructed by constricting the throats in the through-plane direction with a constriction factor. It is found that water invasion has a more severe negative influence on oxygen transport in an anisotropic network. Finally, two new correlations are introduced to determine the oxygen effective diffusivity for the Toray carbon paper GDLs.

Three-dimensional pore network model of biofilter treating toluene: A study of the effect of the pore space morphology

Abstract Treatment of polluted air stream with toluene in a biofilter under quasi-steady-state condition is described with a three-dimensional (3-D) pore network model. The efficiency of the process depends on the pore structure of the biofilter media. The previous models for the process, considered transport and reaction equations mostly in the continuum systems. They cannot show the effect of pore spaces’ morphology, different pore size distributions and connectivity types. We used the 3-D pore network model to simulate the pore structure and to study the effects of biofilm growth on pore size distribution and pore connectivity on the biofilter performance. This model predicts the toluene conversion, pressure drop profiles, biofilm thickness and clogging in the biofilter. Our developed model assumes a nonlinear kinetic for the biodegradation reaction of toluene in the biofilm. The differential equations of the model are solved numerically. Model results indicated that biofilter media with smaller mean pore size and higher connectivity have a higher toluene conversion. To investigate the validity of the model, we compared the model results with experimental data and found satisfying similarities.

Monte Carlo simulation and experimental heat and mass transfer in direct contact membrane distillation

A Monte Carlo (MC) simulation model is developed to study heat and mass transfer through hydrophobic membranes applying direct contact membrane distillation (DCMD) process. In this study, the membrane pore space is described by a three-dimensional network model of inter-connected cylindrical pores with distributive pore size. Vapor flux through membrane pores is described by gas transport mechanism(s) based on the kinetic theory of gases. The present MC model can take into consideration the influence of temperature polarization phenomenon, membrane physical properties including pores interconnectivity and the DCMD fluid dynamic conditions. The developed model can simultaneously predict the DCMD process vapor flux and membrane surface temperatures, contrary to other models in which one of them has to be given in order to solve the other. The model is comprehensive in its approach and does not involve any adjustable parameter. The simulated results were compared with the experimental ones of different membranes and the comparisons were found to be in excellent qualitative and quantitative agreement.

A three-dimensional network model for rubber elasticity: The effect of local entanglements constraints

We present a micro-mechanical model based on the network theory for the description of the elastic response of rubber-like materials at large strains. The material microstructure is characterized by chain-like macromolecules linked together at certain points; therefore an irregular three-dimensional network is formed. The material behaviour at the micro-level is usually described by means of statistical mechanics. Using certain assumptions for the certain distributions, one arrives at a continuum mechanical model of finite elasticity. However, the macromolecules interactions are neglected usually in these approaches. In the present contribution, we propose to add the effect of the interactions between chains of the cross-linked network. Following Arruda and Boyce (1993, 2000) [31,2], a cubic unit cell is defined where the entanglements fluctuations are localised in the corners of the cubic sub unit cell. These entanglements are linked by chains which ensure the interactions between the chains of idealized network (without interactions). These interactions can be represented by chains which are located in the principal directions of the cubic sub unit cell in undeformed state. We assume the probability densities which describe the free chain response of idealized network, and, the chain of constraints networks are independent. Then, the free-energy of the entire network is obtained by adding the free-energies of the free idealized (without interactions) and constraints (due to the chains interactions) networks. The constraint network reduces to four of the three-chain model of James and Guth (1943) [4] in undeformed state. Therefore, the free-energy of constraint network is obtained using the standard three-chain model, and, the free-energy of the free idealized network is constructed by means of the eight-chain model. The constitutive model involves five physical material parameters, namely, the shear modulus at small strains (μ0), the numbers of links that form the macromolecular chain of the eight-chain, and three-chain models (N8,N3) respectively, a micro-macro variable Ki, and, non-dimensional parameters (η,ρ). In order to determine the material parameters, the Langevin function in the single chain configuration is replaced by its first order Pade approximant [see, Cohen (1991) [5]; Perrin (2000) [6]], and, the material parameters are identified. The excellent predictive performance of the proposed model is shown by comparative to various available experimental data of homogeneous tests. However, the present model requires a validation because the relationship between the micro and macro levels needs to be clarified. Indeed, the identification of the physical parameters (μf,μc,N8,N3) from experimental results data at micro is hoped in order to simulate the macroscopic (i.e. bulk) behaviour of the material.

Coupled electrothermal analysis of a micro flow sensor with control circuit using spice

AbstractThis paper reports an electrothermal analysis of a two‐element micro flow sensor (MFS). The measurement principle is based on temperature difference between the upstream and downstream parts of electrically connected heating‐sensing elements. The two‐heater MFS, the thermal fluid flow around MFS, and the electric circuit were modeled together using a commercial general‐purpose circuit simulator based on SPICE (Simulation Program with Integrated Circuit Emphasis). The model has a partial three‐dimensional lumped thermal network model involved in a two‐dimensional one. Two‐dimensional laminar Poiseuille channel flow was assumed as the flow field in the model, and the forced convective heat transfer was calculated by energy balance at each node in the fluid flow. The tendency on the sensor characteristics was in good agreement between the simulation and experiment. © 2009 Wiley Periodicals, Inc. Electron Comm Jpn, 93(1): 58–64, 2010; Published online in Wiley InterScience (www.interscience. wiley.com). DOI 10.1002/ecj.10095

Elastic force of red blood cell membrane during tank-treading motion: Consideration of the membrane's natural state

The elastic force of a red blood cell (RBC) membrane during its tank-treading motion was estimated using a three-dimensional spring network model. An RBC membrane was modelled by an assembly of triangular elements in which stretch/compression and bending springs were placed to express planar shear and out-of-plane bending deformations, respectively. An areal incompressibility of the membrane and a volumetric constraint on the entire RBC were taken into account. Different natural states of an RBC membrane were considered by adjusting reference lengths and angles of the stretch/compression and bending springs, respectively. An elastic motion simulation was conducted using the spring network model to reproduce a tank-treading motion of the membrane for a constant biconcave discoid RBC under a fluid shear force. Given the simulated tank-treading motion, an additional membrane elastic force due to the motion was determined from the elastic energy changes during the motion. It was confirmed that the natural state of the RBC membrane should be nonuniform to generate the additional elastic force. Greater spring constants and greater natural state nonuniformity induced a greater additional elastic force, and the elastic force was regarded as a resistance against the tank-treading motion. Additional elastic forces due to the membrane tank-treading motion for different sets of spring constants and natural state nonuniformity values were determined, and they were compared with fluid shear forces at shear rates within the range of which a transition between tank-treading and tumbling motions of an RBC occurs in experiments. The results suggested that for the experimentally measured elastic moduli, natural state nonuniformity in a physiological state is moderate between that for a spherical or flat shape and that for the biconcave shape. Moderate nonuniformity was also confirmed by a simulated RBC shape in a minimum state of elastic energy.

Investigation on sensitivity of a polymer/carbon nanotube composite strain sensor

Extensive numerical simulation and experimental measurements have been conducted to understand the effects of processing parameters and material properties on sensor sensitivity in polymer/carbon nanotube (CNT) composite sensors. The numerical simulation was based on an improved three-dimensional statistical resistor network model incorporating the tunneling effect between the neighbouring nanotubes, and a fiber reorientation model. The behaviors of a sensor subjected to both tensile and compressive strains were investigated. Both numerical and experimental results indicate that a higher tunneling resistance or higher ratio of the tunneling resistance to the total resistance of the sensor leads to a higher sensor sensitivity. Processing conditions and material properties, such as weight fraction, diameter and conductivity of CNTs, curing temperature, mixing rate and barrier height of polymer matrix all play a role in determining the sensor sensitivity.

Contribution of Rat Endothelial Progenitor Cells on Three-Dimensional Network FormationIn Vitro

Endothelial progenitor cell (EPC) transplantation is a promising treatment option for ischemic diseases, and understanding the mechanism mediating angiogenic effects of EPCs is essential to further improve its effectiveness as well as their application to in vitro tissue engineering. Here we investigated EPC contribution on network formation using an in vitro three-dimensional network model. Bovine microvascular endothelial cells (ECs) were seeded on collagen gel to create a three-dimensional network model. Subsequently, EPCs isolated from rat bone marrow were seeded on top of a confluent endothelial cell (EC) monolayer to create EPC+EC model. In this model, EPCs promoted EC network formation. Quantitative analyses revealed that the total length, number, and depth of networks were significantly enhanced with the addition of EPCs. EPCs tended to localize in networks formed inside collagen gel rather than on a confluent monolayer with increasing experimental duration. In addition, EPCs preferentially distributed near sprout positions in a confluent monolayer. Furthermore, EPC-conditioned medium promoted network formation, and vascular endothelial growth factor was detected in the conditioned medium. Taken together, EPCs contributed to network formation by direct incorporation with on-site growth factor secretion. The angiogenic ability of EPCs offers a possible cell source to reconstruct vascularized tissues in vitro.

The effects of wettability and trapping on relationships between interfacial area, capillary pressure and saturation in porous media: A pore-scale network modeling approach

We use a three-dimensional mixed-wet random pore-scale network model to investigate the impact of wettability and trapping on the relationship between interfacial area, capillary pressure and saturation in two-phase drainage and imbibition processes. The model is a three-dimensional network of interconnected pores and throats of various geometrical shapes. It allows multiple phases to be present in each capillary element in wetting and spreading layers, as well as occupying the center of the pore space. Two different random networks that represent the pore space in Berea and a Saudi Arabia reservoir sandstone are used in this study. We allow the wettability of the rock surfaces contacted by oil to alter after primary drainage. The model takes into account both contact angle and trapping hystereses. We model primary oil drainage and water flooding for mixed-wet conditions, and secondary oil injection for a water-wet system. The total interfacial area for pores and throats are calculated when the system is at capillary equilibrium. They include contributions from the arc menisci (AMs) between the bulk and corner fluids, and from the main terminal menisci (MTMs) between different bulk fluids. We investigate hysteresis in these relationships by performing water injection into systems of varying wettability and initial water saturation. We show that trapping and contact angle hystereses significantly affect the interfacial area. In a strongly water-wet system, a sharp increase is observed at the beginning of water flood, which shifts the area to a higher level than primary drainage. As we change the wettability of the system from strongly water-wet to strongly oil-wet, the trapped oil saturation decreases significantly. Starting water flood from intermediate water saturations, greater than the irreducible water saturation, can also affect the non-wetting phase entrapment, resulting in different interfacial area behaviors. This can increase the interfacial area significantly in oil-wet systems. A qualitative comparison of our results with the experimental data available in literature for glass beads shows, with some expected differences, an encouraging agreement. Also, our results agree well with those generated by the previously developed models.

Variation of Water Retention Characteristics due to Particle Rearrangement under Zero Gravity

Controlled delivery of water to plant root zone remains a challenge in the exploration of plant growth under zero gravity, in which soil water retention characteristics are difficult to predict due to possible soil particle rearrangement and pore restructuring. This paper aims to provide an understanding of the effect of soil particle rearrangement on the water retention characteristics in zero gravity. A three-dimensional pore network model is developed to predict water retention characteristics under two forms of particle packing—cubic packing (most porous) and rhombohedral packing (most compact). The pore-throat distributions, as input parameters to the network model, are derived from particle size distribution under the two forms of particle arrangement. The model simulations reveal the quantitative variation of water retention characteristics due to particle rearrangement. Soil particle rearrangement that occurs during the drying process is shown to significantly change the water retention curve when...

Electrical and thermal conductivities of a silver flake/thermosetting polymer matrix composite

The electrical and thermal conductivities of a silver flake/thermosetting polymer matrix composite were studied experimentally and analytically in terms of silver flake size and size distribution. The electrical volume resistivity and the steady-state thermal conductivity of the composite were measured at various silver flake loading. The analytical study was based on a three-dimensional resistor network model, which takes into account percolation and microscopic conduction mechanisms. The predictions based on the resistor network model were compared with the experimental data, resulting in a reasonably good agreement. It was found that flakes with smaller mean value in size and broader size distribution yield smaller threshold volume fraction of silver flake. It was shown that the predictions by the present thermal resistor network model yields better agreement with the experimental data than those by the effective medium theory such as Eshelby’s model, for a composite with high thermal conductivity ratio of filler to matrix.

Random Walks and Anderson Localization in a Three-Dimensional Class C Network Model

We study the disorder-induced localization transition in a three-dimensional network model that belongs to symmetry class C. The model represents quasiparticle dynamics in a gapless spin-singlet superconductor without time-reversal invariance. It is a special feature of network models with this symmetry that the conductance and density of states can be expressed as averages in a classical system of dense, interacting random walks. Using this mapping, we present a more precise numerical study of critical behavior at an Anderson transition than has been possible previously in any context.

A three-dimensional resistor network model for the linear magnetoresistance of Ag2+δSe and Ag2+δTe bulks

A network model for the linear magnetoresistance (MR) of the Ag2+δSe and Ag2+δTe bulks is proposed. The bulk sample is considered as a two-phase (the metal phase and the semiconductor phase) composite and dispersed into a three-dimensional resistor network. The network is constructed from six-terminal resistor units and the mobility of carriers within the network has a modified Gaussian distribution, i.e., a Gaussian distribution with two constraint conditions. The modified Gaussian distribution is related with the mobility of carriers in the two phases and the volume fraction of the metal phase. The model predicts that the MR increases linearly with the increasing magnetic fields and does not show the saturation at high field. Moreover, the temperature dependence of the MR predicted by the model is discussed. A good agreement is found between the theoretical MR predictions and the available experimental data.

Experiment and simulation study on construction of a three-dimensional network model

The construction of a network model is one of the key techniques in organic combination of microscopic flow experiment and simulation. The construction method of a three-dimensional network model is presented on the basis of CT scanning images in this paper. A series of CT slice images describing microscopic pore structure and fluid distribution of actual rock is obtained with the help of the industrial microfocus CT system. Based on the extraction of pore space skeleton, pore and throat information, the corresponding network model is established, and the conversion from three-dimensional CT image information to pore-throat size distribution and topological information is also achieved. The feature of this method lies in the fact that complicated pore space of rock may be characterized by pores and throats with a simple shape while keeping the geometry and flow characteristics. It is indicated that the calculated results of porosity, permeability, relative permeability curve and microscopic remaining oil distribution match very well the experimental results of water flooding and polymer flooding. This network model may fairly well characterize the rock microscopic pore-throat size and topological characteristics.

Numerical simulation of rock pore-throat structure effects on NMR T2 distribution

We built a three-dimensional irregular network model which can adequately describe reservoir rock pore-throat structures. We carried out numerical simulations to study the NMR T2 distribution of water-saturated rocks. The results indicate that there is a good correlation between T2 distribution and the pore radius frequency histogram. The total T2 distribution can be partitioned into pore body and pore throat parts. The effect of parameters including throat radius, pore-throat ratio, and coordination number of the micropore structure on the T2 distribution can be evaluated individually. The result indicates that: 1) with the increase of the pore throat radius, the T2 distribution moves toward longer relaxation times and its peak intensity increases; 2) with the increase of the pore-throat ratio, the T2 distribution moves towards longer T2 with the peak intensity increasing and the overlap between pore body T2 and pore throat T2 decreasing; 3) With the increase of connectivity, the short T2 component increases and peak signal intensity decreases slightly.

The electrical properties of polymer nanocomposites with carbon nanotube fillers

The electrical properties of polymer nanocomposites containing a small amount of carbonnanotube (CNT) are remarkably superior to those of conventional electronic composites.Based on three-dimensional (3D) statistical percolation and 3D resistor network modeling,the electrical properties of CNT nanocomposites, at and after percolation, were successfullypredicted in this work. The numerical analysis was also extended to investigate the effectsof the aspect ratio, the electrical conductivity, the aggregation and the shape of CNTs onthe electrical properties of the nanocomposites. A simple empirical model was alsoestablished based on present numerical simulations to predict the electrical conductivity inseveral electronic composites with various fillers. This investigation further highlightedthe importance of theoretical and numerical analyses in the exploration of basicphysical phenomena, such as percolation and conductivity in novel nanocomposites.