The Experimental Approach to Effective Stress Law of Coal Mass by Effect of Methane

Effective stress law of all kinds of coal samples, including steam coal, fat coal, corking coal, thin coal and anthracite, under pore pressure of gas, is experimentally studied using a newly developed test machine. These samples are taken from Coal Mines in Wuda, Hebi, Yanzhou, Yangquan, Qingshui, and Gujiao in China. The experiment results show that, under pore pressure of gas, the tested coal samples comply with Biot0/xxlarge8217.gif" alt="rsquo" align="BASELINE" BORDER="0">s effective stress law, 0/11242_2004_Article_5123348_TeX2GIFIE1.gif" alt=" $${\sigma '}_{ij} = {\sigma}_{ij} - {\alpha}p{\delta}_{ij}$$ " align="middle" border="0"> where the Biot0/xxlarge8217.gif" alt="rsquo" align="BASELINE" BORDER="0">s coefficient 0/xxlarge945.gif" alt="agr" align="BASELINE" BORDER="0"> is not a constant, and is bilinear function of volumetric stress (0/xxlarge920.gif" alt="THgr" align="BASELINE" BORDER="0">) and pore pressure (p), that is, 0/11242_2004_Article_5123348_TeX2GIFIE2.gif" alt=" $$\alpha = a_1 + a_2 \Theta + a_3 p + a_4 \Theta p$$ " align="middle" border="0"> We define four areas according to the numerical feature of 0/xxlarge945.gif" alt="agr" align="BASELINE" BORDER="0">, that is, functionless area of pore pressure, normal function area, fracturing function area, and quasi-soil function area. The effective stress law of coal mass introduced by this paper is a constitutive equation in the study of coupled solid and fluid. This has significance in the drainage and outburst of methane in coal seam.     

A lattice Boltzmann method for KDV equation

We prepose a 5-bit lattice Boltzmann model for KdV equation. Using Chapman-Enskog expansion and multiscale technique, we obtained high order moments of equilibrium distribution function, and the 3rd dispersion coefficient and 4th order viscosity. The parameters of this scheme can be determined by analysing the energy dissipation. The project supported by the Foundation of the Laboratory for Nonlinear Mechanics of Continuous Media, Institute of Mechanics, Chinese Academy of Sciences     

Some Results on Dynamics of Special Double-Loop ΣΔ-Modulators

The dynamic behaviour of a specific two-dimensional state space model with discontinuity is studied. This model arises from the study of double-loop 05q83w6tg0527/xxlarge931.gif" alt="Sgr" align="BASELINE" BORDER="0">05q83w6tg0527/xxlarge916.gif" alt="Delta" align="BASELINE" BORDER="0">-modulators with constant input. Using mathematical tools we explain certain simulation results, and some properties are derived. Simulations based on time-varying input are also provided.     

First- and second-order sensitivities of beams with respect to cross-sectional cracks

This paper deals with a variational formulation for the sensitivity problem of beam systems in the context of deformable solids with cracks. Natural frequencies are defined as state variables involved in the energy functional of the system, while the crack0j01n16/xxlarge8217.gif" alt="rsquo" align="BASELINE" BORDER="0">s length and position are treated as system parameters. The hierarchical equation system is formed and solved for the first and second derivatives of the natural frequency functions with respect to the crack0j01n16/xxlarge8217.gif" alt="rsquo" align="BASELINE" BORDER="0">s length and position. An analytical procedure for calculations of the second-order sensitivities of natural frequencies is proposed for the non-symmetrical equation system operator. Numerical algorithms are worked out and implemented computationally. Analytical and numerical aspects of the problem are discussed in detail through a number of illustrative results.The support of this work by the State Committee for Scientific Research (KBN) under Grant No. 4-050-0148/17-98-00 is gratefully acknowledged.     

A phenomenological model of electrorheological fluids

The fundamental assumption of the paper is that the extra stress tensor 0kprf62xtbvd/xxlarge964.gif" alt="tau" align="BASELINE" BORDER="0"> of an electrorheological fluid is an isotropic tensor valued function of the rate of strain tensor D and the vector n (which characterizes the orientation 0kprf62xtbvd/s00397-003-0320-0etIEq1.gif" alt="$${\mathbf{\hat{n}}}$$" align="middle" border="0"> and length N of the fibers formed by application of an electric field). The resulting constitutive equation for 0kprf62xtbvd/xxlarge964.gif" alt="tau" align="BASELINE" BORDER="0"> is supplemented by the solution of the previously studied time evolution equation for n. Plastic behavior for the shear and normal stresses is predicted. Anticipating that the action of increasing shear rate 0kprf62xtbvd/s00397-003-0320-0etIEq14.gif" alt="$$ \dot{\gamma } $$" align="middle" border="0"> is i) to orient the fibers more and more in the direction of flow and ii) simultaneously to break up the fibers leads to the conclusion that for 0kprf62xtbvd/s00397-003-0320-0etIEq15.gif" alt="$$ \dot{\gamma } \to \infty $$" align="middle" border="0"> the same behavior is encountered as without an electric field. Using realistically possible approximation formulas for the dependence of 0kprf62xtbvd/s00397-003-0320-0etIEq2.gif" alt="$${\mathbf{\hat{n}}}$$" align="middle" border="0"> and N on 0kprf62xtbvd/s00397-003-0320-0etIEq16.gif" alt="$$ \dot{\gamma } $$" align="middle" border="0"> leads to the Bingham behavior for 0kprf62xtbvd/s00397-003-0320-0etIEq17.gif" alt="$$ \dot{\gamma } \to 0 $$" align="middle" border="0"> and power law behavior for large shear rates.

Non-gaussian diffusion modeling in composite porous media by homogenization: Tail effect

In the paper anomalous diffusion appearing in a porous medium composed of two porous components of considerably different diffusion characteristics is examined. The differences in diffusivities are supposed to result either from two medium types being present or from variations in pore size (double porosity media). The 0">long-tail0"> effect is predicted using the homogenization approach based on the application of multiple scale asymptotic developments. It is shown that, if the ratio of effective diffusion coefficients of two porous media is of the order of magnitude smaller or equal O(0"> ²), where0"> is a homogenization parameter, then the macroscopic behaviour of the composite may be affected by the presence of 0">tail-effect0">. The results of the theoretical analysis were applied to a problem of diffusion in a bilaminate composite. Analytical calculations were performed to show the presence of the 0">long-tail0"> effect in two particular cases.Notations c _i the concentration of chemical species in water within the medium 0">i0"> - D _i the effective diffusion coefficient for the medium 0">i0"> - D _ij ^eff the macroscopic (or effective) diffusion tensor in the composite - ERV the elementary representative volume - h the thickness of the period - l a chracteristic length of the ERV or the periodic cell - L a characteristic macroscopic length - n the volumetric fraction of the material 2 - 1013;n the volumetric fraction of the material 1 - N the unit vector normal to 0"> - t the time variable - x the macroscopic (or slow) space variable - y the microscopic (or fast) space variable - c _1c ,C _2c ,D _1c ,D _2c the characteristic quantities - T,T _1L ,T _2L ,T _1l ,T _2l the characteristic times - c ₁ ^* ,c ₂ ^* ,D ₁ ^* ,D ₂ ^* ,t ^* the non-dimensional variables - 0"> the homogenization parameter - 0">₁ the domain occupied by the material 1 - 0">₂ the domain occupied by the material 2 - 0"> the interface between the domains 1 and 2 - 0">0">0"> the total volume of the periodic cell - 06.gif" alt="part" align="MIDDLE" BORDER="0">/06.gif" alt="part" align="MIDDLE" BORDER="0">x_i the gradient operator - 0"> the gradient operator     

Numerical Experiments in Scalar Diffusion under Stochastic Convection

We study scalar diffusion, both from Eulerian and Lagrangian perspectives, advected by two dimensional flows. Emphasis is devoted to the problem of scalar diffusion under a synthetic turbulent flow. We present numerical and analytical results for the turbulent diffusion coefficient either from the influence of the turbulent synthetic field and a periodic array of eddies. Preliminary results concerning Lagrangian dispersion are also reported.     

Mixing Layer on the Lee Side of an Obstacle

Two0330311p8/xxlarge8208.gif" alt="dash" align="MIDDLE" BORDER="0">layer miscible flow above an uneven bottom is considered. A mathematical model in the shallow0330311p8/xxlarge8208.gif" alt="dash" align="MIDDLE" BORDER="0">water approximation is constructed for the development of a turbulent layer between homogeneous layers of different density in a two0330311p8/xxlarge8208.gif" alt="dash" align="MIDDLE" BORDER="0">layer channel flow over a local obstacle. The influence of the mixing process on the formation of an initial segment of the steady0330311p8/xxlarge8208.gif" alt="dash" align="MIDDLE" BORDER="0">state density0330311p8/xxlarge8208.gif" alt="dash" align="MIDDLE" BORDER="0">stratified flow on the leeward side of the obstacle is studied.     

An experimental study on effects of solid concentration and ζ-potential on pseudoplastic flow of suspensions

The pseudoplastic flow of suspensions, alumina or styrene-acrylamide copolymer particles in water or an aqueous solution of glycerin has been studied by the step-shear-rate method. The relation between the shear rate,D, and the shear stress,0322415l257t05/xxlarge964.gif" alt="tau" align="BASELINE" BORDER="0">, in the step-shear-rate measurements, where the state of dispersion was considered to be constant, was expressed as0322415l257t05/xxlarge964.gif" alt="tau" align="BASELINE" BORDER="0"> = AD ^1/2 +CD. The effective solid volume fraction,ø _F, andA were dependent on the shear rate and expressed byø _F =aD ^b andA = 0322415l257t05/xxlarge945.gif" alt="agr" align="BASELINE" BORDER="0">D ^{0322415l257t05/xxlarge946.gif" alt="beta" align="MIDDLE" BORDER="0">}. Combining the above relations, the steady flow curve was expressed by0322415l257t05/xxlarge964.gif" alt="tau" align="BASELINE" BORDER="0"> = 0322415l257t05/xxlarge945.gif" alt="agr" align="BASELINE" BORDER="0">D ^{1/2 + 0322415l257t05/xxlarge946.gif" alt="beta" align="MIDDLE" BORDER="0">} +0322415l257t05/xxlarge951.gif" alt="eegr" align="MIDDLE" BORDER="0"> ₀ (1 013; a D ^b/0.74)^013;1.85 D, where0322415l257t05/xxlarge951.gif" alt="eegr" align="MIDDLE" BORDER="0"> ₀ is the viscosity of the medium.With an increase in solid volume fraction and a decreases in the absolute value of the0322415l257t05/xxlarge950.gif" alt="zeta" align="MIDDLE" BORDER="0">-potential, the flow behavior of the suspensions changed from Newtonian (0322415l257t05/xxlarge945.gif" alt="agr" align="BASELINE" BORDER="0"> = 0322415l257t05/xxlarge946.gif" alt="beta" align="MIDDLE" BORDER="0"> = b = 0), slightly pseudoplastic (0322415l257t05/xxlarge946.gif" alt="beta" align="MIDDLE" BORDER="0"> = b = 0), pseudoplastic (0322415l257t05/xxlarge946.gif" alt="beta" align="MIDDLE" BORDER="0"> = 0) to a Bingham-like behavior.The change in viscosity of the medium had an effect on the change in the effective volume fraction.