Quy-Dong To

Closed-form solutions for the effective conductivity of two-phase periodic composites with spherical inclusions

In this paper, we use approximate solutions of Nemat-Nasser et al. to estimate the effective conductivity of two-phase periodic composites with non-overlapping spherical inclusions. Systems with different inclusion distributions are considered: cubic lattice distributions (simple cubic, body-centred cubic and face-centred cubic) and random distributions. The effective conductivities of the former are obtained in closed form and compared with exact solutions from the fast Fourier transform-based methods. For systems containing randomly distributed spherical inclusions, the solutions are shown to be directly related to the static structure factor, and we obtain its analytical expression in the infinite-volume limit.

Properties of water confined in hydroxyapatite nanopores as derived from molecular dynamics simulations

Abstract Bone tissue is characterized by nanopores inside the collagen-apatite matrix where fluid can exist and flow. The description of the fluid flow within the bone has however mostly relied on a macroscopic continuum mechanical treatment of the system, and, for this reason, the role of these nanopores has been largely overlooked. However, neglecting the nanoscopic behaviour of fluid within the bone volume could result in large errors in the overall description of the dynamics of fluid. In this work, we have investigated the nanoscopic origin of fluid motion by conducting atomistic molecular dynamics simulations of water confined between two parallel surfaces of hydroxyapatite (HAP), which is the main mineral phase of mammalian bone. The polarizable core–shell interatomic potential model used in this work to simulate the HAP–water system has been extensively assessed with respect to ab initio calculations and experimental data. The structural (pair distribution functions), dynamical (self-diffusion coefficients) and transport (shear viscosity coefficients) properties of confined water have been computed as a function of the size of the nanopore and the temperature of the system. Analysis of the results shows that the dynamical and transport properties of water are significantly affected by the confinement, which is explained in terms of the layering of water on the surface of HAP as a consequence of the molecular interactions between the water molecules and the calcium and phosphate ions at the surface. Using molecular dynamics simulations, we have also computed the slip length of water on the surface of HAP, the value of which has never been reported before.

Argon Interaction with Gold Surfaces: Ab Initio-Assisted Determination of Pair Ar–Au Potentials for Molecular Dynamics Simulations

Global potentials for the interaction between the Ar atom and gold surfaces are investigated and Ar-Au pair potentials suitable for molecular dynamics simulations are derived. Using a periodic plane-wave representation of the electronic wave function, the nonlocal van-der-Waals vdW-DF2 and vdW-OptB86 approaches have been proved to describe better the interaction. These global interaction potentials have been decomposed to produce pair potentials. Then, the pair potentials have been compared with those derived by combining the dispersionless density functional dlDF for the repulsive part with an effective pairwise dispersion interaction. These repulsive potentials have been obtained from the decomposition of the repulsive interaction between the Ar atom and the Au2 and Au4 clusters and the dispersion coefficients have been evaluated by means of ab initio calculations on the Ar+Au2 complex using symmetry adapted perturbation theory. The pair potentials agree very well with those evaluated through periodic vdW-DF2 calculations. For benchmarking purposes, CCSD(T) calculations have also been performed for the ArAu and Ar+Au2 systems using large basis sets and extrapolations to the complete basis set limit. This work highlights that ab initio calculations using very small surface clusters can be used either as an independent cross-check to compare the performance of state-of-the-art vdW-corrected periodic DFT approaches or, directly, to calculate the pair potentials necessary in further molecular dynamics calculations.

Conductivity estimates of spherical-particle suspensions based on triplet structure factors.

In this paper, we present an estimation of the conductivity of composites constituted of identical spheres embedded in a host material. A family of polarization integral equations for the localization problem is constructed and the operator is then minimized to yield an optimal integral equation. As a result, the corresponding Neumann series converges with the fastest rate and can be used to estimate the effective conductivity. By combining this series and integral approximation, one can derive explicit expressions for the overall property using expansions in Fourier domain. For random hard-sphere systems, relations to structure factors and triplet structure factors have been made and Kirkwood superposition approximation is used to evaluate the effective conductivity, taking into account third-order correlations. This presents an original means to account for the statistical information up to third-order correlation when determining the effective properties of composite materials.

Boundary conditions for gas flow problems from anisotropic scattering kernels

The paper presents an interface model for gas flowing through a channel constituted of anisotropic wall surfaces. Using anisotropic scattering kernels and Chapman Enskog phase density, the boundary conditions (BCs) for velocity, temperature, and discontinuities including velocity slip and temperature jump at the wall are obtained. Two scattering kernels, Dadzie and Meolans (DM) kernel, and generalized anisotropic Cercignani-Lampis (ACL) are examined in the present paper, yielding simple BCs at the wall fluid interface. With these two kernels, we rigorously recover the analytical expression for orientation dependent slip shown in our previous works [Pham et al., Phys. Rev. E 86, 051201 (2012) and To et al., J. Heat Transfer 137, 091002 (2015)] which is in good agreement with molecular dynamics simulation results. More important, our models include both thermal transpiration effect and new equations for the temperature jump. While the same expression depending on the two tangential accommodation coefficients is obtained for slip velocity, the DM and ACL temperature equations are significantly different. The derived BC equations associated with these two kernels are of interest for the gas simulations since they are able to capture the direction dependent slip behavior of anisotropic interfaces.

Multiscale Study of Gas Slip Flows in Nanochannels

The slip velocity effect at the wall interface becomes important when the Knudsen number is above 0.01. In most problems, the Maxwell slip model is used based on the Tangential Momentum Accommodation Coefficient (TMAC), a gas-wall couple constant. The original Maxwell slip theory is isotropic which is not suitable for strongly anisotropic surfaces. The present work presents a multi-scale analysis of the anisotropic slip phenomenon which comprises three stages: i) the ab-initio study of the gas-wall interaction potential ii) Molecular Dynamic (MD) computation of the isotropic/anisotropic TMAC coefficients on different surfaces iii) MD simulation of gas flows using an anisotropic surface model and comparison with the slip theory. The interaction between an Ar gas atom and a solid Pt fcc (111) slab is carried out using CRYSTAL 09 software and PBE functional for solids (PBEsol). The ab-initio based results including equilibrium distance and adsorption energy are in good agreement with empirical results in literature. The gas-wall potential is then decomposed to pair-wise potentials for Molecular Dynamics simulation. Next, the TMAC coefficients are computed using MD method with the pair-wise potential. The gas atoms are projected onto the solid slabs with different arriving angle and relative momentum changes are measured to determine the TMAC coefficients. Different types of surfaces are considered in this paper including perfectly smooth crystalline surface, randomly rough surfaces obtained from atom deposition simulations and, anisotropic surfaces with stripes. The phantom layer technique is used to maintain the bulk solid atoms at constant temperature allowing the study of the temperature effect. The orientation dependency of TMACs is computed and analyzed in comparison with isotropic/anisotropic scattering kernel models. Finally, we use MD method to simulate gas flows in nano channel. Instead of describing explicitly the solid atomic wall, an effective anisotropic gas wall collision mechanism with TMAC coefficients determined previously is adopted. A special MD wall boundary condition is proposed to mimic the mechanism. Both pressure and acceleration driven methods are used to simulate gas flows in slip and transitional regimes. In the former method, a constant gravity-like force is applied to the gas atoms. The latter method controls the kinetic pressure difference between the inlet and the outlet. Numerical results are then compared with analytical solutions issued from the anisotropic slip theory. It is shown that the extension of the Maxwells model using two TMAC parameters can describe quite well the anistropic slip effect in the slip regime.

Molecular dynamics simulations of pressure-driven flows and comparison with acceleration-driven flows

We use molecular dynamics to simulate fluid flows between two parallel plates with constant wall temperature. Unlike the usual approach in molecular dynamics, instead of applying an external force on the molecules, the periodic boundary conditions are modified to create a pressure difference between the inlet and the outlet sections of the computational domain. The simulation results include velocity, pressure, density, and temperature profiles obtained by the new method. These results are compared with approximate solutions for nonisothermal Poiseuille flows. The method is also applied to simulate a flow in a rib-roughened channel.

A numerical-analytical coupling computational method for homogenization of effective thermal conductivity of periodic composites

BackgroundIn the framework of periodic homogenization, the conduction problem can be formulated as an integral equation whose solution can be represented by a Neumann series. From the theory, many efficient numerical computation methods and analytical estimations have been proposed to compute the effective conductivity of composites.MethodsWe combine a Fast Fourier Transform (FFT) numerical method based on the Neumann series and analytical estimation based on the integral equation to solve the problem. Specifically, the analytical approximation is used to estimate the remainder of the series.ResultsFrom some numerical examples, the coupling method have shown to improve significantly the original FFT iteration scheme and results are also superior to the analytical estimation.ConclusionsWe have proposed a new efficient computation method to determine the effective conductivity of composites. This method combines the advantages of the FFT numerical methods and the analytical estimation based on integral equation.

Non-parametric wall model and methods of identifying boundary conditions for moments in gas flow equations

In this paper, we use Molecular Dynamics (MD) simulation method to study gas-wall boundary conditions. Discrete scattering information of gas molecules at the wall surface are obtained from collision simulations. The collision data can be used to identify the accommodation coefficients for parametric wall models such as Maxwell, Cercignani-Lampis scattering kernels. Since these scattering kernels are based on a limited number of accommodation coefficients, we adopt non-parametric statistical methods to construct the kernel to overcome these issues. Different from parametric kernels, the non-parametric kernels require no parameter (i.e accommodation coefficients) and no predefined distribution. We also propose approaches to derive directly the Navier friction and Kapitza thermal resistance coefficients as well as other interface coefficients associated to moment equations from the non-parametric kernels. The methods are applied successfully to systems composed of CH 4 or CO 2 and graphite, which are of interest to the petroleum industry.

Strain-induced friction anisotropy between graphene and molecular liquids

In this paper, we study the friction behavior of molecular liquids with anisotropically strained graphene. Due to the changes of lattice and the potential energy surface, the friction is orientation dependent and can be computed by tensorial Green-Kubo formula. Simple quantitative estimations are also proposed for the zero-time response and agree reasonably well with the molecular dynamics results. From simulations, we can obtain the information of structures, dynamics of the system, and study the influence of strain and molecular shapes on the anisotropy degree. It is found that unilateral strain can increase friction in all directions but the strain direction is privileged. Numerical evidences also show that nonspherical molecules are more sensitive to strain and give rise to more pronounced anisotropy effects.