A Particle Resistance Model for Flow through Porous Media

A particle model for resistance of flow in isotropic porous media is developed based on the fractal geometry theory and on the drag force flowing around sphere. The proposed model is expressed as a function of porosity, fluid property, particle size, fluid velocity （or Reynolds number） and fractal characters D f of particles in porous media. The model predictions are in good agreement with the experimental data. The validity of the proposed model is thus verified.     

Numerical study on permeability characteristics of fractal porous media

The fractal Brownian motion is utilized to describe pore structures in porous media. A numerical model of laminar flow in porous media is developed, and the flow characteristics are comprehensively analyzed and compared with those of homogeneous porous media. Moreover, the roles of the fractal dimension and porosity in permeability are quantitatively described. The results indicate that the pore structures of porous media significantly affect their seepage behaviors. The distributions of pressure and velocity in fractal porous media are both non-uniform; the streamline is no longer straight but tortuous. When Reynolds number Re 1, the dimensionless permeability is independent of Reynolds number, but its further increase will lead to a smaller permeability. Moreover, due to the higher connectivity and enlarged equivalent aperture of internal channel network, the augment in porosity leads to the permeability enhancement, while it is small and insensitive to porosity variation when ε 0.6. Fractal dimension also plays a significant role in the permeability of porous media. The increase in fractal dimension leads to the enhancement in pore connectivity and a decrease in channel tortuosity,which reduces the flow resistance and improves the transport capacity of porous media.     

Simultaneous effects of magnetic field and space porosity on compressible Maxwell fluid transport induced by a surface acoustic wave in a microchannel

Peristaltic motion induced by a surface acoustic wave of a viscous, compressible and electrically conducting Maxwell fluid in a confined parallel-plane microchannel through a porous medium is investigated in the presence of a constant magnetic field. The slip velocity is considered and the problem is discussed only for the free pumping case. A perturbation technique is employed to analyze the problem in terms of a small amplitude ratio. The phenomenon of a “backward flow” is found to exist in the center and at the boundaries of the channel. In the second order approximation, the net axial velocity is calculated for various values of the fluid parameters. Finally, the effects of the parameters of interest on the mean axial velocity, the reversal flow, and the perturbation function are discussed and shown graphically. We find that in the non-Newtonian regime, there is a possibility of a fluid flow in the direction opposite to the propagation of the traveling wave. This work is the most general model of peristalsis created to date with wide-ranging applications in biological, geophysical and industrial fluid dynamics.     

Velocity overshoot of start-up flow for a Maxwellfluid in a porous half-space

Stokes' first problem has been investigated for a Maxwell fluid in a porous half-space for gaining insight into the effect of viscoelasticity on the start-up flow in a porous medium. An exact solution was obtained by using the Fourier sine transform. It was found that at large values of the relaxation time the velocity overshoot occurs obviously and the system exhibits viscoelastic behaviours. On the other hand, for short relaxation time the velocity overshoot disappears and the system exhibits viscous behaviours. A critical value of the relaxation time was obtained for the emergence of the velocity overshoot. Furthermore, it was found that the velocity overshoot is caused by both the viscoelasticity of the Maxwell fluid and the Darcy resistance resulting from the structure of the micropore in the porous medium.     

Fractal Analysis of Power-Law Fluid in a Single Capillary

The fractai expressions for flow rate and hydraulic conductivity for power-law fluids in a single capillary are derived based on the fractai nature of tortuous capillaries. Every parameter in the proposed expressions has clear physical meaning. The flow rate and hydraulic conductivity for power-law fluids are found to be related to the tortuosity fractal dimension and the power-law index. The flow rate for power-law fluids increases with the increasing power-law index but decreases with the increasing tortuosity fractal dimension. Good agreement between the model predictions for flow in a fractai capillary and in a converging-diverging duct is obtained. The results suggest that the fractal capillary model can be used to model the power-law fluids with different rheologicai properties.     

A Fractal Model for the Transverse Thermal Dispersion Conductivity in Porous Media

A quasi-analytical model, i.e. the fractal model, for the transverse thermal dispersion conductivity in porous media is presented based on the fractal characteristics of tortuous flow paths/streamlines in porous media. The fractal dimension of tortuous flow paths, the spatial deviation velocity and the transverse thermal dispersion conductivity are derived. The proposed model is expressed as functions of the fractal dimension of tortuous flow paths/streamlines, Peclet number, porosity and structural parameters. The present results are compared with those from the existing correlation, and good agreement is found between the present model predictions and those from the existing correlation.     

Measurement of Threshold Pressure Gradient of Microchannels by Static Method

The development of oil fields and laboratory experiment present the threshold pressure gradient （TPG） of liquid flow in low permeability porous media, which is called the micro-size effect in porous media. Some micro-size effects in micro-electro-mechanism systems （MEMS） are not always in agreement with each other. We propose an experiment setup to measure the TPG of microchannels by static method in the microchannels with the diameter ranging from 20-320μm. The results present the existence of TPG in microchannel, and show an effect that the TPG of microchannel increases with decreasing hydrodynamic diameter. The relation between TPG and diameter is in agreement with single-log normalization. Additionally, the influence of errors in the experiment shows the data of experiment are valid. Finally, the mechanism of micro-size effects is discussed by revealing the facial force between liquid and solid and theory of boundary liquid, but the explanation is still not good, and needs further study.     

Wave dispersion and attenuation in viscoelastic isotropic media containing multiphase flow and its application

In this paper,we introduce the complex modulus to express the viscoelasticity of a medium.According to the correspondence principle,the Biot-Squirt(BISQ)equations in the steady-state case are presented for the space-frequency domain described by solid displacements and fluid pressure in a homogeneous viscoelastic medium.The effective bulk modulus of a multiphase flow is computed by the Voigt formula,and the characteristic squirt-flow length is revised for the gas-included case.We then build a viscoelastic BISQ model containing a multiphase flow.Through using this model,wave dispersion and attenuation are studied in a medium with low porosity and low permeability.Furthermore,this model is applied to observed interwell seismic data.Analysis of these data reveals that the viscoelastic parameter tanδ is not a constant.Thus,we present a linear frequency-dependent function in the interwell seismic frequency range to express tanδ.This improves the fit between the observed data and theoretical results.     

Velocity field of wave-induced local fluid flow in double-porosity media

Under the excitation of elastic waves,local fluid flow in a complex porous medium is a major cause for wave dispersion and attenuation.When the local fluid flow process is simulated with wave propagation equations in the double-porosity medium,two porous skeletons are usually assumed,namely,host and inclusions.Of them,the volume ratio of inclusion skeletons is low.All previous studies have ignored the consideration of local fluid flow velocity field in inclusions,and therefore they can not completely describe the physical process of local flow oscillation and should not be applied to the situation where the fluid kinetic energy in inclusions cannot be neglected.In this paper,we analyze the local fluid flow velocity fields inside and outside the inclusion,rewrite the kinetic energy function and dissipation function based on the double-porosity medium model containing spherical inclusions,and derive the reformulated Biot-Rayleigh(BR)equations of elastic wave propagation based on Hamilton’s principle.We present simulation examples with different rock and fluid types.Comparisons between BR equations and reformulated BR equations show that there are significant differences in wave response characteristics.Finally,we compare the reformulated BR equations with the previous theories and experimental data,and the results show that the theoretical results of this paper are correct and effective.     

A Geometry Model for Tortuosity of Flow Path in Porous Media

A simple geometry model for tortuosity of flow path in porous media is proposed based on the assumption that some particles in a porous medium are unrestrictedly overlapped and the others are not. The proposed model is expressed as a function of porosity and there is no empirical constant in this model. The model predictions are compared with those from available correlations obtained numerically and experimentally, both of which are in agreement with each other. The present model can also give the tortuosity with a good approximation near the percolation threshold. The validity of the present tortuosity model is thus verified.     

Kinetics of Infection-Driven Growth Model with Birth and Death

We propose a two-species infection model, in which an infected aggregate can gain one monomer from a healthy one due to infection when they meet together. Moreover, both the healthy and infected aggregates may lose one monomer because of self-death, but a healthy aggregate can spontaneously yield a new monomer. Consider a simple system in which the birth/death rates are directly proportional to the aggregate size, namely, the birth and death rates of the healthy aggregate of size k are J1 k and J2k while the self-death rate of the infected aggregate of size k is J3k. We then investigate the kinetics of such a system by means of rate equation approach. For the J1 〉 J2 case, the aggregate size distribution of either species approaches the generalized scaling form and the typical size of either species increases wavily at large times. For the J1 = J2 case, the size distribution of healthy aggregates approaches the generalized scaling form while that of infected aggregates satisfies the modified scaling form. For the J1 〈 J2 case, the size distribution of healthy aggregates satisfies the modified scaling form, but that of infected aggregates does not scale.     

Aggregation Processes with Catalysis-Driven Decomposition

We propose a three-species aggregation model with catalysis-driven decomposition. Based on the mean-field rate equations, we investigate the evoIution behavior of the system with the size-dependent catalysis-driven decomposition rate J（i; j; k） = Jijk^v and the constant aggregation rates. The results show that the cluster size distribution of the species without decomposition can always obey the conventional scaling law in the case of 0 ≤v ≤ 1, while the kinetic evolution of the decomposed species depends crucially on the index v. Moreover, the total size of the species without decomposition can keep a nonzero value at large times, while the total size of the decomposed species decreases exponentially with time and vanishes finally.     

Invariant Sets and Exact Solutions to Nonlinear Diffusion Equations with x-Dependent Convection and Absorption

In this paper, we introduce a new invariant set Eo={u：ux=f＇（x）F（u）＋ε[g＇（x）-f＇（x）g（x）]F（u）×exp（-∫^u1/F（z）dz）}where f and g are some smooth functions of x, ε is a constant, and F is a smooth function to be determined. The invariant sets and exact sohltions to nonlinear diffusion equation ut = （ D（u）ux）x ＋ Q（x, u）ux ＋ P（x, u）, are discussed. It is shown that there exist several classes of solutions to the equation that belong to the invariant set Eo.     

Synthesis of boron,nitrogen co-doped porous carbon from asphaltene for high-performance supercapacitors

Oxidized asphaltene(OA), a thermosetting material with plenty of functional groups, is synthesized from asphaltene(A) using HNO3/H2SO4as the oxidizing agent. Boron, nitrogen co-doped porous carbon(BNC–OA) is prepared by carbonization of the mixture of boric acid and OA at 1173 K in an argon atmosphere. X-ray photoelectron spectroscopy(XPS) characterization reveals that the BNC–OA has a nitrogen content of 3.26 at.% and a boron content of 1.31 at.%, while its oxidation-free counterpart(BNC–SA) has a nitrogen content of 1.61 at.% and a boron content of 3.02 at.%. The specific surface area and total pore volume of BNC–OA are 1103 m2·g-1and 0.921 cm3·g-1, respectively. At a current density of0.1 A·g-1, the specific capacitance of BNC–OA is 335 F·g-1and the capacitance retention can still reach 83% at 1 A·g-1.The analysis shows that the superior electrochemical performance of the BNC–OA is attributed to the pseudocapacitance behavior of surface heteroatom functional groups and an abundant pore-structure. Boron, nitrogen co-doped porous carbon is a promising electrode material for supercapacitors.     

Unsteady MHD flow and heat transfer near stagnation point over a stretching/shrinking sheet in porous medium filled with a nanofluid

In this article, the unsteady magnetohydrodynamic （MHD） stagnation point flow and heat transfer of a nanofluid over a stretching/shrinking sheet is investigated numerically. The similarity solution is used to reduce the governing system of partial differential equations to a set of nonlinear ordinary differential equations which are then solved numerically using the fourth-order Runge-Kutta method with shooting technique. The ambient fluid velocity, stretching/shrinking velocity of sheet, and the wall temperature are assumed to vary linearly with the distance from the stagnation point. To investigate the influence of various pertinent parameters, graphical results for the local Nusselt number, the skin friction coefficient, velocity profile, and temperature profile are presented for different values of the governing parameters for three types of nanoparticles, namely copper, alumina, and titania in the water-based fluid. It is found that the dual solution exists for the decelerating flow. Numerical results show that the extent of the dual solution domain increases with the increases of velocity ratio, magnetic parameter, and permeability parameter whereas it remains constant as the value of solid volume fraction of nanoparticles changes. Also, it is found that permeability parameter has a greater effect on the flow and heat transfer of a nanofluid than the magnetic parameter.     

Identification of pore size in porous SiO2 thin film by positron annihilation

Positron annihilation lifetime and Doppler broadening of annihilation line techniques have been used to obtain information about the small pore structure and size of porous SiO2 thin film produced by sputtered Al-Si thin film and etched Al-Si thin film. The film is prepared by an Al/Si 75：25 at.-% （A175Si25） target with the radiofrequency （RF） power of 66 W at room temperature. A 5 wt.-% phosphoric acid solution is used to etch the Al cylinders. All the A1 cylinders dissolved in the solution after 15 h at room temperature, and the sample is subsequently rinsed in pure water. In this way, the porous SiO2 on the Si substrate is produced. From our results, the values of all lifetime components in the spectra of Al-Si thin film are less than 1 ns, but the value of one of the lifetime components in the spectra of porous SiO2 thin film is τ = 7.80 ns. With these values of lifetime, RTE （Rectangular Pore Extension） model has been used to analyze the pore size.     

A Micro-Mechanism Model for Porous Media

Based on the tortuous-expanding path/channel model, a micro-mechanism model for porous media is de- veloped. The proposed model is expressed as a function of tortuosity, porosity, resistance coefficient, and fluid properties. Every parameter in the proposed model has clear physical meaning. The results show that the model predictions are in good agreement with those from the existing experimental data.     

Second-order two-scale computations for conductive radiative heat transfer problem in periodic porous materials

In this paper, a kind of second-order two-scale （SOTS） computation is developed for conductive-radiative heat trans- fer problem in periodic porous materials. First of all, by the asymptotic expansion of the temperature field, the cell problem, homogenization problem, and second-order correctors are obtained successively. Then, the corresponding finite element al- gorithms are proposed. Finally, some numerical results are presented and compared with theoretical results. The numerical results of the proposed algorithm conform with those of the FE algorithm well, demonstrating the accuracy of the present method and its potential applications in thermal engineering of porous materials.     

Critical Behaviors in a Stochastic Local Limited One-Dimensional Rice-Pile Model

A stochastic local limited one-dimensional rice-pile model is numerically investigated. The distributions for avalanche sizes have a clear power-law behavior and it displays a simple finite size scaling. We obtain the avalanche exponents Ts= 1.54±0.10,βs = 2.17±0.10 and TT = 1.80±0.10, βT =1.46 ± 0.10. This self-organized critical model belongs to the same universality class with the Oslo rice-pile model studied by K. Christensen et al. [Phys. Rev. Lett. 77 （1996） 107], a rice-pile model studied by L.A.N. Amaral et al. [Phys. Rev. E 54 （1996） 4512], and a simple deterministic self-organized critical model studied by M.S. Vieira [Phys. Rev. E 61 （2000） 6056].     

Characteristic parameters from a human of electromagnetic signals heart system

The electromagnetic field of a human heart system is a bioelectromagnetic field. Electrocardiography （ECG） and magnetocardiography （MCG） are both carriers of electromagnetic information about the cardiac system, and they are nonstationary signals. In this study, ECG and MCG data from healthy subjects are acquired; the MCG data are captured using a high-Tc radio frequency superconducting quantum interference device （HTc rf SQUIDs） and the QRS complexes in these data are analysed by the evolutionary spectrum analysis method. The results show that the quality factor Q and the central frequency fz of the QRS complex evolutionary spectrum are the characteristic parameters （CHPs） of ECG and MCG in the time-frequency domain. The confidence intervals of the mean values of the CHPs are estimated by the Student t distribution method in mathematical statistics. We believe that there are threshold ranges of the mean values of Q and fz for healthy subjects. We have postulated the following criterion： if the mean values of CHPs are in the proper ranges, the cardiac system is in a normal condition and it possesses the capability of homeostasis. In contrast, if the mean values of the CHPs do not lie in the proper ranges, the homeostasis of the cardiac system is lacking and some cardiac disease may follow. The results and procedure of MCG CHPs in the study afford a technological route for the application of HTc rf SQUIDs in cardiology.