Numerical Stability and Accuracy of Contact Angle Schemes in Pseudopotential Lattice Boltzmann Model for Simulating Static Wetting and Dynamic Wetting

There are five most widely used contact angle schemes in the pseudopotential lattice Boltzmann(LB)model for simulating the wetting phenomenon:The pseudopotential-based scheme(PB scheme),the improved virtualdensity scheme(IVD scheme),the modified pseudopotential-based scheme with a ghost fluid layer constructed by using the fluid layer density above the wall(MPB-C scheme),the modified pseudopotential-based scheme with a ghost fluid layer constructed by using the weighted average density of surrounding fluid nodes(MPB-W scheme)and the geometric formulation scheme(GF scheme).But the numerical stability and accuracy of the schemes for wetting simulation remain unclear in the past.In this paper,the numerical stability and accuracy of these schemes are clarified for the first time,by applying the five widely used contact angle schemes to simulate a two-dimensional(2D)sessile droplet on wall and capillary imbibition in a 2D channel as the examples of static wetting and dynamic wetting simulations respectively.(i)It is shown that the simulated contact angles by the GF scheme are consistent at different density ratios for the same prescribed contact angle,but the simulated contact angles by the PB scheme,IVD scheme,MPB-C scheme and MPB-W scheme change with density ratios for the same fluid-solid interaction strength.The PB scheme is found to be the most unstable scheme for simulating static wetting at increased density ratios.(ii)Although the spurious velocity increases with the increased liquid/vapor density ratio for all the contact angle schemes,the magnitude of the spurious velocity in the PB scheme,IVD scheme and GF scheme are smaller than that in the MPB-C scheme and MPB-W scheme.(iii)The fluid density variation near the wall in the PB scheme is the most significant,and the variation can be diminished in the IVD scheme,MPB-C scheme andMPBWscheme.The variation totally disappeared in the GF scheme.(iv)For the simulation of capillary imbibition,the MPB-C scheme,MPB-Wscheme and GF scheme simulate the dynamics of the liquid-vapor interface well,with the GF scheme being the most accurate.The accuracy of the IVD scheme is low at a small contact angle(44 degrees)but gets high at a large contact angle(60 degrees).However,the PB scheme is the most inaccurate in simulating the dynamics of the liquid-vapor interface.As a whole,it is most suggested to apply the GF scheme to simulate static wetting or dynamic wetting,while it is the least suggested to use the PB scheme to simulate static wetting or dynamic wetting.

Pseudopotential multi-relaxation-time lattice Boltzmann model for cavitation bubble collapse with high density ratio

The dynamics of the cavitation bubble collapse is a fundamental issue for the bubble collapse application and prevention. In the present work, the modified forcing scheme for the pseudopotential multi-relaxation-time lattice Boltzmann model developed by Li Q et al. [ Li Q, Luo K H and Li X J 2013 Phys. Rev. E 87 053301] is adopted to develop a cavitation bubble collapse model. In the respects of coexistence curves and Laplace law verification, the improved pseudopotential multi-relaxation-time lattice Boltzmann model is investigated. It is found that the thermodynamic consistency and surface tension are independent of kinematic viscosity. By homogeneous and heterogeneous cavitation simulation, the ability of the present model to describe the cavitation bubble development as well as the cavitation inception is verified. The bubble collapse between two parallel walls is simulated. The dynamic process of a collapsing bubble is consistent with the results from experiments and simulations by other numerical methods. It is demonstrated that the present pseudopotential multirelaxation-time lattice Boltzmann model is applicable and efficient, and the lattice Boltzmann method is an alternative tool for collapsing bubble modeling.

Modeling for Collapsing Cavitation Bubble near Rough Solid Wall by Mulit-Relaxation-Time Pseudopotential Lattice Boltzmann Model

Cavitation bubble collapse near rough solid wall is modeled by the multi-relaxation-time (MRT) pseudopotential lattice Boltzmann (LB) model. The modified forcing scheme, which can achieve LB model’s thermodynamic consistency by tuning a parameter related with the particle interaction range, is adopted to achieve desired stability and density ratio. The bubble collapse near rough solid wall was simulated by the improved MRT pseudopotential LB model. The mechanism of bubble collapse is studied by investigating the bubble profiles, pressure field and velocity field evolution. The eroding effects of collapsing bubble are analyzed in details. It is found that the process and the effect of the interaction between bubble collapse and rough solid wall are affected seriously by the geometry of solid boundary. At the same time, it demonstrates that the MRT pseudopotential LB model is a potential tool for the investigation of the interaction mechanism between the collapsing bubble and complex geometry boundary.

Perfect plane-wave source for a high-order symplectic finite-difference time-domain scheme

The method of splitting a plane-wave finite-difference time-domain （SP-FDTD） algorithm is presented for the initiation of plane-wave source in the total-field / scattered-field （TF/SF） formulation of high-order symplectic finite- difference time-domain （SFDTD） scheme for the first time. By splitting the fields on one-dimensional grid and using the nature of numerical plane-wave in finite-difference time-domain （FDTD）, the identical dispersion relation can be obtained and proved between the one-dimensional and three-dimensional grids. An efficient plane-wave source is simulated on one-dimensional grid and a perfect match can be achieved for a plane-wave propagating at any angle forming an integer grid cell ratio. Numerical simulations show that the method is valid for SFDTD and the residual field in SF region is shrinked down to -300 dB.

Pseudopotential generation

Different classes of first-principle pseudopotentials are compared and various schemes for pseudo-potential generation based on norm conservation are discussed in this paper.BHS(Bachelet,Hamann,and Schlueter)-scheme and V(Vanderbilt)-modifications are used to derive the KB(Kleinman and Bylander).pseudopotentials and pseudo wave functions of bismuth.Quality test of pseudopotemtials shows tha no ghost states occur in the logarithmic deriuatives of pseudo wave functions of Bismuth,The obtained bond length of bismuth dimer with this type of pseudopotentials is in good agreement with previous accurately calculated ab initio quantum chemical result.

Investigation of cavitation bubble collapse in hydrophobic concave using the pseudopotential multi-relaxation-time lattice Boltzmann method

The interaction between cavitation bubble and solid surface is a fundamental topic which is deeply concerned for the utilization or avoidance of cavitation effect.The complexity of this topic is that the cavitation bubble collapse includes many extreme physical phenomena and variability of different solid surface properties.In the present work,the cavitation bubble collapse in hydrophobic concave is studied using the pseudopotential multi-relaxation-time lattice Boltzmann model(MRT-LB).The model is modified by involving the piecewise linear equation of state and improved forcing scheme.The fluid-solid interaction in the model is employed to adjust the wettability of solid surface.Moreover,the validity of the model is verified by comparison with experimental results and grid-independence verification.Finally,the cavitation bubble collapse in a hydrophobic concave is studied by investigating density field,pressure field,collapse time,and jet velocity.The superimposed effect of the surface hydrophobicity and concave geometry is analyzed and explained in the framework of the pseudopotential LBM.The study shows that the hydrophobic concave can enhance cavitation effect by decreasing cavitation threshold,accelerating collapse and increasing jet velocity.

Some Properties of Si,Ge,and α-Sn Using Pseudopotential Theory

在有我们的很好确定的单身的参量的模型潜力的第二份订单以外的 pseudopotential 理论被采用计算全部的水晶精力，静态的体积模量，在Jones地区脸和 Si 的压力卷关系(在压力下面的状态的方程)上的点 X 的精力乐队差距，用 Nagy 的静态的本地域修正的 Ge 和 -Sn 工作。结果与那些相比使用很少获得另外的本地地修正功能。全部的精力的现在的结果在对试验性的数据的好同意。屏蔽功能完美地与 Ge 和 -Sn 的试验性的结果正在匹配的由 Nagy 的家计算的体积模量。一些偏差在精力乐队差距的价值被发现。

Pseudopotentials,Lax Pairs and Bcklund Transformations for Generalized Fifth-Order KdV Equation

Based on the method developed by Nucci,the pseudopotentials,Lax pairs and the singularity manifoldequations of the generalized fifth-order KdV equation are derived.By choosing different coefficient,the correspondingresults and the Backlund transformations can be obtained on three conditioners which include Caudrey-Dodd-GibbonSawada-Kotera equation,the Lax equation and the Kaup-kupershmidt equation.

Pseudopotential Density-Functional Calculations for Structures of Small CarbonClusters CN （N=2-8）

We introduce a first-principles density-fumctional theory,i.e.the finite-differcnce pseudopotential density-functional theory in real space and the langevin molecular dynamics annealing technique,to the descriptions of structures and some properties of small carbon clusters(CN,N=2-8).It is shown that the odd-numbered clusters have linear structures and most of the even-numbered clusters prefer cyclic structures.

Study of Thermodynamics of Liquid Noble-Metals Alloys Through a Pseudopotential Theory

The Gibbs-Bogoliubov (GB) inequality is applied to investigate the thermodynamic properties of someequiatomic noble metal alloys in liquid phase such as Au-Cu,Ag-Cu,and Ag-Au using well recognized pseudopotentialformalism.For description of the structure,well known Percus-Yevick (PY) hard sphere model is used as a referencesystem.By applying a variation method the best hard core diameters have been found which correspond to minimumfree energy.With this procedure the thermodynamic properties such as entropy and heat of mixing have been computed.The influence of local held correction function viz;Hartree (H),Taylor (T),Ichimaru-Utsumi (IU),Farid et al.(F),and Sarkar et al.(S) is also investigated.The computed results of the excess entropy compares favourably in the caseof liquid alloys while the agreement with experiment is poor in the case of heats of mixing.This may be due to thesensitivity of the heats of mixing with the potential parameters and the dielectric function.

Structural and mass transport properties of liquid ytterbium in the temperature range 1123 K–1473 K

We have studied the structural and atomic transport properties of liquid f-shell Yb in the temperature range 1123 K–1473 K. Pair interactions between atoms are derived using a local pseudopotential. The potential parameters are fitted to the phonon dispersion curve at room temperature. The local pseudopotential used in the present study is computationally more efficient with only three parameters, and it is found to be transferable to the liquid phase without changing the parameters.Since the various computed properties agree with reported theoretical and experimental findings, the adopted fitting scheme is justified. As a significant outcome of the study, we find that(i) the melting in Yb is governed by the Lindemann's law,(ii)the mass transport mechanism obeys the Arrhenius law,(iii) the role of the three-particle correlation function in deriving the velocity autocorrelation function is small,(iv) the mean-square atomic displacement is more sensitive to the choice of interaction potential than the other bulk properties, and(v) liquid Yb does not show liquid–liquid phase transition within the studied temperature range. Further, due to the good description of the structural and mass transport properties, we propose that Yb remains divalent at reduced density.

Sub-nano Layers of Li, Be, and Al on the Si(100) Surface: Electronic Structure and Silicide Formation

Within the framework of the density functional theory and the pseudopotential method,the electronic structure calculations of the“metal-Si(100)”systems with Li,Be and Al as metal coverings of one to four monolayers(ML)thickness,were carried out.Calculations showed that band gaps of 1.02 eV,0.98 eV and 0.5 eV,respectively,appear in the densities of electronic states when the thickness of Li,Be and Al coverings is one ML.These gaps disappear with increasing thickness of the metal layers:first in the Li-Si system(for two ML),then in the Al-Si system(for three ML)and then in the Be-Si system(for four ML).This behavior of the band gap can be explained by the passivation of the substrate surface states and the peculiarities of the electronic structure of the adsorbed metals.In common the results can be interpreted as describing the possibility of the formation of a two-dimensional silicide with semiconducting properties in Li-Si(100),Be-Si(100)and Al-Si(100)systems.

First principles study on the charge density and the bulk modulus of the transition metals and their carbides and nitrides

A first principles study of the electronic properties and bulk modulus （B0） of the fcc and bcc transition metals, transition metal carbides and nitrides is presented. The calculations were performed by plane-wave pseudopotential method in the framework of the density functional theory with local density approximation. The density of states and the valence charge densities of these solids are plotted. The results show that B0 does not vary monotonically when the number of the valence d electrons increases. B0 reaches a maximum and then decreases for each of the four sorts of solids. It is related to the occupation of the bonding and anti-bonding states in the solid. The value of the valence charge density at the midpoint between the two nearest metal atoms tends to be proportional to B0.

B2-RuAl点缺陷结构的第一原理计算

采用第一原理赝势平面波方法,计算了B2-RuAl金属间化合物的基本物性及其点缺陷结构的几何、能态与电子结构,通过对不同点缺陷结构形成热与形成能的计算与比较,分析和预测了RuAl金属间化合物中点缺陷结构的种类与存在形式。结果表明:RuAl金属间化合物的点缺陷主要是Ru空位和Al反位,在富Ru合金中主要为Ru反位,在富Al合金中则主要是Al反位。这些点缺陷主要以Ru-Ru双空位和Al-Al双反位的组态结构形式出现,并且双空位以Ru-Ru为第一近邻时其点缺陷结构最稳定,而双反位则是以Al-Al为第三近邻时稳定性最高。进一步通过对NiAl和RuAl不同点缺陷结构Cauchy压力的比较,发现点缺陷对RuAl塑性的降低程度比NiAl低,因而含有点缺陷的实际合金的室温塑性RuAl比NiAl好。

第一原理方法在材料科学中的应用

为了从理论上阐明材料结构与其特性的关系,应用第一原理方法计算材料的电子状态,可以获得材料的特征参数,从而能够表征、预测甚至设计材料的结构与性能.选择密度泛函理论和基于第一原理的赝势方法,计算得到了Al、Si、BN等的晶格常数、体弹性模量、电子密度分布和能带结构,并介绍了这些基态物理性质在材料科学中成功应用的典型事例.

NiAl力学性质合金化效应的第一原理计算

采用第一原理赝势平面波方法,计算几种合金化元素X(X=Cr、Mn、Fe、Co和Cu)与不同Fe含量(0,3.125%,4.167%,6.25%,摩尔分数)(NiFe)Al超胞的几何与电子结构,并采用如下几个力学参数:弹性常数C44、Cauchy压力参数(C12-C44)、弹性模量E和剪切模量G及比值G/B0等,表征和评判了合金化元素X与不同Fe含量对NiAl金属间化合物延性与硬度的影响。结果表明:高浓度(6.25%)合金化虽可提高NiAl晶体的硬度,但却导致NiAl延展性降低,合金化后NiAl硬度增加的次序为:(Ni7Mn)Al8>(Ni7Co)Al8>(Ni7Fe)Al8>(Ni7Cr)Al8>(Ni7Cu)Al8>NiAl,其延性降低次序则与硬度增加次序相反;随着Fe含量的升高,NiAl晶体的硬度增加,但其使硬度增加的上限约为4%,而随着Fe含量的降低,NiAl晶体的延性逐步增大,当Fe含量低到一定程度时,可改善NiAl晶体的本征脆性。

Fe对NiAl力学性能影响的第一原理计算

采用第一原理赝势平面波方法,基于虚拟晶体势函数近似(VCA),计算Fe合金化(浓度x<3.0%,原子分数,下同)时完整与缺陷B2-NiAl晶体的弹性性质,并采用弹性常数C44、Cauchy压力参数(C12-C44)、杨氏模量E、剪切模量G及其与体模量B0的比值G/B0等,表征和评判Fe合金化浓度x对NiAl金属间化合物延性与硬度的影响。结果表明:无论是无缺陷的理想NiAl晶体,还是含Ni空位或Ni反位的NiAl缺陷晶体,x<0.6%的Fe合金化均可使其硬度大幅提高。Fe合金化浓度低于0.5%时,虽然完整NiAl晶体的延性变差,但含Ni空位的缺陷NiAl晶体的延性却可明显改善,并以x=0.2%～0.4%时韧化效果最好。Ni空位或Ni反位降低B2-NiAl晶体的本征延性。实验中0.20%～0.25%的Fe合金化对NiAl晶体延性的改善很可能源于Fe原子与NiAl晶体中Ni空位间的关联与协同作用。

N掺杂p-型ZnO的第一性原理计算

采用基于密度泛函理论(DFT)的第一性原理平面波超软赝势方法,计算了纤锌矿ZnO和N掺杂p-型ZnO晶体的电子结构,分析了N掺杂p-型ZnO晶体的能带结构、电子态密度、差分电荷分布以及H原子和N2分子对p-型掺杂ZnO的影响.

L1_0-TiA l金属间化合物Mn,Nb合金化电子结构的计算

采用第一原理赝势平面波方法计算了L10型TiA l金属间化合物中掺入Mn,Nb后的电子结构和价键结构。通过合金原子形成热得出:Mn优先占据A l点阵位置,Nb优先占据Ti点阵位置。Mu lliken聚居数分析发现:Mn或Nb合金化后,分别降低了(001)和(002)面内的原子间键合强度,掺入Nb还降低了层间的原子间键合强度,而掺入Mn,则使层间原子间键合强度增加。整体上来讲,掺入Mn有利于改善TiA l的室温脆性,而掺入Nb,不利于改善TiA l的室温脆性。

碘化钠弹性常数和声速的量子力学从头算

采用从头算平面波赝势（PWP）方法结合电子交换关联能的广义梯度近似（GGA）理论,对不同压力下碘化钠的晶体结构进行几何优化计算,得到体系的最稳定优化构型和相应的能量,利用胡克定律计算得到了相应压力下的弹性性质,取得了碘化钠单晶在零温条件下、压力0～30 GPa范围内弹性常数与压力的关系.根据弹性波在晶体中的传播行为求解了碘化钠单晶[100]、[110]、[111]三个主要方向的声速.