Surface Stress Model Research Articles

Comparison of surface tension models for the simulation of two-phase flow in an ISPH-FVM coupling method

In the simulation of two-phase flow dominated by surface tension, accurate surface tension modeling is beneficial to better reproduce and understand the mechanism of interphase flow. In this paper, based on an ISPH-FVM coupling framework, three different surface tension models are implemented and tested respectively, including the generally used continuum surface force (CSF) model, the continuous surface stress (CSS) model and the height function (HF) model. In the present ISPH-FVM coupling framework, the ISPH particle approximate interpolation technique combined with a volume fraction correction scheme is employed to ensure the volume conservation in the computational domain during the information transfer between particles and grids. Meanwhile, the three surface tension models are discretized and calculated by the volume fraction defined on the FVM grid. The volume fraction of the FVM grid is obtained by approximate interpolation of ISPH particles within the grid support domain. Several benchmark cases are tested to verify the performance of three surface tension models in the ISPH-FVM coupling method. The results show that the CSF model and CSS model have less spurious currents and better robustness than HF model under the present coupling method. In addition, the CSF model and CSS model can simulate the flow regime involving complex interface topology changes more accurately than HF model.

A volume of fluid method for three dimensional direct numerical simulations of immiscible droplet collisions

This paper presents an advanced Volume of Fluid (VOF) method that enables performant three dimensional Direct Numerical Simulations (DNS) of the interaction of two immiscible fluids in a gaseous environment with large topology changes, e.g., binary droplet collisions. One of the challenges associated with the introduction of a third immiscible phase into the VOF method is the reconstruction of the phase boundaries near the triple line in arbitrary arrangements. For this purpose, an efficient method based on a Piecewise Linear Interface Calculation (PLIC) is shown. Moreover, the surface force modeling with the robust Continuous Surface Stress (CSS) model was enhanced to treat such three-phase situations with large topology changes and thin films. A consistent scaling of the fluid properties at the interfaces ensures energy conservation.The implementation of these methods in the multi-phase flow solver Free Surface 3D (FS3D) allowed a successful validation. A qualitative comparison of the morphology in binary collisions of immiscible droplets as well as a quantitative comparison regarding the threshold velocities that distinguish different collision regimes shows excellent agreement with experimental results.These simulations enable the evaluation of experimentally inaccessible data like the contributions of kinetic, surface and dissipative energy of both immiscible liquids during the collision process. Furthermore, the comparison against binary collisions of the same liquids highlights similarities and differences between immiscible and equal droplet collisions. Both can support the modeling of the immiscible liquid interaction in the future.

A partitioned continuous surface stress model for multiphase smoothed particle hydrodynamics

A density partitioned continuous surface-stress (CSS) model is presented within a multi-phase smoothed particle hydrodynamics (SPH) framework. We follow the original work of Adami et al. (2010) [1] to partition the surface-tension force from a zeroth-order consistent continuum surface-stress model. As a consequence of the scaled surface-tension force, both the surface-tension based artificial speed of sound and the numerical time step criteria can be relaxed for phase interfaces with high density ratio. A new color-gradient treatment and a static contact angle based surface-stress boundary condition is introduced to incorporate wetting behavior. All models are validated by comparison to analytical solutions of several surface-tension dominated flows. The resulting scheme is demonstrated to handle both capillary and Marangoni forces for high density and viscosity ratios.

Size-Dependent and Multi-Field Coupling Behavior of Layered Multiferroic Nanocomposites.

The prediction of magnetoelectric (ME) coupling in nano-scaled multiferroic composites is significant for nano-devices. In this paper, we propose a nonlinear multi-field coupling model for ME effect in layered multiferroic nanocomposites based on the surface stress model, strain gradient theory and nonlinear magneto-elastic-thermal coupling constitutive relation. With this novel model, the influence of external fields on strain gradient and flexoelectricity is discussed for the first time. Meanwhile, a comprehensive investigation on the influence of size-dependent parameters and multi-field conditions on ME performance is made. The numerical results show that ME coupling is remarkably size-dependent as the thickness of the composites reduces to nanoscale. Especially, the ME coefficient is enhanced by either surface effect or flexoelectricity. The strain gradient in composites at the nano-scale is significant and influenced by the external stimuli at different levels via the change in materials’ properties. More importantly, due to the nonlinear multi-field coupling behavior of ferromagnetic materials, appropriate compressive stress and temperature may improve the value of ME coefficient and reduce the required magnetic field. This paper provides a theoretical basis to analyze and evaluate multi-field coupling characteristics of nanostructure-based ME devices.

A quasistatic hysteresis model for magnetoelectric effect in multiferroic nanostructured films with surface effect

The investigation of hysteresis induced self-biased magnetoelectric (ME) coupling in multiferroic nanostructured films is significant for self-biased nano-devices. In this paper, we propose a quasistatic hysteresis model for ME effect in multiferroic nanostructured films based on surface stress model and multi-field coupled hysteretic constitutive model. For an asymmetric structure consisting of different magnetostrictive phases, the flexural strain is considered in the theoretical model. It is revealed that ME coupling in ME composites with nano-scale thickness is significantly size-dependent below critical size, which is enhanced by surface effect. Self-biased ME hysteretic behavior can be observed by considering the hysteretic effect of magnetostrictive materials, resulting in a large ME voltage coefficient in absence of bias magnetic field. The self-biased ME voltage coefficient is affected by pre-stress and thermal variation due to the complex magneto-elastic-thermal coupling characteristics of constituent materials. The proposed model provides a method to analyze and evaluate the nonlinear ME coupling characteristics of self-biased nano-devices operating under extreme stress or temperature conditions.

Dynamic behaviors of the coalescence between two droplets with different temperatures simulated by the VOF method

The photothermal effect of a laser can be advantageously used to manipulate the droplets coalescence, which usually encounters the coalescence between two droplets with different temperatures. In this study, the dynamic behavior of the coalescence between two droplets with different temperatures in oil is simulated using the volume of fluid (VOF) method. The continuum surface stress (CSS) model is used to describe the interfacial tension force. It is found that the temperature difference between two droplets can cause the self-propelled migration of the coalesced droplet as a consequence of the pressure difference and the induced thermocapillary flow. Particularly, in the cases of large temperature difference, low thermal conductivity and viscosity of the oil phase, the high-temperature region easily shift from one side to another side because of strong thermocapillary flow. Therefore, not only the migration velocity is increased but also the migration direction can change. These results will be helpful for the future operation encountered in the coalescence of two droplets with different temperatures towards the applications of the droplet-based microfluidics.

Modeling of nonlinear magnetoelectric coupling in layered magnetoelectric nanocomposites with surface effect

Multiferroic magnetoelectric (ME) composites are widely discussed for new kinds of smart structures. However, studies on nonlinear ME coupling in layered composites with nano-scale thickness which have unique superiorities are rather limited. It is well known that the physical and mechanical properties of nanostructures are size-dependent. Considering surface effect and nonlinear material characteristics, this work proposes a nonlinear theoretical model for ME nanocomposites with different magnetostrictive materials based on the surface stress model. The results show that surface effect can enhance the ME coupling in the composites with nano-scale thickness. The ME voltage coefficient can be suppressed due to the consideration of flexural strain and imperfect interfacial conditions. The weak-bonding interface makes the optimal volume fraction shift to PZT-rich composites. Moreover, when subjected to combined pre-stress and magnetic loadings, ME nanocomposites exhibit complex magneto-mechanical coupling characteristics. The proposed model provides a method to analyze and evaluate the nonlinear ME coupling characteristics of nanostructures-based devices.

Field-Dependent Resonant Behavior of Thin Nickel Film-Coated Microcantilever

Herein we describe the vibration of a thin nickel film-coated microcantilever at resonance under an external magnetic field. The resonance frequency and the mechanical loss—experimentally observed while varying the magnetic field—closely follow the field-dependence of the magnetostriction coefficient, indicating the strong coupling between the mechanical motion and the magnetostriction through the surface stress. Comparing to the surface stress model based on uniformly distributed axial load, the magnetostriction coefficient of a nickel film has been estimated, and its value is comparable to the reported one. Our study suggests that the nature of the surface stress originating from the magnetostrictive film can govern and modulate the resonant behavior of miniaturized mechanical systems.

Linear and nonlinear vibrations of fractional viscoelastic Timoshenko nanobeams considering surface energy effects

In this paper, the linear and nonlinear vibrations of fractional viscoelastic Timoshenko nanobeams are studied based on the Gurtin–Murdoch surface stress theory. Firstly, the constitutive equations of fractional viscoelasticity theory are considered, and based on the Gurtin–Murdoch model, stress components on the surface of the nanobeam are incorporated into the axial stress tensor. Afterward, using Hamilton's principle, equations governing the two-dimensional vibrations of fractional viscoelastic nanobeams are derived. Finally, two solution procedures are utilized to describe the time responses of nanobeams. In the first method, which is fully numerical, the generalized differential quadrature and finite difference methods are used to discretize the linear part of the governing equations in spatial and time domains. In the second method, which is semi-analytical, the Galerkin approach is first used to discretize nonlinear partial differential governing equations in the spatial domain, and the obtained set of fractional-order ordinary differential equations are then solved by the predictor–corrector method. The accuracy of the results for the linear and nonlinear vibrations of fractional viscoelastic nanobeams with different boundary conditions is shown. Also, by comparing obtained results for different values of some parameters such as viscoelasticity coefficient, order of fractional derivative and parameters of surface stress model, their effects on the frequency and damping of vibrations of the fractional viscoelastic nanobeams are investigated.

Numerical Simulation of Non-Newtonian Core Annular Flow through Rectangle Return Bends

The volume of fluid (VOF) model together with the continuum surface stress (CSS) model is proposed to simulate the core annular of non-Newtonian oil and water flow through the rectangle return bends (∏-bends). A comprehensive investigation is conducted to generate the profiles of volume fraction, pressure and velocity. The influences of oil properties, flow direction, and bend geometric parameters on hydrodynamic of nonNewtonian oil and water core annular flow in ∏-bends are discussed. Through computational simulations the proper bend geometric parameters were identified, these results are useful for designing and optimizing the pipefitting system.

The Mathematical Model Research on MIG Groove Welding Process

Through analysis the MIG groove welding process and the welding experimental result, a complete two-dimensional mathematical model of weld section molten pool characteristics was established. Use Gaussian heat source distribution to describe the weld heat source, introduced the welding speed to establish transient heat source model on the cross section. By introducing scalar of liquid fraction, mushy region dynamic character which was described using “Darcy” model proposed for porous media, and phase change which was taken into account using source-based method, establish a unified liquid and solid control equation, CFD model was established to simulate transient heat and mass transfer phenomena in welding process. The effect of surface tension was considered in the molten pool free surface stress model. The reliability of the model was verified by experiments. The effect of groove angle, groove depth and the welding speed on the molten pool were discussed in this paper.

Size-dependent free vibration analysis of nanoshells based on the surface stress elasticity

Based upon the Gurtin–Murdoch elasticity theory capturing the surface stress effect, a size-dependent continuum model is developed to investigate the free vibrations of nanoscale cylindrical shells. The equations of motion including the surface stress effect are derived based on the first-order shear deformation theory (FSDT) and using Hamilton's principle. A Galerkin-based closed-form solution technique together with modal beam functions is also utilized to solve the problem. Comprehensive results for the size-dependent vibration behavior of nanoshells under various boundary conditions are given. The results from the present analysis, where possible, are shown to be in very good agreement with the existing data from the literature. A comparison is also made between the predictions of surface stress model and those of its classical counterpart, and it is revealed that the surface stress has a significant influence on the resonant frequency of very thin nanoshells. Moreover, the effects of surface properties including surface elastic moduli, surface residual tension and surface mass density on the vibration characteristics of nanoshells are studied.

Verification of a multiscale surface stress model near voids in copper under the load induced by external high electric field

In the current study we use a model of surface stress for finite element method calculations to complement existing bulk stress models. The resulting combined model improves the accuracy of stress calculations near nanoscale imperfections in the material. We verify the results by simulating differently-shaped voids in single crystal copper both with FEM and with molecular dynamics, and compare the resulting stress distributions. The compared results agree well within small uncertainties, indicating that the implemented surface stress model is able to capture all the major features of the stress distributions in the material. Discrepancies occur near surfaces, where the crystal faces were not defined explicitly in the model. The fast and accurate FEM calculations can be used to estimate the stress concentration of specific extended defects, such as voids, while studying the dislocation-mediated mechanisms near these defects in the presence of external stresses by atomistic techniques.

Quantitative relationship between crystallite size and adhesion strength of the electroforming layer during microelectroforming process

Many micrometal devices are fabricated by microelectroforming technology in microelectromechanical systems. Micrometal devices usually suffer from poor interfacial adhesion strength, which restricts the application of microelectroforming technology. To solve this problem, in this reported work the influence of the electroforming crystallite size on practical adhesion energy is investigated. Furthermore, based on the energy balance criterion of fracture mechanics, the Miedema model of experimental electron theory (Miedema model) and the surface stress model, the equations between the crystallite size and the practical adhesion energy are established originally. Concerning the equations, the results show that the practical adhesion energy keeps an increasing trend and approaches basic adhesion energy as the crystallite size increases. To prove the equations, microelectroforming experiments were performed. The practical adhesion energy was measured by a scratch test. The crystallite size of the electroforming layer was tested by X-ray diffraction technology. The results of the experiments show that, within the range of the crystallite size, the practical adhesion energy keeps an increasing trend and approaches 15 J/m2. The theoretical and the experimental results show the same trend. The equations are verified by the experiments and this work may guide the microelectroforming process.

Nano piezoelectric/piezomagnetic energy harvester with surface effect based on thickness shear mode

BackgroundEnergy harvesters with piezoelectric materials are widely discussed for the new kinds of smart structures. However, reports on the energy harvesters at the nano scale which have large potential applications in the future are rather limited. MethodsIt’s well known that the surface or interface stress can affect the mechanical properties of nanostructures. This work proposes the nano energy harvester with piezoelectric/piezomagnetic structure, in which the thickness-shear mode is considered by the surface stress model. ResultsThe vibration motion and output power density are derived and calculated. The peak value of the power density can be enlarged by increasing the residual surface stress and the surface effect on the nano-plate energy harvester can be influenced by both the surface piezoelectric and piezomagnetic elastic constants. Moreover, the harvesting ability can be improved by increasing the thickness of the piezoelectric layer. ConclusionThe capability of the energy harvester depends on the residual surface stress and the surface material constants. The proposed model provides the possibility of applying nano composite structures to the energy harvester.

Size-dependent resonance and buckling behavior of nanoplates with high-order surface stress effects

This work presents a theoretical study of the resonance frequency and buckling load of nanoplates with high-order surface stress model. A classical thin plate theory based on Kirchhoff–Love assumption is implemented with surface effects. Circular and rectangular nanoplates with simply supported end conditions are exemplified. The size-dependent solutions are compared with the simplified solutions based on simple surface stress model, and also on the classical theory of elasticity. We aim to explore the scope of applicability so that the modified continuum mechanics model could serve as a refined approach in the prediction of mechanical behavior of nanoplates.

Transverse vibrations of embedded nanowires under axial compression with high-order surface stress effects

Implementing the high-order surface stress model into the Bernoulli–Euler beam theory, the transverse vibration of an axially compressed nanowire embedded in elastic medium is investigated. Closed-form expression is obtained for the natural frequency of a simply supported nanowire. The influences of compressive axial load, high-order surface stress and surrounding elastic medium on the natural frequency are discussed. Additionally, the analytical solution of axial buckling load for the simply supported nanowire is derived, which takes into account the effects of high-order surface stress and surrounding elastic medium. It is concluded from numerical results that the natural frequency of transverse vibration of the nanowire is dependent upon axial load, surrounding elastic medium, and high-order surface stress. Similarly, the dependences of the buckling load on surrounding elastic medium and high-order surface stress are significant.

Adding complex terrain and stable atmospheric condition capability to the OpenFOAM-based flow solver of the simulator for on/offshore wind farm applications (SOWFA)

The National Renewable Energy Laboratory's Simulator for On/Offshore Wind Farm Applications contains an OpenFOAM-based flow solver for performing large-eddy simulation of flow through wind plants. The solver computes the atmospheric boundary layer flow and models turbines with actuator lines. Until recently, the solver was limited to flows over flat terrain and could only use the standard Smagorinsky subgrid-scale model. In this work, we present our improvements to the flow solver that enable us to 1) use any OpenFOAM-standard subgrid-scale model and 2) simulate flow over complex terrain. We used the flow solver to compute a stably stratified atmospheric boundary layer using both the standard and the Lagrangian-averaged scale-independent dynamic Smagorinsky models. Surprisingly, the results using the standard Smagorinsky model compare well to other researchers' results of the same case, although it is often said that the standard Smagorinsky model is too dissipative for accurate stable stratification calculations. The scale-independent dynamic subgrid-scale model produced poor results, probably due to the spikes in model constant with values as high as 4.6. We applied a simple bounding of the model constant to remove these spikes, which caused the model to produce results much more in line with other researchers' results. We also computed flow over a simple hilly terrain and performed some basic qualitative analysis to verify the proper operation of the terrain-local surface stress model we employed.

Bending and resonance behavior of nanowires based on Timoshenko beam theory with high-order surface stress effects

A high-order surface stress model is incorporated in a continuum mechanics model based on Timoshenko beam theory to investigate the bending and resonance behavior of nanowires (NWs). Closed-form expressions are derived for the deflection curves and the rotation angle for bending of NWs with different boundary conditions. Normalized maximum deflection, effective size-dependent Young's moduli, and resonance frequency of NWs are also presented in analytic forms in terms of the diameter of the NWs and other material parameters. Our results are compared with the experimental data and with previous results based on classical models of Euler–Bernoulli beam theory with simple and refined surface stress model. We find that for NWs with relatively small cross-sectional size the effect of high-order surface stress is significant. While for NWs with relatively large cross-sections the Timoshenko beam model, accounting for the shearing deformation effect, is critical to attain a sufficient accuracy. This suggests that, for a continuum mechanics modeling of NWs valid for a wide range of slenderness ratio, the present continuum mechanics method, utilizing the Timoshenko beam model together with the high-order surface stress effects, could be a feasible tool to analyze the bending and resonance behavior for NWs.

Origin of surface stress on late transition metal surfaces:Ab initiolocal stress and tight-binding model

We present a stress model, ``the Friedel stress'' model, based on the second-moment tight-binding approach, as a quantitative model of in-plane surface stress on transition metal surfaces. By comparing the results obtained with the stress model and ab initio local stress calculation on fcc (111) surfaces, we demonstrate that the in-plane surface stress originates from a surface $d$-band width change due to the reduced coordination number. This indicates that surface stress can occur without the direct effects of charge redistribution, which is widely accepted as the origin of surface stress. The variation in in-plane stress induced by the strain parallel to the surface is also reproduced correctly by the Friedel stress, which further proves the dependence of surface stress on the surface $d$-band width. We demonstrate that surface stress has a strong correlation with the surface chemical reactivity mediated by the surface $d$-band behavior.