Lagrangian particle model for multiphase flows

A Lagrangian particle model for multiphase multicomponent fluid flow, based on smoothed particle hydrodynamics (SPH), was developed and used to simulate the flow of an emulsion consisting of bubbles of a non-wetting liquid surrounded by a wetting liquid. In SPH simulations, fluids are represented by sets of particles that are used as discretization points to solve the Navier-Stokes fluid dynamics equations. In the multiphase multicomponent SPH model, a modified van der Waals equation of state is used to close the system of flow equations. The combination of the momentum conservation equation with the van der Waals equation of state results in a particle equation of motion in which the total force acting on each particle consists of many-body repulsive and viscous forces, two-body (particle-particle) attractive forces, and body forces such as gravitational forces. Similar to molecular dynamics, for a given fluid component the combination of repulsive and attractive forces causes phase separation. The surface tension at liquid-liquid interfaces is imposed through component dependent attractive forces. The wetting behavior of the fluids is controlled by phase dependent attractive interactions between the fluid particles and stationary particles that represent the solid phase. The dynamics of fluids away from the interface is governed by purely hydrodynamic forces. Comparison with analytical solutions for static conditions and relatively simple flows demonstrates the accuracy of the SPH model.     

An Optimization-based SPH Solver for Simulation of Hyperelastic Solids

This paper proposes a novel method for simulating hyperelastic solids with Smoothed Particle Hydrodynamics (SPH). The proposed method extends the coverage of the state-of-the-art elastic SPH solid method to include different types of hyperelastic materials, such as the Neo-Hookean and the St. Venant-Kirchoff models. To this end, we reformulate an implicit integration scheme for SPH elastic solids into an optimization problem and solve the problem using a general-purpose quasi-Newton method. Our experiments show that the Limited-memory BFGS (L-BFGS) algorithm can be employed to efficiently solve our optimization problem in the SPH framework and demonstrate its stable and efficient simulations for complex materials in the SPH framework. Thanks to the nature of our unified representation for both solids and fluids, the SPH formulation simplifies coupling between different materials and handling collisions.     

Lattice Boltzmann simulation of the dispersion of aggregated particles under shear flows

The lattice Boltzmann method (LBM) for multicomponent immiscible fluids is applied to simulations of the deformation and breakup of a particle-cluster aggregate in shear flows. In the simulations, the solid particle is modeled by a droplet with strong interfacial tension and large viscosity. The van der Waals attraction force is taken into account for the interaction between the particles. The ratio of the hydrodynamic drag force to cohesive force, I, is introduced, and the effect of I on the aggregate deformation and breakup in shear flows is investigated. It is found that the aggregate is easier to deform and to be dispersed when I is over 100.     

Modeling the instability of CNT tweezers using a continuum model

Carbon nanotube (CNT) tweezers are composed of two parallel cantilever CNTs with a distance in between. In this paper, the static response and instability of CNT-made nano-tweezers is theoretically investigated considering the effects of Coulomb electrostatic force and van der Waals molecular attraction. For this purpose, a nano-scale continuum model is employed to obtain the nonlinear constitutive equation of the nano-tweezers. The Euler–Bernoulli beam theory is applied to model the elastic response of the CNT. The van der Waals attraction is computed from the simplified Lennard-Jones potential. In order to solve the nonlinear constitutive equation of the system, three approaches, e.g. the hemotopy perturbation method (HPM), the Adomian decomposition (AD) and the finite difference method (FDM) are employed. The obtained results are in good agreement with the experimental measurements. As a case study, freestanding CNT tweezers has been investigated and the detachment length and minimum initial gap of the tweezers are determined. Moreover, the effective operation range of the van der Waals attraction that affects the instability behavior of the CNT tweezers is discussed.     

An Implicit SPH Formulation for Incompressible Linearly Elastic Solids

We propose a novel smoothed particle hydrodynamics (SPH) formulation for deformable solids. Key aspects of our method are implicit elastic forces and an adapted SPH formulation for the deformation gradient that—in contrast to previous work—allows a rotation extraction directly from the SPH deformation gradient. The proposed implicit concept is entirely based on linear formulations. As a linear strain tensor is used, a rotation‐aware computation of the deformation gradient is required. In contrast to existing work, the respective rotation estimation is entirely realized within the SPH concept using a novel formulation with incorporated kernel gradient correction for first‐order consistency. The proposed implicit formulation and the adapted rotation estimation allow for significantly larger time steps and higher stiffness compared to explicit forms. Performance gain factors of up to one hundred are presented. Incompressibility of deformable solids is accounted for with an ISPH pressure solver. This further allows for a pressure‐based boundary handling and a unified processing of deformables interacting with SPH fluids and rigids. Self‐collisions are implicitly handled by the pressure solver.     

A Local Discontinuous Galerkin Method for the Propagation of Phase Transition in Solids and Fluids

A local discontinuous Galerkin (LDG) finite element method for the solution of a hyperbolic–elliptic system modeling the propagation of phase transition in solids and fluids is presented. Viscosity and capillarity terms are added to select the physically relevant solution. The $L^2-$ stability of the LDG method is proven for basis functions of arbitrary polynomial order. In addition, using a priori error analysis, we provide an error estimate for the LDG discretization of the phase transition model when the stress–strain relation is linear, assuming that the solution is sufficiently smooth and the system is hyperbolic. Also, results of a linear stability analysis to determine the time step are presented. To obtain a reference exact solution we solved a Riemann problem for a trilinear strain–stress relation using a kinetic relation to select the unique admissible solution. This exact solution contains both shocks and phase transitions. The LDG method is demonstrated by computing several model problems representing phase transition in solids and in fluids with a Van der Waals equation of state. The results show the convergence properties of the LDG method.     

Efficient heat transfer enhancement by elastic turbulence with polymer solution in a curved microchannel

Heat and mass transfer in microscale flows are limited due to extremely low Reynolds number (Re). In a curved microchannel, however, complex flow behaviors, such as elastic instability and elastic turbulence, can be induced via viscoelastic fluid at vanishingly low-Re conditions, which is of great potential to enhance the heat transfer performance. The influence of elastic instabilities and turbulence on heat dissipation of exothermic components is experimentally investigated in this study. The heat transfer performance of both viscoelastic (polymer solutions) and Newtonian (sucrose solutions) fluid flows in a curved microchannel with a square cross section is experimentally characterized. Titanium–platinum (Ti–Pt) thin films embedded at the bottom wall of the polydimethylsiloxane (PDMS) microchannel serve as both microheater and temperature sensor. For viscoelastic fluids, the spectrum of outlet temperature fluctuation in broad frequency (f) region fits the power law of f ^?1.1. Heat transfer enhancement due to the elastic turbulence in a curved microchannel is thereby identified by the drastic growth of the Nusselt number (Nu, the ratio of convective to conductive heat transfer normal to the boundary) with the increase in the Weissenberg number (Wi, the ratio of elastic stress to viscous stress). The mechanism of heat transfer enhanced by the convection effect of elastic turbulence is also elucidated.     

Theoretical study of van der Waals dispersion force between macroscopic bodies with a periodic material distribution

A method has been developed for calculating the van der Waals dispersion force between a macroscopic body consisting of a uniform material and a macroscopic body with a spatially periodic material distribution. The periodic material distribution is one dimensional in the x-direction. The periodically distributed material property function is expanded as a Fourier series. The van der Waals forces for a distribution of two materials were then calculated as a typical example of a periodic material distribution. The effects of parameters such as the duty ratio of the material distribution, the refractive index ratio of the two materials, and the length of the uniform body on the van der Waals force were shown.     

范德华力作用下粗糙表面静态粘附的研究

通过在硅微接触表面上涂覆低表面能的憎水性OTS膜以除去接触面间的表面张力,把两表面均接地以除去接触面间的静电力,研究了仅有范德华力作用时硅微结构接触表面的粘附.根据实际粗糙表面凸峰自相似的高度分布,计算了发生粘附后,微观接触表面产生弹性和塑性变形的两种情况下的范德华粘附能,分析了表面形貌对其影响.     

具有外部干扰的不稳定剪切梁的输入–状态稳定

本文针对一端受到范德华力的不稳定剪切梁方程,考虑其输入–状态稳定性问题.通过可逆变换把方程等价地变成一个具有反馈循环的2×2的一阶运输方程与常微分方程的耦合系统.通过自抗扰控制方法,给出具有时变增益的扩张状态观测器来估计干扰.应用Backstepping变换和干扰估计量,设计系统的反馈控制来补偿系统本身的不稳定以及消除匹配干扰.通过C₀–半群方法证明闭环系统的适定性,以及Lyapunov方法证明闭环系统的输入–状态稳定性.数值仿真验证理论结果的正确性.     

Characterizing the nonlinear behaviour of double walled carbon nanotube based nano mass sensor

This work deals with the evaluation of nonlinear behaviour of a curved double walled carbon nanotube (DWCNT) when used for mass sensing applications. The DWCNT is considered to be doubly clamped at a source and a drain. To judge the nonlinear behaviour, equations of motion have been derived using Euler beam theory and Hamilton principle, considering nonlinear van der Waals interaction nonlinear oscillations of a double walled carbon nanotube excited harmonically near its primary resonance are considered. The nonlinear free vibration of double-walled carbon nanotubes based on the elasticity theory is studied in this paper. Modelling of the weak van der Waals force of attraction between the inner and outer tubes is represented using a spring element. The equation of motion involves four nonlinear terms due to the curved geometry and the stretching of the central plane. The dynamic response of the double walled carbon nanotube based mass sensor is analyzed in the context of the time response, Poincaré maps, and fast Fourier transformation diagrams. The results show the appearance of instability and chaos in the dynamic response as the mass on carbon nanotube is changed. The appearance of regions of periodic, subharmonic, and chaotic behavior is observed to be strongly dependent on mass, inner and outer tubes and the geometric imperfections of double walled carbon nanotube.

     

Linear interaction energy models for β-secretase (BACE) inhibitors: Role of van der Waals,electrostatic, and continuum-solvation terms

Computing the binding affinity of a protein–ligand complex is one of the most fundamental and difficult tasks in computer-aided drug design. Many approaches for computing binding affinities can be classified as linear interaction energy (LIE) models as they rely on some type of linear fit of computed interaction energies between ligand and protein. We have examined the computed interaction energies of a series of β-secretase (BACE) inhibitors in terms of van der Waals, coulombic, and continuum-solvation contributions to ligand binding. We have also systematically examined the effect of different protonation states of the protein and ligands. We find that the binding affinities are relatively insensitive to the protonation state of the protein when neutral ligands are considered. Inclusion of charged ligands leads to large deviations in the coulomb, solvation, and even van der Waals terms. The latter is due to increased repulsive van der Waals interactions in the complex due to the strong coulomb attraction found between oppositely charged functional groups in the protein and ligand. In general, we find that the best models are obtained when the protein is judiciously charged (e.g. Asp32⁻, Arg235⁺) and the potentially charged ligands are treated as neutral.     

The oblique collision efficiency of nanoparticles at different angles in Brownian coagulation

The oblique collision efficiency of nanoparticles at different colliding angles in Brownian coagulation is investigated. A model of central oblique collision between two nanoparticles is presented to derive equations which are solved to get the collision efficiency by considering van der Waals force and elastic deformation force. Based on the calculated data of collision efficiency under different colliding angles and particle diameters, a new expression relating central oblique collision efficiency at different colliding angles to particle diameter is brought forward.     

Small scale effect on the pull-in instability and vibration of graphene sheets

Microsystem Technologies - In this paper, the small scale effect on the pull-in instability and frequency of graphene sheets subjected to electrostatic and van der Waals forces is studied....     

Hybrid Simulation of Miscible Mixing with Viscous Fingering

By modeling mass transfer phenomena, we simulate solids and liquids dissolving or changing to other substances. We also deal with the very small‐scale phenomena that occur when a fluid spreads out at the interface of another fluid. We model the pressure at the interfaces between fluids with Darcy's Law and represent the viscous fingering phenomenon in which a fluid interface spreads out with a fractal‐like shape. We use hybrid grid‐based simulation and smoothed particle hydrodynamics (SPH) to simulate intermolecular diffusion and attraction using particles at a computable scale. We have produced animations showing fluids mixing and objects dissolving.     

Theoretical study of van der Waals dispersion pressures considering one-dimensional material distributions in the in-plane direction

The van der Waals dispersion pressures between a half-space consisting of a uniform material and a half-space with a one-dimensional material distribution in the in-plane direction have been theoretically derived. Two patterns of material distribution were considered: a periodic distribution of materials (Pattern 1) and a distribution of two materials with a single interface (Pattern 2). The van der Waals pressure for Pattern 1 was derived based on a Fourier series, while the van der Waals pressure for Pattern 2 was derived as elementary functions. Both of the van der Waals pressures derived consist of two terms: a conventional term between half-spaces made of uniform materials and a spatial fluctuation term due to the material distribution. The basic characteristics of these van der Waals pressures were quantitatively clarified. Furthermore, an approximate method for obtaining the van der Waals pressure of Pattern 1 from Pattern 2 was proposed.     

Evaluation of the absolute affinity of neuraminidase inhibitor using steered molecular dynamics simulations

The absolute free energy difference of binding (ΔG) between neuraminidase and its inhibitor was evaluated using fast pulling of ligand (FPL) method over steered molecular dynamics (SMD) simulations. The metric was computed through linear interaction approximation. Binding nature was described by free energy differences of electrostatic and van der Waals (vdW) interactions. The finding indicates that vdW metric is dominant over electrostatics in binding process. The computed values are in good agreement with experimental data with a correlation coefficient of R = 0.82 and error of σΔG_exp = 2.2 kcal/mol. The results were observed using Amber99SB-ILDN force field in comparison with CHARMM27 and GROMOS96 43a1 force fields. Obtained results may stimulate the search for an Influenza therapy.     

noloco: An efficient implementation of van der Waals density functionals based on a Monte-Carlo integration technique

The treatment of van der Waals interactions in density functional theory is an important field of ongoing research. Among different approaches developed recently to capture these non-local interactions, the van der Waals density functional (vdW-DF) developed in the groups of Langreth and Lundqvist is becoming increasingly popular. It does not rely on empirical parameters, and has been successfully applied to molecules, surface systems, and weakly-bound solids. As the vdW-DF requires the evaluation of a six-dimensional integral, it scales, however, unfavorably with system size. In this work, we present a numerically efficient implementation based on the Monte-Carlo technique for multi-dimensional integration. It can handle different versions of vdW-DF. Applications range from simple dimers to complex structures such as molecular crystals and organic molecules physisorbed on metal surfaces.     

Influence of van der Waals force on the pull-in parameters of cantilever type nanoscale electrostatic actuators

In this paper, the influence of the van der Waals force on two main parameters describing an instability point of cantilever type nanomechanical switches, which are the pull-in voltage and deflection are investigated by using a distributed parameter model. The fringing field effect is also taken into account. The nonlinear differential equation of the model is transformed into the integral form by using the Green’s function of the cantilever beam. The integral equation is solved analytically by assuming an appropriate shape function for the beam deflection. The detachment length and the minimum initial gap of the cantilever type switches are given, which are the basic design parameters for NEMS switches. The pull-in parameters of micromechanical electrostatic actuators are also investigated as a special case of our study by neglecting the van der Waals force.     

The elastic problem for fractal media: basic theory and finite element formulation

In a previous paper [Comput. Methods Appl. Mech. Eng. 190 (2001) 6053], the framework for the mechanics of solids, deformable over fractal subsets, was outlined. Anomalous mechanical quantities with fractal dimensions were introduced, i.e., the fractal stress [σ∗], the fractal strain [ε∗] and the fractal work of deformation W∗. By means of the local fractional operators, the static and kinematic equations were obtained, and the Principle of Virtual Work for fractal media was demonstrated. In this paper, the constitutive equations of fractal elasticity are put forward. From the definition of the fractal elastic potential φ∗, the linear elastic constitutive relation is derived. The physical dimensions of the second derivatives of the elastic potential depend on the fractal dimensions of both stress and strain. Thereby, the elastic constants undergo positive or negative scaling, depending on the topological character of deformation patterns and stress flux. The direct formulation of elastic equilibrium is derived in terms of the fractional Lamé operators and of the equivalence equations at the boundary. The variational form of the elastic problem is also obtained, through minimization of the total potential energy. Finally, discretization of the fractal medium is proposed, in the spirit of the Ritz-Galerkin approach, and a finite element formulation is obtained by means of devil’s staircase interpolating splines.