Mechanical Equilibrium Conditions Research Articles

Geomechanical risk assessment for CO2 storage in deep saline aquifers

We study CO2 injection into a saline aquifer intersected by a tectonic fault using a coupled modeling approach to evaluate potential geomechanical risks. The simulation approach integrates the reservoir and mechanical simulators through a data transfer algorithm. MUFITS simulates non-isothermal multiphase flow in the reservoir, while FLAC3D calculates its mechanical equilibrium state. We accurately describe the tectonic fault, which consists of damage and core zones, and derive novel analytical closure relations governing the permeability alteration in the fault zone. We estimate the permeability of the activated fracture network in the damage zone and calculate the permeability of the main crack in the fault core, which opens on asperities due to slip. The coupled model is applied to simulate CO2 injection into synthetic and realistic reservoirs. In the synthetic reservoir model, we examine the impact of formation depth and initial tectonic stresses on geomechanical risks. Pronounced tectonic stresses lead to inelastic deformations in the fault zone. Regardless of the magnitude of tectonic stress, slip along the fault plane occurs, and the main crack in the fault core opens on asperities, causing CO2 leakage out of the storage aquifer. In the realistic reservoir model, we demonstrate that sufficiently high bottomhole pressure induces plastic deformations in the near-wellbore zone, interpreted as rock fracturing, without slippage along the fault plane. We perform a sensitivity analysis of the coupled model, varying the mechanical and flow properties of the storage layers and fault zone to assess fault stability and associated geomechanical risks.

The influences of the mechanical equilibrium among interfacial tensions at triple junction on the morphological evolution of eutectic lamella

In this work, the influence of the mechanical equilibrium among interfacial tensions at three-phase triple junctions on the morphological evolution of growing eutectic lamella was quantitatively investigated through the phase-field simulations. We found that, when eutectic lamella grows at the steady-state, the orientations of the three interfacial tensions under mechanical equilibrium state are highly coincident with the tangent lines of the contour of the corresponding interfacial morphologies at the three phases’ triple junction. It is argued that the eutectic lamellar growth is unable to reach the steady state when the interfacial tensions fail to achieve mechanical equilibrium at the triple junctions. Moreover, a strong dependence of interfacial morphology on the state of the mechanical equilibrium between interfacial tensions is determined, and quantified through the change of lamella spacing and local curvature radius of lamella with the interfacial tensions. Furthermore, the underlying mechanism about the effects of mechanical equilibrium state on eutectic morphological evolution is also explained. We conclude that the final steady-state of eutectic growth is determined by the complex interplay among solute diffusion, eutectic morphology and the mechanical equilibrium of interfacial tensions.

Metastable and unstable hydrodynamics in multiphase lattice Boltzmann.

Metastability in liquids is at the foundation of complex phase transformation dynamics such as nucleation and cavitation. Intermolecular interaction details, beyond the equationof state, and thermal hydrodynamic fluctuations play a crucial role. However, most numerical approaches suffer from a slow time and space convergence, thus hindering the convergence to the hydrodynamic limit. This work shows that the Shan-Chen lattice Boltzmann model has the unique capability of simulating the hydrodynamics of the metastable state. The structure factor of density fluctuations is theoretically obtained and numerically verified to a high precision, for all simulated wave vectors, reduced temperatures, and pressures, deep into the metastable region. Such remarkable agreement between the theory and simulations leverages the exact implementation at the lattice level of the mechanical equilibrium condition. The static structure factor is found to consistently diverge as the temperature approaches the critical point or the density approaches the spinodal line at a subcritical temperature. Theoretically predicted critical exponents are observed in both cases. Finally, the phase separation in the unstable branch follows the same pattern, i.e., the generation of interfaces with different topology, as observed in molecular dynamics simulations.

Thermodynamic stability of the meniscus oil film between air/solid/water and its relevance to flotation

The behavior of oil is an important aspect in the area of mineral flotation or oil-water separation. This paper proposes a specific phenomenon that a meniscus oil film may form between the air bubble and the solid surface under water surroundings. A thermodynamic system containing an air bubble, an oil droplet, a solid matrix, and water surroundings was constructed. The mechanical equilibrium state of the oil meniscus film was solved. The free energy difference ∆B between the oil film-formed state and a reference state based on the Gibbs surface thermodynamic theory is applied to characterize the stability of the meniscus oil film. The impacts of the oil-gas volume ratio and the interfacial tensions are taken into consideration. The results show that the equilibrium morphologies of the system are directly correlated with the interfacial tensions. A minimal ∆Bmin can be found at a certain volume ratio and the case ∆B<0 generally exists. It indicates the formation of oil film leads the system to a lower energy state which is thermodynamically stable. The batch flotation using glass beads and n-alkane collectors was conducted. The flotation results show that the oil can improve the particle recovery and the results can be well interpreted by the mechanism correlated to meniscus oil film.

Free-surface proximity induced bistability and semi-semicoherency in precipitation systems

In systems without a ‘high misfit’ and in the early stage of growth, the precipitates tend to remain coherent with the parent matrix. On further growth beyond a critical size (r*), the precipitates undergo a coherent to semi-coherent transition by formation of interfacial misfit dislocation loops to minimize the total strain energy of the system. The variation of r* with domain size has been studied and the concept of re-entrant interface transition to the coherent state was demonstrated in finite crystals. Dislocations can exist in a state of mechanical equilibrium; but are thermodynamically metastable. In the proximity of ‘interfaces’ dislocations experience a configurational force. The current work pertains to study the stability of an interfacial misfit dislocation loop in the proximity of a free-surface; wherein we evaluate configurational effects in a semi-infinite body. The Cu-2 wt%γFe alloy is used as a model system in this study. In this work we: (i) demonstrate the stabilization of the coherent state (divergence of r*), induced by the proximity of the free-surface; (ii) discover the existence of bistability in materials at the microstructural scale, resulting from the destabilization of the equatorial position of the dislocation loop and arising from symmetry breaking in climb of the interfacial loop due to the vicinity of a free-surface. (iii) identify regimes of ‘equi-bistablity’ and regions with asymmetry in energy wells, (iv) establish the existence of a ‘semi’-semicoherent state. Here, one specific system has been chosen to illustrate the effects; however, we expect the conclusions to have a broader applicability.

Variational field theory of macroscopic forces in coulomb fluids.

Based on the variational field theory framework, we extend our previous mean-field formalism [Y. A. Budkov and A. L. Kolesnikov, JStatMech 2022, 053205.2022], taking into account the electrostatic correlations of the ions. We employ a general covariant approach and derive a total stress tensor that considers the electrostatic correlations of ions. This is accomplished through an additional term that depends on the autocorrelation function of the local electric field fluctuations. Utilizing the derived total stress tensor and applying the mechanical equilibrium condition, we establish a general expression for the disjoining pressure of the Coulomb fluids, confined in a pore with a slit-like geometry. Using this equation, we derive an asymptotic expression for the disjoining pressure in a slit-like pore with non-electrified conductive walls. Present theory is the basis for future modeling of the mechanical stresses that occur in electrode pores with conductive charged walls, immersed in liquid phase electrolytes beyond the mean-field theory.

An analytical solution for the load-settlement relation of hollow composite piles with ultra-large diameters

The load transfer mechanism is significantly more complex due to its heterogeneous radial distribution properties. To solve this problem, smart sensors and actuators are the good candidates for the improvement of structural reliability and robustness. This study investigates the load transfer characteristics of hollow composite piles with ultra-large diameters, and finds out the load transfer path. Based on the shear deformation transfer method and the assumptions of no relative slide between hollow pile, grouting body and cement mixing pile interface, a mechanical analysis model of hollow piles with ultra-large diameters-grouting body-cement mixing pile, is then developed. The basic equations of load-settlement relation of piles are deduced from the mechanical equilibrium conditions. Based on the hyperbolic model, the equivalent elastic modulus is introduced to improve the transfer function method. Afterwards, analytical solutions for the load-settlement relation of hollow composite piles with ultra-large diameters are presented. Finally, the analytical solution based on the two methods is compared with the finite element solution in order to verify their rationality and feasibility. The results indicate that under vertical load, the load transfer path to pile side (radial) is as follows: hollow pile → grouting body → cement mixing pile → foundation soil. Moreover, the transfer path of load to pile tip (vertical) is directly transferred to foundation soil, which is consistent with the traditional large-diameter solid pile. Compared with the shear deformation transfer method, the transfer function method can better simulate the nonlinear soil, which is more consistent with the finite element results.

Mechanical Equilibrium of a Nonmagnetic Body Immersed in a Cylindrical Container with a Magnetic Fluid Magnetized by an External Homogeneous Magnetic Field

Purpose. Analytical and numerical description of the magnetohydrodynamic forces acting on a small nonmagnetic spherical body in a cylindrical container with magnetic fluid (magnetofluid dispenser and separator approximation) that determine the hydrostatic mechanical equilibrium in the system.Methods. The numerical study solves the magnetostatic problem by the finite element method in the FEMM program package using the Lua script language. The system of Maxwell’s equations is solved by the standard method in the vector potential formulation. The analytical solution of the magnetostatic problem is obtained by the mirror image method using a simplifying model representation of the linear law of magnetization of a magnetic fluid. The ponderomotive force acting on a body immersed in a magnetic fluid is calculated using the Rosensweig formula and the energy approach.Results. A refined expression for the magnetic ponderomotive force acting on a nonmagnetic sphere immersed in a cylindrical container with magnetized magnetic fluid is obtained. Direct numerical simulation of the laboratory experiment is performed, which allows us to compare the accuracy of the numerical and analytical solutions with the experimental data. Despite violating the limits of applicability of the analytical theory, the new expression correctly describes the nonmonotone coordinate dependence of the force, and the error in determining the coordinate extremums does not exceed 6 % and 26 % in absolute value. The physical justification for the condition of mechanical equilibrium in the model system under study is given.Conclusion. The competition of two oppositely directed magnetic forces leads to the fact that a nonmagnetic sphere in a cylindrical container with magnetized magnetic fluid has one unstable mechanical equilibrium position in the center of the container, so that the body is pressed against the wall, or (additionally) two stable equilibrium positions that allow the body to levitate near the container wall without touching it.

Theory of electrolyte solutions in a slit charged pore: Effects of structural interactions and specific adsorption of ions.

In this paper, we present a continuation of our research on modeling electrolyte solutions within charged pores. We make use of the model developed by Blossey et al. [Phys. Rev. E 95, 060602 (2017)], which takes into account the structural interactions between ions through a bilinear form over the gradients of local ionic concentrations in the grand thermodynamic potential, as well as their steric interactions through the lattice gas model. The structural interactions may describe the effects of the molecular structure of ions at a phenomenological level. For example, these effects include steric effects due to non-spherical shapes of ions, their conformational lability, and solvent effects. In addition, we explore their specific interactions with the pore walls by incorporating external attractive potentials. Our primary focus is on observing the behavior of ionic concentration profiles and the disjoining pressure as the pore width changes. By starting with the local mechanical equilibrium condition, we derive a general expression for the disjoining pressure. Our findings indicate that considering the structural interactions of ions leads to a pronounced minimum on the disjoining pressure profiles at small pore widths. We attribute this minimum to the formation of electric double layers on the electrified surfaces of the pore. In addition, our results demonstrate that the inclusion of the attractive interactions of ions with the pore walls enhances this minimum and shifts it to smaller pore thicknesses. Our theoretical discoveries may be useful for those involved in supercapacitor electrochemical engineering, particularly when working with porous electrodes that have been infused with concentrated electrolyte solutions.

Analysis of the Conditions of Mechanical Equilibrium on the Curved Surface of a Vapor–Liquid System in a Gravitational Field

A thermodynamic analysis of mechanical equilibrium conditions is performed for the curved interface of a vapor–liquid system in the gravitational field potential with regard to ratios of experimental times of relaxation of thermodynamic parameters (momentum, energy, and mass). In a kinetic analysis of the relaxation stage of reaching the equilibrium state, it is revealed that it is important to consider the physical nature of the boundary of separating phases. The mechanical model of the boundary is one with an intermediate foreign film preventing the attainment of chemical equilibrium between the neighboring phases. The real boundary of coexisting phases has a variable density profile corresponding to the condition of the constant chemical potential throughout the region of transition and in the neighboring coexisting phases. The absence of an intermediate film excludes the priority of the mechanical equilibrium over the chemical equilibrium and results in pressure being the function of local temperature and chemical potential values (excluding the application of the Laplace equation). Considering times of relaxation is found to change the familiar Gibbs expression for the pressure jump between coexisting vapor and fluid as functions of the boundary in the gravitational field potential. A consequence of considering the correct ratio of momentum and mass times of relaxation is discussed: the phase equilibrium conditions of a separating vapor–liquid system in combined gravitational and surface force fields must be analyzed in order to solve problems of the capillary theory.

Analysis of the Conditions of Mechanical Equilibrium on the Curved Surface of a Vapor–Liquid System in a Gravitational Field

Analysis of the Conditions of Mechanical Equilibrium on the Curved Surface of a Vapor–Liquid System in a Gravitational Field

Formation and informative content of photoplethysmographic signal under the conditions of controllable external compression

The physical nature and quantitative characteristics of the photoplethysmographic (PPG) signal under conditions of external compression of the studied tissue area are theoretically investigated. Dependences of the constant and variable components of the PPG signal on the applied pressure are revealed, which have maxima at certain compression values. The physical model of the PPG signal formation process takes into account the optical and mechanical properties of biological tissues. The model is based on the consideration of the diffuse propagation of light in a two-component scattering medium (blood + surrounding tissues) and employs the Kubelka – Munk two-stream theory; in this case, the amount of blood in the tissues is determined by the conditions of mechanical equilibrium and the laws of tissue deformation.&#x0D; It is shown that the developed model correctly describes the observed qualitative features of the PPG signal, and the condition for the best agreement between theoretical and experimental curves allows real-time determination of the peripheral microcirculation quantitative characteristics (mean value and amplitude of the blood pressure fluctuations in precapillaries, erythrocyte concentration, average degree of blood oxygenation, the vessel walls elasticity, etc.). The developed methods for determining the blood circulation parameters can be used as the basis for inexpensive and effective express methods of research and medical diagnostics, which are especially useful in mass surveys or in environmental monitoring.

Controlling kinetics of self-propelled rod-like swimmers near multi sinusoidal substrate

Motility is defined as the movement of cells by some form of self-propulsion. Some organisms motile by using long flagella that quickly rotate to propel them over various surfaces (in swarming and swimming mechanism), while few motile without the aid of flagella (in twitching, sliding and gliding mechanism). Among these modes, gliding motility is adopted by a rod-shaped organism famously known as gliding bacteria. It is hypothesized that in such type of motility, organism motile under their own power by secreting a layer of slime on the substrate. In this study, an active wall is considered as a substrate and a two-dimensional wavy sheet as an organism. Slip effects are also employed in the current work. The physical properties of the slime are governed by a suitable constitutive equation of couple stress model. A sixth order BVP is obtained by utilizing lubrication assumption. For an appropriate fixed pair of flow rate and organism speed the BVP is solved by MATLAB built-in function bvp-5c. This solution is utilized in the mechanical equilibrium conditions which are obviously not satisfied yet. To satisfy these conditions, the pair of flow rate and gliding speed is refined by a root finding algorithm (modified Newton–Raphson method). By employing this numerical scheme, various figures are shown to demonstrate the effect of several associated parameters on organism speed, flow rate, energy expended by the glider, streamlines and longitudinal velocity. It is observed from the graphical results that organism speed and energy consumption is directly proportional to the couple stress parameter and slip effects.

Multiphysics-informed deep learning for swelling of pH/temperature sensitive cationic hydrogels and its inverse problem

This paper proposes a field theory of constrained swelling of pH/temperature sensitive cationic hydrogels in equilibrium with their chemical and mechanical environment. A general formulation is obtained based on a variational approach, yielding a set of governing equations coupling mechanical and chemical equilibrium conditions, which is employed to investigate some benchmark problems involving homogeneous and inhomogeneous swelling of the pH/temperature sensitive cationic hydrogels. The simulation results are compared with experimental data available in the literature to verify the present model. By encoding the underlying physical and chemical laws into the deep learning neural networks as prior information, we introduce the multiphysics-informed deep learning (MIDL) to investigate the effects of temperature and pH on the distributions of concentration of solvent and stresses in the hydrogel shell. In addition, the MIDL is extended to solve inverse identification problem of inhomogeneous swelling of core-shell hydrogels, which yields a reasonable identification accuracy even if the observed data is corrupted due to uncorrelated noise.

Nonlinear characteristics of semirigid and semiflexible segment joints of submerged floating tunnels under the combined axial force and bending moment

As an important part and a weak link in submerged floating tunnels (SFTs), segment joints are related to the safety of the overall structure. However, there is still a lack of research on joint structural designing and joint characteristics under complex external loads. In this paper, the semirigid and semiflexible SFT segment joint structure is proposed, and the stiffness mathematical model and numerical model of the joint structure are established based on the geometric deformation coordination, mechanical equilibrium conditions and the infinitesimal method. The above model was used to investigate the coupling effects of the axial force and bending moment on the axial displacement, rotation angle and stiffness of the joint, as well as the nonlinear characteristics of the SFT joint under the combined load of the axial force and bending moment. The results show that the nonlinear characteristics of the SFT joints are linked to the nonlinear properties of the materials at the joints as well as the multiple working states of the joints, as reflected in the characteristics of three loading modes and two transition points. Under the axial force-bending moment combined load, the axial force controls the working state and nonlinear characteristics of the joint, while the bending moment affects the working state and nonlinear characteristics of the joint on the basis of the axial force. The research results provide a theoretical basis and technical support for the study of the overall dynamic response of SFTs and the construction of the project.

A Study of Contact Detection between Noncircular Particles in Discrete Element Method

One of the key points of modeling noncircular particles in the discrete element method is the contact detection of particles. In this study, a general contact detection algorithm of two-dimensional particles with analytic shape functions is provided. The contact detection of particles with strictly convex shape function, such as ellipses and superellipses, is solved by Newton–Raphson method, and a grid method is provided to deal with heart-shaped particles. The grid method can be generalized into a particle system, in which the shape function is not convex. The accuracy and stability of the algorithm are verified by a series of tests. For the collision of a pair of ellipses with an aspect ratio of α = a / b = 1000, the efficiency is not worse than the Newton–Raphson method. For random packing under gravity, no residual kinetic energy is observed, and the force that acts on the bottom is equal to the gravity, that is, the system reaches a mechanical equilibrium state. After equilibrium, the process of hopper discharge is also simulated. The present method is suitable for arbitrarily shaped particles with analytic shape functions in two-dimensional cases. In addition to superellipses, the method can also be applied to other particle systems as long as the shape functions are given.

Effect of balance acupotomy combined with warm needling in treatment of cervical spondylosis of vertebral artery type

To observe the clinical efficacy of balance acupotomy combined with warm needling in treatment of cervical spondylopathy of vertebral artery type (CSA). Ninety patients were randomly divided into a warm needling group, a balance acupotomy group and a combined treatment group, 30 cases in each one. In the warm needling group, warm needling was given, once daily, for 5 days consecutively, with the interval of 2 days every week, and the treatment was conducted for 3 weeks. In the combined treatment group, on the base of the treatment as the warm needling group, the balance acupotomy was exerted, for consecutive 3 weeks. In the balance acupotomy group, the balance acupotomy was adopted, once a week, for 3 weeks consecutively. Clinical efficacy, the mean blood flow velocity of left vertebral artery (LVA), right vertebral artery (RVA) and basilar artery (BA), the pulse index (PI) and the resistance index (RI) were observed in 3 groups separately. The score of vertigo symptom and function was compared before and after treatment in 3 groups. In comparison with before treatment, the score of evaluation scale for cervical vertigo (ESCV) and the mean blood flow velocity of LVA, RVA and BA were all increased (P<0.05). while PI and RI reduced (P<0.05) in each group after treatment. In comparison with those in the warm needling group and the balance acupotomy group, ESCV score and the mean blood flow velocity of LVA, RVA and BA were increased (P<0.05), while PI and RI decreased (P<0.05) in the combined treatment group after treatment. Compared with the balance acupotomy group, the mean blood flow velocity of LVA, RVA and BA was increased (P<0.05), and PI and RI reduced (P<0.05) in the warm needling group after treatment. The total effective rate was 73.3% (22/30) in the warm needling group, 70.0% (21/30) in the balance acupotomy group and 93.3% (28/30) in the combined treatment group respectively. The total effective rate in the combined treatment group was higher than that either in the warm needling group or in the balance acupotomy group (P<0.05). Balance acupotomy combined with warm needling may restore the mechanical equilibrium state of the neck, and effectively improve the change of vertebral-basilar artery blood flow and relieve vertigo symptoms in patient with of cervical spondylosis of vertebral artery type.

Equivalent modeling for a finite element analysis of the mechanical properties of a bolted joint with a superelastic shape memory alloy

In this study, a beam element model with tension–compression asymmetry is constructed by using the improved Brinson model. A comparison between the calculated and experimental results verifies the computational effectiveness of the beam element. Then, a new mechanical property analysis model of a shape memory alloy (SMA) bolted joint based on the beam element model is proposed. Combined with a constructed convergence function, the mechanical equilibrium state of the SMA bolted joint under preload and external load is solved iteratively by the bisection method. Consequently, the stress–strain response curve of the SMA bolt rod and the root of the first thread, the deformation law of each thread and the separation conditions of the contact surface of members are analyzed by the proposed model. It is shown that the new proposed method can greatly improve the calculation efficiency with high calculation precision compared with the traditional calculation method.

Shear behaviour of reinforced straw-bale plaster sheathed cold-formed steel-framed shear walls

The introduction of cold-formed thin-walled steel (CFS) framed systems into straw-bale construction is a new development construction. A CFS stud frame without blocking or strap-brace provides little in-plane shear stiffness, however it can provide lateral support for the thin and low-reinforcement sheathing through self-tapping screw anchorage, allowing the sheathing to subject to shear failure rather than buckling failure. Straw-bales with different thicknesses can satisfy different requirements for heat transfer and sound insulation. Since straw-bales are reliably bonded to the sheathing, the straw-bales can provide lateral support for the thin sheathing and can also effectively slow down the decline of the shear strength after the sheathing cracks. Moreover, the anchorage slip and the shear deformation of the sheathing material are the major factors affecting shear stiffness. The theory presented in this paper predicts the shear deformation response of the reinforced straw-bale plaster sheathed CFS framed shear wall specimen. The behaviour of the self-tapping screw anchorage was defined using power curve to predict the wall deformation due to anchorage slip. The deformation caused by shear in the sheathing material was estimated using refined softened truss model, which was based on the mechanical equilibrium condition, strain compatibility condition, and the constitutive relationship of softened cement mortar and mesh wire embedded in cement mortar. Comparing the theoretical results with the experimental data, the two were in good agreement. The shear strength of different configurations of reinforced straw-bale walls described in the literature were estimated, which proved the applicability of the theory. • Introduction of cold-formed thin-walled steel (CFS) framed system into straw-bale construction. • Estimation of the two major factors affecting the wall shear stiffness. • Validation of the predicted results according to experimental data. • Prediction for the shear strength of reinforced plaster straw-bale walls with different configurations.

Shape multistability in flexible tubular crystals through interactions of mobile dislocations

We study avenues to shape multistability and shape morphing in flexible crystalline membranes of cylindrical topology, enabled by glide mobility of dislocations. Using computational modeling, we obtain states of mechanical equilibrium presenting a wide variety of tubular crystal deformation geometries, due to an interplay of effective defect interactions with out-of-tangent-plane deformations that reorient the tube axis. Importantly, this interplay often stabilizes defect configurations quite distinct from those predicted for a two-dimensional crystal confined to the surface of a rigid cylinder. We find that relative and absolute stability of competing states depend strongly on control parameters such as bending rigidity, applied stress, and spontaneous curvature. Using stable dislocation pair arrangements as building blocks, we demonstrate that targeted macroscopic three-dimensional conformations of thin crystalline tubes can be programmed by imposing certain sparse patterns of defects. Our findings reveal a broad design space for controllable and reconfigurable colloidal tube geometries, with potential relevance also to architected carbon nanotubes and microtubules.