Buoyancy Effects on Upward Brine Displacement Caused by CO2 Injection

Upward displacement of brine from deep reservoirs driven by pressure increases resulting from CO₂ injection for geologic carbon sequestration may occur through improperly sealed abandoned wells, through permeable faults, or through permeable channels between pinch-outs of shale formations. The concern about upward brine flow is that, upon intrusion into aquifers containing groundwater resources, the brine may degrade groundwater. Because both salinity and temperature increase with depth in sedimentary basins, upward displacement of brine involves lifting fluid that is saline but also warm into shallower regions that contain fresher, cooler water. We have carried out dynamic simulations using TOUGH2/EOS7 of upward displacement of warm, salty water into cooler, fresher aquifers in a highly idealized two-dimensional model consisting of a vertical conduit (representing a well or permeable fault) connecting a deep and a shallow reservoir. Our simulations show that for small pressure increases and/or high-salinity-gradient cases, brine is pushed up the conduit to a new static steady-state equilibrium. On the other hand, if the pressure rise is large enough that brine is pushed up the conduit and into the overlying upper aquifer, flow may be sustained if the dense brine is allowed to spread laterally. In this scenario, dense brine only contacts the lower-most region of the upper aquifer. In a hypothetical case in which strong cooling of the dense brine occurs in the upper reservoir, the brine becomes sufficiently dense that it flows back down into the deeper reservoir from where it came. The brine then heats again in the lower aquifer and moves back up the conduit to repeat the cycle. Parameter studies delineate steady-state (static) and oscillatory solutions and reveal the character and period of oscillatory solutions. Such oscillatory solutions are mostly a curiosity rather than an expected natural phenomenon because in nature the geothermal gradient prevents the cooling in the upper aquifer that occurs in the model. The expected effect of upward brine displacement is either establishment of a new hydrostatic equilibrium or sustained upward flux into the bottom-most region of the upper aquifer.     

Adhesive Frictionless Contact Between an Elastic Isotropic Half-Space and a Rigid Axi-Symmetric Punch

In this paper we consider the problem of adhesive frictionless contact of an elastic half-space by an axi-symmetric punch. We obtain integral equations that define the tractions and displacements normal to the surface of the half-space, as well as the size of the contact regions, for the cases of circular and annular contact regions. The novelty of our approach resides in the use of Betti’s reciprocity theorem to impose equilibrium, and of Abel transforms to either solve or substantially simplify the resulting integral equations. Additionally, the radii that define the annular or circular contact region are defined as local minimizers of the function obtained by evaluating the potential energy at the equilibrium solutions for each pair of radii. With this approach, we rather easily recover Sneddon’s formulas (Sneddon, Int. J. Eng. Sci., 3(1):47–57, 1965) for circular contact regions. For the annular contact region, we obtain a new integral equation that defines the inverse Abel transform of the surface normal displacement. We solve this equation numerically for two particular punches: a flat annular punch, and a concave punch.     

Thermal contact stresses of bi-metal strip thermostat

The distribution of shearing and normal stresses on the contact surface of the two strips composing a thermostat is found in closed form. They are of local type and concentrated near the ends of the strip along a length almost equal to the thickness of the strip.     

Electro-mechanical frictionless contact behavior of a functionally graded piezoelectric layered half-plane under a rigid punch

The frictionless contact problem of a functionally graded piezoelectric layered half-plane in-plane strain state under the action of a rigid flat or cylindrical punch is investigated in this paper. It is assumed that the punch is a perfect electrical conductor with a constant potential. The electro-elastic properties of the functionally graded piezoelectric materials (FGPMs) vary exponentially along the thickness direction. The problem is reduced to a pair of coupled Cauchy singular integral equations by using the Fourier integral transform technique and then is numerically solved to determine the contact pressure, surface electric charge distribution, normal stress and electric displacement fields. For a flat punch, the normal stress intensity factor and electric displacement intensity factor are also given to quantitatively characterize the singularity behavior at the punch ends. Numerical results show that both material property gradient of the FGPM layer and punch geometry have a significant influence on the contact performance of the FGPM layered half-plane.     

INTERLAMINAR STRESSES OF A LAMINATED COMPOSITE BAR UNDER BENDING(Ⅰ)

A laminated composite bar of rectangular cross section consists of(?) portion ofone material and upper and lower iden(?) cover plates of another(?)Compressiveand tensile forces each equal to P are (?)(?)at the ends of the upper andlower cover plates Fig (?)They form (?)(?)ends of the bar.Our (?)is to find theinterlaminar stresses or how the forces are (?) through the (?)(?)faces.     

Frictionless indentation by an elastic punch: a dynamic Hertzian contact problem

Frictionless indentation of an elastic half-plane by a relatively blunt, symmetric elastic punch at an ar: bitrary speed is analyzed by treating the more general problem of frictionless Hertzian contact between elastic solids. As in the quasi-static problem, the analysis assumes that the solid surface contours are approximately flat. In addition, the contact strip expands at a constant rate and the imposed rigid body motions and surface contours are represented by polynomial curves. Homogeneous function techniques allow analytic solutions to the basic mathematical problem. As an example, the general results are then applied to the uniformly accelerating parabolic punch on a half-plane.     

Adhesion and friction of an elastic half-space in contact with a slightly wavy rigid surface

The paper deals with the estimation of the pressure distribution, the shape of contact and the friction force at the interface of a flat soft elastic solid moving on a rigid half-space with a slightly wavy surface. In this case an unsymmetrical contact is considered and justified with the adhesion hysteresis. For soft solids as rubber and polymers the friction originates mainly from two different contributions: the internal friction due to the viscoelastic properties of the bulk and the adhesive processes at the interface of the two solids. In the paper the authors focus on the latter contribution to friction. It is known, indeed, that for soft solids, as rubber, the adhesion hysteresis is, at least qualitatively, related to friction: the larger the adhesion hysteresis the larger the friction. Several mechanisms may govern the adhesion hysteresis, such as the interdigitation process between the polymer chains, the local small-scale viscoelasticity or the local elastic instabilities. In the paper the authors propose a model to link, from the continuum mechanics point of view, the friction to the adhesion hysteresis. A simple one-length scale roughness model is considered having a sinusoidal profile. For partial contact conditions the detached zone is taken to be a mode I propagating crack. Due to the adhesion hysteresis, the crack is affected by two different values of the strain energy release rate at the advancing and receding edges respectively. As a result, an unsymmetrical contact and a friction force arise. Additionally, the stability of the equilibrium configurations is discussed and the adherence force for jumping out of contact and the critical load for snapping into full contact are estimated.     

Interaction of two spark-generated bubbles near a confined free surface

In this paper, the oscillation of two spark-generated bubbles placed on a vertical column in close proximity to a confined free surface is considered. The confined free surface is accorded by the top opening of different configurations. These configurations include (i) a centrally perforated horizontal flat plate (\({\theta=90^{\circ})}\), (ii) vertically placed cylinder (\({\theta=0^{\circ})}\) and (iii) nozzle (\({\theta >0^{\circ})}\). The main objective of the present work is to study the effects of key parameters such as the nozzle geometry, the locations of the energy input (i.e., initial position of the bubbles with respect to each other and relative to the free surface) on the dynamics of the two bubbles and the free surface. It was found that the lifetime of the upper bubble decreases from the vertical cylinder to the flat plate case. In addition, by reducing the inter-bubble distance, the lifetime of the upper bubble becomes longer and the repulsion between two bubbles during the expansion phase is stronger. Finally, by reducing the upper bubble-free surface distance, the repulsion between two bubbles during expansion phase increases, the tendency of the upper bubble to rebound and initiate another oscillation cycle decreases, and the amplitude of elevation of the free surface increases.     

Phase-field modeling of interfacial dynamics in emulsion flows: Nonequilibrium surface tension

A weakly nonlocal phase-field model is used to define the surface tension in liquid binary mixtures in terms of the composition gradient in the interfacial region so that, at equilibrium, it depends linearly on the characteristic length that defines the interfacial width. Contrary to previous works suggesting that the surface tension in a phase-field model is fixed, we define the surface tension for a curved interface and far-from-equilibrium conditions as the integral of the free energy excess (i.e., above the thermodynamic component of the free energy) across the interface profile in a direction parallel to the composition gradient. Consequently, the nonequilibrium surface tension can be widely different from its equilibrium value under dynamic conditions, while it reduces to its thermodynamic value for a flat interface at local equilibrium. In nonequilibrium conditions, the surface tension changes with time: during mixing, it decreases as the inverse square root of time, while in the linear regime of spinodal decomposition, it increases exponentially to its equilibrium value, as nonlinear effects saturate the exponential growth. In addition, since temperature gradients modify the steepness of the concentration profile in the interfacial region, they induce gradients in the nonequilibrium surface tension, leading to the Marangoni thermocapillary migration of an isolated drop. Similarly, Marangoni stresses are induced in a composition gradient, leading to diffusiophoresis. We also review results on the nonequilibrium surface tension for a wall-bound pendant drop near detachment, which help to explain a discrepancy between our numerically determined static contact angle dependence of the critical Bond number and its sharp-interface counterpart from a static stability analysis of equilibrium shapes after numerical integration of the Young-Laplace equation. Finally, we present new results from phase-field simulations of the motion of an isolated droplet down an incline in gravity, showing that dynamic contact angle hysteresis can be explained in terms of the nonequilibrium surface tension.     

Mathematical model of inchworm locomotion

Inchworms are caterpillars. Their locomotion, involving arching of much of the central portion of their body length, has not been studied as extensively as the peristaltic locomotion of worms or the crawling locomotion of many other caterpillars. A mathematical model is developed to describe the shapes and bending strains of typical inchworm motions. The inchworm is assumed to travel in a straight line on a rigid horizontal substrate. Two basic types of cycles are considered. In Case I, the inchworm body arches and then reverses that motion in becoming flat again. In Case II, the body arches, then cantilevers upward, and then falls down to a flat shape. A continuum model based on an elastica is adopted. The results may be useful in the development of soft robots exhibiting an inchworm mode of motion.     

Linear Elastic Solutions for Slotted Plates

Two-dimensional problems of finite-length blunted cracks cut into infinite plates subject to remote tractions are solved using complex variable theory. The slot geometry is composed of two flat surfaces connected by rounded ends. This special geometrical shape was derived by Riabouchinsky in the study of two-dimensional ideal fluid flow around parallel plates. The simpler antiplane slotted plate problem is addressed initially for this geometry. From this exact solution, the equivalent of a Westergaard stress potential is found and applied to the two other principal modes of fracture, which are plane elasticity problems. For a plate subject to uniform radial tension at infinity, an analytical solution is obtained that will reduce to the familiar mode I singular crack solution as the separation between the parallel faces of the slot becomes zero. For finite-width mode I slots, the rounded ends have tensile tractions which terminate at the adjoining flat surfaces of the slot, which remain traction-free. In this respect, the finite-width mode I slot problem resembles a Barenblatt cohesive zone model of a plane crack or a Dugdale plastic strip model of a plane crack, although the tractions will vary in magnitude along the slot ends rather than remaining uniform as in the former type of crack problems. Similarly, in the case of the finite-width mode II slot problem, the rounded ends of the slot have shear tractions, while the flat surfaces remain load-free. A distinguishing feature of the mode II slot solution over the mode I slot problem is that the maximum in-plane shear stress is constant along the rounded ends of the slot. Because of this, those particular regions of the boundary can represent incipient plastic yield based on either the Mises or Tresca yield condition under plane strain loading conditions. In this way, the problem resembles the plastic strip models of Dugdale, Cherepanov, Bilby-Cottrell-Swinden, and others. Notably, the mode III slot problem also has a constant maximum shear stress along the curved portions of the slot, while the entire slot boundary remains traction-free, unlike the mode II slot problem. Consequently, the mode III slot problem represents both a generalization of the standard mode III crack problem geometry, while simultaneously satisfying the boundary conditions of a plastic strip model.     

Mobility‐dependent bifurcations in capillarity‐driven two‐phase fluid systems by using a lattice Boltzmann phase‐field model

Bifurcations in capillarity‐driven two‐phase fluid systems, due to different mobilities in phase‐field models for such systems, are studied by using a lattice Boltzmann method (LBM). Specifically, two‐dimensional (2D) and three‐dimensional (3D) droplets on a flat wall with given wettability variations are investigated. It is found that the mobility controls the rate of diffusive relaxation of the phase field from non‐equilibrium toward equilibrium, and similar to previous findings on mechanically driven two‐phase systems, the mobility is closely related to the contact line velocity. For the cases investigated, different mobilities across a critical value result in fundamentally different system evolution routes and final stable equilibrium states. These results may provide some implications for phase‐field study of droplet manipulations by surface wettability adjustments in microfluidics. Copyright © 2008 John Wiley & Sons, Ltd.     

Flow patterns and interfacial velocities near a moving contact line

Experimental data on velocity fields and flow patterns near a moving contact line is shown to be at variance with existing hydrodynamic theories. The discrepancy points to a new hydrodynamic paradox and suggests that the hydrodynamic approach may be incomplete and further parameters or forces affecting the surfaces may have to be included. A contact line is the line of intersection of three phases: (1) a solid, (2) a liquid, and (3) a fluid (liquid or gas) phase. A moving contact line develops when the contact line moves along the solid surface. A flat plate moved up and down, inside and out of a liquid pool defines a simple, reliable experimental model to characterize dynamic contact lines. Highlighted are three important conclusions from the experimental results that should be prominent in the development of new theoretical models for this flow. First, the velocity along the streamline configuring the liquid–fluid interface is remarkably constant within a distance of a couple of millimeters from the contact line. Second, the relative velocity of the liquid–fluid interface, defined as the ratio of the velocity along the interface to the velocity of the solid surface, is independent of the solid surface velocity. Third, the relative interface velocity is a function of the dynamic contact angle.     

Deformation and the strip necking zone in a cracked steel sheet

When a tensile stress is applied to a thin cracked plate, a strip necking region results ahead of a crack tip. The relative opening displacement between the crack surfaces and between the upper and lower boundaries of the strip necking region were measured by the moiré method. The strains ahead of the strip necking region and the thickness reduction (therein) were also measured. The measured relative opening displacements were compared with the calculated values using the Dugdale strip necking model. The thickness reduction in the strip necking region is equal to the relative opening displacement.     

冷弯厚壁矩形型钢板材力学性能分析

为了对冷弯厚壁型钢管的生产工艺改进、产品性能分析、结构强度设计和数值模拟结果的验证提供依据,从母材性能分析入手,针对两批断面规格为200×300×9.2的冷弯厚壁矩形型钢管,对从辊式冷弯成型过程中长型材上截取的平板试件、弯角试件的力学性能进行了测试。在此基础上,结合冷弯生产工艺和母材性能,对平板、弯角试件力学性能随冷弯道次的变化规律作了较详细的讨论和分析,并将本文实测值与相关文献中厚壁型钢的冷作硬化效应作了对比。结果表明:型钢全截面上平板件的性能分布极不均匀,竖直配辊冷弯厚壁矩形钢管时,两竖直侧平板件强度低于母材;板材冷作硬化效应主要取决于母材的强度、伸长率和强屈比,其中强屈比对型钢的冷作硬化效应影响最大;为了改善冷弯型钢性能,还应保证热轧板带的质量。     

Unsteady shear flow of a viscoplastic material

A viscoplastic, or yield-stress, liquid occupies the space between two infinite parallel plates. Initially the whole system is at rest. The lower plate is suddenly jerked into motion with given speed or shear stress, while the upper plate is kept fixed. The flow consists of two regions; (1) a lower sheared region bounded above by the yield surface, (2) an upper unyielded region bounded below by the yield surface. The yield surface propagates to the upper plate as time proceeds. We first consider the equivalent one plate problem of flow over a jerked plate, and find similarity solutions and small time asymptotic solutions for prescribed shear and speed cases respectively. These solutions are used as initial solutions for the two plate case. The motion of the yield surface and the time taken for the entire material to yield are investigated. The problems considered here are two dimensional representations of some control devices, for example the light duty clutch, which consists of two corotating, coaxial discs separated by a layer of electrorheological material. In this application it is useful to know the time taken for all the material to yield.     

A receding contact plane problem between a functionally graded layer and a homogeneous substrate

In this paper, we consider the plane problem of a frictionless receding contact between an elastic functionally graded layer and a homogeneous half-space, when the two bodies are pressed together. The graded layer is modeled as a nonhomogeneous medium with an isotropic stress–strain law and over a certain segment of its top surface is subjected to normal tractions while the rest of this surface is free of tractions. Since the contact between the two bodies is assumed to be frictionless, then only compressive normal tractions can be transmitted in the contact area. Using integral transforms, the plane elasticity equations are converted analytically into a singular integral equation in which the unknowns are the contact pressure and the receding contact half-length. The global equilibrium condition of the layer is supplemented to solve the problem. The singular integral equation is solved numerically using Chebychev polynomials and an iterative scheme is employed to obtain the correct receding contact half-length that satisfies the global equilibrium condition. The main objective of the paper is to study the effect of the material nonhomogeneity parameter and the thickness of the graded layer on the contact pressure and on the length of the receding contact.     

Effects of the moving speed of a rigid stamp on contact behaviors of anisotropic materials based on real fundamental solutions

The paper studies contact problem of a rigid stamp moving at a constant speed over the surface of anisotropic materials. The solution method is based on Galilean transformation, Fourier transform and singular integral equation. The stated mixed boundary value problem is reduced to a Cauchy type singular integral equation based on real fundamental solutions, which is solved exactly in the case of a rigid flat or cylindrical stamp. Explicit expressions for various stresses are obtained in terms of elementary functions. In particular, explicit formula is derived to determine the unknown contact region for the cylindrical stamp. For a flat stamp, detailed calculations are provided to show the influences of dimensionless moving speed on the normal and in-plane stress. For a cylindrical stamp, the effects of dimensionless moving speed, the mechanical loading and the radius on the contact region, the normal and in-plane stress are analyzed in detail.     

Crack nucleation from a single notch caused by stress-dependent surface reactions

The surface of a solid under stress is unstable if there is mass exchange and transportation along the surface. A notch on the surface can be a preferred site for crack nucleation. This paper studies the evolution of a surface notch under stress dependant reaction. The surface is represented by a family of curves with many degrees of freedom, and the elastic field is solved using complex conformal mapping method. In the numerical simulations, the notch either deepens immediately and forms singular tip; or becomes perfectly flat after long time; or becomes blunter first, evolving slowly for a long time, then nucleates new surface instability and finally forms sharp tip; or becomes near flat first, then forms a bump on the surface. When the activation strain is small or the reaction is near equilibrium, the notch stability is mainly determined by the competition of strain energy and surface energy, and the sign of stress has little effect. When the surface reaction is away from equilibrium and activation strain is not small, stresses with different signs give totally different surface stability behaviors, depending on whether the solid is losing mass to or gaining mass from the environment.     

Stability of the equilibrium of a capillary fluid in a horizontal slit

The stability of axisymmetric shapes of equilibrium of a capillary fluid between two horizontal plates is investigated. It is shown that stability is lost with respect to axisymmetric perturbations. The boundaries of the stability region are calculated in the case when the wetting angles on the lower and upper plates are the same.