Tribological properties of magnetite nanoparticles with various morphologies as lubricating additives

The manipulation of matter at the nanoscale has unleashed a great potential for engineering biomedical drug carriers, but the transport of nanoparticles (NPs) under nanoscale confinement is still poorly understood. Using colloidal physics to describe NP interactions, we have computationally studied the passive transport of NPs using experimentally relevant conditions from bulk into a nanochannel of 60–90 nm height. NP size, channel height, and the Debye length are comparable so that changes in nanoscale dimensions may induce substantial changes in NP transport kinetics. We show that subtle changes in nanochannel dimensions may alter the energy barrier by about six orders of magnitude resulting in different NP penetration depths and diffusion mechanisms: ballistic, first-order and quasi zero-order transport regimes. The analysis of NP diffusion by continuum methods reveals that apparent diffusivity is reduced by decreasing channel size. The continuum finite element (FE) numerical method reproduced the colloidal model results only when surface interactions were accounted for. These results give a new insight into NP passive transport at the boundaries of nanoconfined domains, and have implications on the design of nanoscale fluidics and NP systems for biomedical and engineering applications.     

Numerical simulation of continuum models for fluid-fluid interface dynamics

This paper is concerned with numerical methods for two-phase incompressible flows assuming a sharp interface model for interfacial stresses. Standard continuum models for the fluid dynamics in the bulk phases, for mass transport of a solute between the phases and for surfactant transport on the interface are given. We review some recently developed finite element methods for the appropriate discretization of such models, e.?g., a pressure extended finite element (XFE) space which is suitable to represent the pressure jump, a space-time extended finite element discretization for the mass transport equation of a solute and a surface finite element method (SurFEM) for surfactant transport. Numerical experiments based on level set interface capturing and adaptive multilevel finite element discretization are presented for rising droplets with a clean interface model and a spherical droplet in a Poisseuille flow with a Boussinesq-Scriven interface model.     

A general finite element model for numerical simulation of structure dynamics

A finite element model used to simulate the dynamics with continuum and discontinuum is presented. This new approach is conducted by constructing the general contact model. The conventional discrete element is treated as a standard finite element with one node in this new method. The one-node element has the same features as other finite elements, such as element stress and strain. Thus, a general finite element model that is consistent with the existed finite element model is set up. This new model is simple in mathematical concept and is straightforward to be combined into the existing standard finite element code. Numerical example demonstrates that this new approach is more effective to perform the dynamic process analysis in which the interactions among a large number of discrete bodies and continuum objects are included.     

Quasibound states in semiconductor quantum well structures

We present a study on quasibound states in multiple quantum well structures using a finite element model (FEM). The FEM is implemented for solving the effective mass Schrödinger equation in arbitrary layered semiconductor nanostructures with an arbitrary applied potential. The model also includes nonparabolicity effects by using an energy dependent effective mass, where the resulting nonlinear eigenvalue problem was solved using an iterative approach. We focus on quasibound/continuum states above the barrier potential and show that such states can be determined using cyclic boundary conditions. This new method enables the determination of both bound and quasibound states simultaneously, making it more efficient than other methods where different boundary conditions have to be used in extracting the relevant states. Furthermore, the new method lifted the problem of quasibound state divergence commonly seen with many other methods of calculation. Hence enabling accurate determination of dipole matrix elements involving both bound and quasibound states. Such calculations are vital in the design of intersubband optoelectronic devices and reveal the interesting properties of quasibound states above the potential barriers.     

An implicit immersed boundary method for three-dimensional fluid–membrane interactions

We present an implicit immersed boundary method for the incompressible Navier–Stokes equations capable of handling three-dimensional membrane–fluid flow interactions. The goal of our approach is to greatly improve the time step by using the Jacobian-free Newton–Krylov method (JFNK) to advance the location of the elastic membrane implicitly. The most attractive feature of this Jacobian-free approach is Newton-like nonlinear convergence without the cost of forming and storing the true Jacobian. The Generalized Minimal Residual method (GMRES), which is a widely used Krylov-subspace iterative method, is used to update the search direction required for each Newton iteration. Each GMRES iteration only requires the action of the Jacobian in the form of matrix–vector products and therefore avoids the need of forming and storing the Jacobian matrix explicitly. Once the location of the boundary is obtained, the elastic forces acting at the discrete nodes of the membrane are computed using a finite element model. We then use the immersed boundary method to calculate the hydrodynamic effects and fluid–structure interaction effects such as membrane deformation. The present scheme has been validated by several examples including an oscillatory membrane initially placed in a still fluid, capsule membranes in shear flows and large deformation of red blood cells subjected to stretching force.     

An evaluation of solution algorithms and numerical approximation methods for modeling an ion exchange process

The focus of this work is on the modeling of an ion exchange process that occurs in drinking water treatment applications. The model formulation consists of a two-scale model in which a set of microscale diffusion equations representing ion exchange resin particles that vary in size and age are coupled through a boundary condition with a macroscopic ordinary differential equation (ODE), which represents the concentration of a species in a well-mixed reactor. We introduce a new age-averaged model (AAM) that averages all ion exchange particle ages for a given size particle to avoid the expensive Monte-Carlo simulation associated with previous modeling applications. We discuss two different numerical schemes to approximate both the original Monte-Carlo algorithm and the new AAM for this two-scale problem. The first scheme is based on the finite element formulation in space coupled with an existing backward difference formula-based ODE solver in time. The second scheme uses an integral equation based Krylov deferred correction (KDC) method and a fast elliptic solver (FES) for the resulting elliptic equations. Numerical results are presented to validate the new AAM algorithm, which is also shown to be more computationally efficient than the original Monte-Carlo algorithm. We also demonstrate that the higher order KDC scheme is more efficient than the traditional finite element solution approach and this advantage becomes increasingly important as the desired accuracy of the solution increases. We also discuss issues of smoothness, which affect the efficiency of the KDC–FES approach, and outline additional algorithmic changes that would further improve the efficiency of these developing methods for a wide range of applications.     

Stress influence on high temperature oxide scale growth: Modeling and investigation on a thermal barrier coating system

In thermal barrier coating (TBC) systems, an oxide layer develops at high temperature below the ceramic coating, leading in the long term to the mechanical failure of the structure upon cooling. The mechanism of stress-affected oxidation likely to induce the growth of a non-uniform oxide scale detrimental to the TBC lifetime was investigated. A continuum thermodynamics formulation is derived accounting for the influence of the stress and strain situation at the sharp metal/oxide phase boundary on the local oxidation kinetics. It specially includes the contributions of the large volumetric strain and the mass consumption associated with metal oxidation. A continuum mechanics/mass diffusion framework is used along with the developed formulation for the interface evolution to study the growth of an oxide layer coupled with local stress development. The implementation of the model has required the development of a specific simulation tool, based on a finite element method completed with an external routine for the phase boundary propagation. Results on an electron-beam physical vapor deposited (EB-PVD) TBC case are presented. The processes resulting in a non-uniform oxide scale growth are analyzed and the main influences are discussed.     

Stabilization of the Eulerian model for incompressible multiphase flow by artificial diffusion

The commonly used Eulerian or continuum model for incompressible multiphase flow is known to be unstable to perturbations for all wavenumbers, even if viscosity terms are used in the momentum equations. In the present work the model is stabilized by adding explicit artificial diffusion to the mass equations. The artificial diffusion terms lead to improved stability properties: uniform flow becomes linearly stable for large wavenumbers, and above an analytically derived threshold for the artificial diffusivity, stability for all wavenumbers is achieved. The artificial diffusivity reappears in the momentum equations, in such a way that fundamental properties of the standard equations remain valid: Galilean invariance is maintained, total mass and momentum are conserved, decay of total kinetic energy is ensured in the absence of external forces, and a flow initially at rest at hydrostatic pressure remains unchanged, even if the spatial distribution of volume fractions is nonuniform. A staggered finite volume pressure correction method using central differencing (leading to energy conserving discretization of convective and pressure terms) is presented. Application of the method to one-dimensional two-phase flow of falling particles particles confirms that the equations are stable with and unstable without artificial diffusion in the volume fraction equation.     

SAMR网格上扩散方程有限体格式的逼近性与两层网格算法

针对结构自适应加密网格(SAMR)上扩散方程的求解,分析几种有限体格式的逼近性,同时设计和分析一种两层网格算法.首先,讨论一种常见的守恒型有限体格式,并给出网格加密区域和细化/粗化插值算子的条件;接着,通过在粗细界面附近引入辅助三角形单元,消除粗细界面处的非协调单元,设计了一种保对称有限体元(SFVE)格式,分析表明,该格式具有更好的逼近性,且对网格加密区域和插值算子的限制更弱;最后,为SFVE格式构造一种两层网格(TL)算法,理论分析和数值实验表明该算法的一致收敛性.     

An hybrid finite volume–finite element method for variable density incompressible flows

This paper is devoted to the numerical simulation of variable density incompressible flows, modeled by the Navier–Stokes system. We introduce an hybrid scheme which combines a finite volume approach for treating the mass conservation equation and a finite element method to deal with the momentum equation and the divergence free constraint. The breakthrough relies on the definition of a suitable footbridge between the two methods, through the design of compatibility condition. In turn, the method is very flexible and allows to deal with unstructured meshes. Several numerical tests are performed to show the scheme capabilities. In particular, the viscous Rayleigh–Taylor instability evolution is carefully investigated.     

量子化学中有限元法的并行计算

在有限元方法的框架下,将量子化学中的基组展开方法和普通有限元方法结合起来,提出了一个新方案。在曙光1000并行机上,采用新方案,计算了Li₂、LiH、BH分子的基态总能量。新方案在相同计算量下,可获得比普通有限元方法高得多的精度。     

Morphological evolution and migration of void in bi-piezoelectric interface based on nonlocal phase field method

This paper reports the result of investigation into the morphological evolution and migration of void in bi-piezoelectric material interface by utilizing nonlocal phase field model and finite element method (FEM), where the small scale effect containing the long-range forces among atoms is considered. The nonlocal elastic strain energy and the nonlocal electric energy around the void are firstly calculated by the finite element method. Then based on the finite difference method (FDM), the thermodynamic equilibrium equation containing the surface energy and anisotropic diffusivity is solved to simulate the morphological evolution and migration of elliptical void in bi-piezoelectric films interface. Results show that the way of load condition plays a significant role in the evolution process, and the boundary of void's long axis gradually collapses toward the center of ellipse. In addition, the evolutionary speed of left boundary gradually decreases with scale effect coefficient growth. This work can provide references for the safety evaluation of piezoelectric materials in micro electro mechanical system.     

An anti-diffusive numerical scheme for the simulation of interfaces between compressible fluids by means of a five-equation model

We propose a discretization method of a five-equation model with isobaric closure for the simulation of interfaces between compressible fluids. This numerical solver is a Lagrange–Remap scheme that aims at controlling the numerical diffusion of the interface between both fluids. This method does not involve any interface reconstruction procedure. The solver is equipped with built-in stability and consistency properties and is conservative with respect to mass, momentum, total energy and partial masses. This numerical scheme works with a very broad range of equations of state, including tabulated laws. Properties that ensure a good treatment of the Riemann invariants across the interface are proven. As a consequence, the numerical method does not create spurious pressure oscillations at the interface. We show one-dimensional and two-dimensional classic numerical tests. The results are compared with the approximate solutions obtained with the classic upwind Lagrange–Remap approach, and with experimental and previously published results of a reference test case.     

微流燃料电池空气阴极物质传输孔隙尺度模拟

采用格子Boltzmann方法研究了微流燃料电池空气阴极多孔扩散层内多组分物质传输特性。随机重构了扩散层,获得渗透率及有效扩散系数。建立了耦合边界电化学反应的二维模型,研究了过电位、孔隙率对氧气、水蒸气浓度分布及局部反应速率的影响。结果表明,常用的Bruggeman经验关联式会高估氧气有效扩散系数;扩散层孔隙结构对物质传输有重要影响,孔隙率减小使得传质阻力增大,导致局部氧气浓度降低,局部反应速率降低,而水蒸气浓度增大,当孔隙率从0.83降至0.7,催化界面平均氧气浓度从8.472降至8.466 mol·m^-3。     

Numerical study of grain boundary diffusion in nanocrystalline ionic materials including blocking space charges

Diffusion in two grain boundary networks (parallel boundaries and square grains) was considered in order to analyze the effects of space charge layers on diffusion profiles. The space charge zones are supposed to be depleted of mobile charge carriers, leading to a blocking of transport of diffusing species. The finite element method was used to numerically calculate the concentration distribution and the corresponding integrated diffusion profiles. The accuracy of determining the grain boundary diffusivity from the simulated profiles, applying conventional equations was estimated. Blocking space charge layers lead to a possible overestimation of the grain boundary diffusivity in the type-B kinetic regime. Moreover, they lead to a significant shifting of kinetic regimes and extremely large diffusion times should be used to reduce errors, when determining the grain boundary diffusivity in the type-A regime.     

On the estimation of the curvatures and bending rigidity of membrane networks via a local maximum-entropy approach

We present a meshfree method for the curvature estimation of membrane networks based on the local maximum entropy approach recently presented in [1]. A continuum regularization of the network is carried out by balancing the maximization of the information entropy corresponding to the nodal data, with the minimization of the total width of the shape functions. The accuracy and convergence properties of the given curvature prediction procedure are assessed through numerical applications to benchmark problems, which include coarse grained molecular dynamics simulations of the fluctuations of red blood cell membranes [2], [3]. We also provide an energetic discrete-to-continuum approach to the prediction of the zero-temperature bending rigidity of membrane networks, which is based on the integration of the local curvature estimates. The local maximum entropy approach is easily applicable to the continuum regularization of fluctuating membranes, and the prediction of membrane and bending elasticities of molecular dynamics models.     

The solution flow through the nanochannel of MCM-41: a spin-probe study

A spin-probe electron spin resonance (ESR) study was made on the alcoholic solution flowing through a quartz column packed with MCM-41 to clarify the dynamics of the liquid molecules in the nanochannel. The ESR spectra of a few hydrophobic spin probes showed that they undergo rotational diffusion preferentially along the longest molecular axis, indicating that the nanochannel is effectively narrowed further for these radicals by the influence of the solvent. Since almost identical ESR spectra were observed for the static samples, which were prepared in vacuo by introducing the solutions into the quartz tube with the MCM-41 powder and sealing off, the solution in the above-mentioned experiment should really flow through the nanochannel of MCM-41. Although a laminar flow is expected from the classical theory, the calculated flow rate is almost zero. In addition, the duration for the spin-probe molecules to flow through the column was basically not dependent on their affinity to the silica surface. To explain all these phenomena, we propose a model that the liquid molecules flow collectively by slipping on the surface of the nanochannel.     

Diffusivity control in nanoporous membrane through organic-inorganic hybridization

Nanoporous inorganic materials have attracted great interest due to their potential application as nanofilters, drug delivery carriers and adsorbents. In order to control the molecular passage through nanopores, we have modified the pore channel of inorganic materials with organic moieties and investigated the diffusion pattern of small molecules. The surface was modified by octyltriethoxysilane (OTS) by refluxing in toluene for 12 h. The water contact angle of OTS modified zirconia membrane was observed ∼110° showing hydrophobic surface. Contact angles to various solvents were also examined to verify the self-assembled monolayer of octyl chains on the inorganic membrane. The molecular passage patterns of both pristine and modified nanoporous membrane were evaluated by means of the diffusivity of small dye molecule, azobenzene. The diffusion coefficients of azobenzene on both membranes were measured in various solvents on the basis of Fick’s diffusion law. The diffusivities in various solvents for pristine and its modified zirconia membrane were determined. The diffusivity was observed to be influenced by surface energy of both membrane and solvent as well as the polarity of solvents.