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.

Exploration of the coupled lattice Boltzmann model based on a multiphase field model:A study of the solid-liquid-gas interaction mechanism in the solidification process

A multiphase field model coupled with a lattice Boltzmann(PF-LBM)model is proposed to simulate the distribution mechanism of bubbles and solutes at the solid-liquid interface,the interaction between dendrites and bubbles,and the effects of different temperatures,anisotropic strengths and tilting angles on the solidified organization of the SCN-0.24wt.%butanedinitrile alloy during the solidification process.The model adopts a multiphase field model to simulate the growth of dendrites,calculates the growth motions of dendrites based on the interfacial solute equilibrium;and adopts a lattice Boltzmann model(LBM)based on the Shan-Chen multiphase flow to simulate the growth and motions of bubbles in the liquid phase,which includes the interaction between solid-liquid-gas phases.The simulation results show that during the directional growth of columnar dendrites,bubbles first precipitate out slowly at the very bottom of the dendrites,and then rise up due to the different solid-liquid densities and pressure differences.The bubbles will interact with the dendrite in the process of flow migration,such as extrusion,overflow,fusion and disappearance.In the case of wide gaps in the dendrite channels,bubbles will fuse to form larger irregular bubbles,and in the case of dense channels,bubbles will deform due to the extrusion of dendrites.In the simulated region,as the dendrites converge and diverge,the bubbles precipitate out of the dendrites by compression and diffusion,which also causes physical phenomena such as fusion and spillage of the bubbles.These results reveal the physical mechanisms of bubble nucleation,growth and kinematic evolution during solidification and interaction with dendrite growth.

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.

Cavitation Bubble Collapse near a Curved Wall by the Multiple-Relaxation-Time Shan-Chen Lattice Boltzmann Model

The cavitation bubble collapse near a cell can cause damage to the cell wall. This effect has received increasing attention in biomedical supersonics. Based on the lattice Boltzmann method, a multiple-relaxation-time Shan–Chen model is built to study the cavitation bubble collapse. Using this model, the cavitation phenomena induced by density perturbation are simulated to obtain the coexistence densities at certain temperature and to demonstrate the Young–Laplace equation. Then, the cavitation bubble collapse near a curved rigid wall and the consequent high-speed jet towards the wall are simulated. Moreover, the influences of initial pressure difference and bubble-wall distance on the cavitation bubble collapse are investigated.

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 some equiatomic noble metal alloys in liquid phase such as Au-Cu, Ag-Cu, and Ag-Au using well recognized pseudopotential formalism. For description of the structure, well known Percus-Yevick （PY） hard sphere model is used as a reference system. By applying a variation method the best hard core diameters have been found which correspond to minimum free energy. With this procedure the thermodynamic properties such as entropy and heat of mixing have been computed. The influence of local field correction function viz; Hartree （H）, Taylor （T）, lehimaru-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 case of liquid alloys while the agreement with experiment is poor in the case of heats of mixing. This may be due to the sensitivity of the heats of mixing with the potential parameters and the dielectric function.

Pseudopotential-based discrete unified gas kinetic scheme for modeling multiphase fluid flows

To directly incorporate the intermolecular interaction effects into the discrete unified gas-kinetic scheme(DUGKS)for simulations of multiphase fluid flow,we developed a pseudopotential-based DUGKS by coupling the pseudopotential model that mimics the intermolecular interaction into DUGKS.Due to the flux reconstruction procedure,additional terms that break the isotropic requirements of the pseudopotential model will be introduced.To eliminate the influences of nonisotropic terms,the expression of equilibrium distribution functions is reformulated in a moment-based form.With the isotropy-preserving parameter appropriately tuned,the nonisotropic effects can be properly canceled out.The fundamental capabilities are validated by the flat interface test and the quiescent droplet test.It has been proved that the proposed pseudopotential-based DUGKS managed to produce and maintain isotropic interfaces.The isotropy-preserving property of pseudopotential-based DUGKS in transient conditions is further confirmed by the spinodal decomposition.Stability superiority of the pseudopotential-based DUGKS over the lattice Boltzmann method is also demonstrated by predicting the coexistence densities complying with the van der Waals equation of state.By directly incorporating the intermolecular interactions,the pseudopotential-based DUGKS offers a mesoscopic perspective of understanding multiphase behaviors,which could help gain fresh insights into multiphase fluid flow.

考虑壁面浸润性的光滑岩体微裂隙渗流特性数值模拟研究

在工程岩体中存在大量的微裂隙,由于隙宽尺寸微小,其壁面浸润性显著影响着流体在裂隙内的运动特性。为此,基于Shan-Chen伪势模型的格子Boltzmann方法,建立了光滑岩体微裂隙渗流的数值模型,并结合蒸汽中的悬浮液滴和壁面接触角的模拟,证明了该模型的有效性。最后,考虑壁面浸润性、裂隙隙宽、压力梯度及流体黏滞性等因素的影响,研究了重力驱动下光滑岩体微裂隙的渗流特性。研究结果表明:疏水壁面对附近流体的排斥作用产生加速效果,而亲水性壁面则产生阻碍作用,从总体变化趋势看,疏水壁面对微裂隙渗流的影响比亲水壁面更加显著。随着微裂隙隙宽的减小,其壁面浸润性对渗流流速的影响逐渐增大,且壁面亲/疏水性越强,隙宽对其渗流特性的影响越突出。裂隙的平均渗流流速随压力梯度的增加而增大,两者呈线性关系,且壁面疏水能力越强,其直线斜率越大。此外,流体的运动黏度越大,其流动阻力也越大,从而导致微裂隙渗流的平均流速越小,且流体的运动黏度与平均渗流流速呈反比例关系。

液态法制备复合材料的多组分伪势LBM模拟

采用修正的多组分伪势模型(EFM)模拟了液态法制备金属基复合材料过程中多孔介质内的浸渗过程,研究了黏度比(M)、壁面润湿性、雷诺数(Re)、孔隙率以及不同分形结构对浸渗过程的影响.结果表明:黏度比越大,浸渗饱和度(S)越低、浸渗时间(t)越短,并且M>90时,黏度比对饱和度和浸渗时间影响可忽略不计,此时接触角的影响较小; Re越小,浸渗饱和度越高、浸渗时间越长,同时壁面润湿性的影响越大;当入口Re一定时,孔隙率越小,分形多孔的渗透率越低,由于孔隙分布不均,造成流体在局部优先浸渗,导致浸渗时间减少、饱和度降低;对不同的分形多孔介质,壁面润湿性的影响有着明显的差异,对A类(标准分形)和C类(固体骨架偏右)的多孔介质,接触角(θ)越大,饱和度越低、浸渗时间越短;对B(固体骨架偏上)和D类(固体骨架偏左上)分形多孔,随接触角的增大,饱和度和浸渗时间均呈现先增加后减小的趋势,并且在接触角小于90°的区间内出现极值.

PEMFC碳纸气体扩散层内气液两相流格子Boltzmann模拟

为了提高质子交换膜燃料电池(PEMFC)水管理,本文借助多相流格子Boltzmann模型(LBM)模拟分析了PEMFC碳纸气体扩散层(GDL)内的气液两相输运过程,主要研究了GDL疏水性对气液两相流的影响。结果表明:液态水流路径不仅受到GDL结构形态的影响,而且受到材料疏水性影响。液态水在疏水性弱的GDL中不仅容易沁入,而且容易在孔隙中达到饱和;相反,在疏水性较强的GDL中,液态水很难突破沁入小尺寸孔隙,而从孔径较大的孔隙流通,从而形成毛细力主导的指进流动。

近复杂几何固壁空泡溃灭的伪势格子Boltzmann建模

格子Boltzmann方法伪势多相模型具有高效性和复杂几何边界实施的简易性。该文采用改进作用力的伪势多相模型,通过优化参数实现最大程度的热力学一致性,进而提高模型的密度比和稳定性。分别从伪速度、网格不变性、Young-Laplace验证等方面研究了改进模型的性能。通过改进的模型模拟了复杂几何固壁附近空泡溃灭过程。分析了空化泡溃灭阶段的密度场、压力场和速度场演化过程,以及复杂几何固壁附近的空泡动力学特性。结果表明伪势格子Boltzmann方法在探索空泡溃灭和复杂几何固壁间的相互作用规律研究中是一种有效的工具。

倾斜壁面浸润性梯度驱动液滴运动过程的格子Boltzmann模型研究

基于介观模型的多组分伪势格子Boltzmann方法,模拟了倾斜壁面浸润性梯度驱动液滴的运动过程,研究了壁面浸润性梯度、壁面倾斜角度对液滴运动过程的影响.结果表明,对于一定倾斜角度的壁面,当壁面上浸润性梯度足够大时,液滴能够克服重力的作用实现"爬坡";液滴在运动过程中,其前进及后退接触角与当地静态接触角间存在差值;增大壁面浸润性梯度时,液滴能够获得更快的加速,并且前进及后退接触角与当地静态接触角之间的差值也随之增大;增大壁面倾斜角度时,液滴的运动受到阻碍,前进及后退接触角与当地静态接触角的差值小幅减小.

基于改进伪势LBM的空泡溃灭建模

为研究空化泡溃灭阶段的数值仿真,本文以格子Boltzmann方法为基础,采用改进作用力引进格式,对改变力学稳定性条件相关参数进行优化。通过最优参数提取,提高该多相格子Boltzmann模型密度比,从而最大程度保证热力学一致性及模型稳定性。并通过共存密度曲线对比及误差值计算,确定了参数的最优值。基于改进伪势格子Boltzmann模型对空泡溃灭进行建模,并将计算结果和实验结果对比,验证了空泡溃灭模型的有效性,对实际运用有一定的指导意义。

Lattice Boltzmann simulation of liquid vapor system by incorporating a surface tension term

In this study, we investigate the pseudopotential multiphase model of lattice Boltzmann method（LBM） and incorporate a surface tension term to implement the particle interaction force. By using the Carnahan–Starling（CS） equation of state（EOS） with a proper critical pressure–density ratio, a density ratio over 160000 is obtained with satisfactory numerical stability. The added surface tension term offers a flexible choice to adjust the surface tension strength. Numerical tests of the Laplace rule are conducted, proving that smaller spurious velocity and better numerical stability can be acquired as the surface tension becomes stronger. Moreover, by wall adhesion and heterogeneous cavitation tests, the surface tension term shows its practical application in dealing with problems in which the surface tension plays an important role.

液滴撞击具有浸润性分布的倾斜固壁铺展行为的格子Boltzmann研究

采用基于单组分多相伪势模型的格子Boltzmann方法,模拟了三维液滴撞击左右两侧浸润性不同的倾斜固壁的铺展过程,获得了液滴在壁面两侧的铺展因子、相对铺展宽度、相对高度和液滴运动速度随时间的变化情况,研究了壁面浸润性分布和壁面倾斜角度对液滴铺展过程的影响.结果表明,液滴在倾斜壁面的铺展过程受到重力和表面力的综合作用,重力影响液滴的铺展和沿壁面向下的滑动,壁面浸润性分布影响液滴向壁面亲水侧横向移动.

基于格子Boltzmann方法的液润表面减阻规律

[目的]近年来,液润表面(LIS)作为一种新型的减阻表面被提出。它将传统疏水表面微沟槽中残存的气体替换为润滑油,进而提高了减阻效果的稳定性。为了更全面地认识液润表面,研究润滑油溶解性对滑移长度的影响。[方法]基于格子Boltzmann方法(LBM)伪势模型,对液润表面的滑移现象进行数值模拟,研究润滑油溶解密度和外部剪切率对滑移长度的影响规律。[结果]液润表面可以产生滑移现象,当润滑油完全混溶或极难溶时,滑移长度与组分间分子作用强度有较好的线性关系。[结论]润滑油难溶于水时,组分间作用力越大,减阻效果越好。且滑移长度不显著依赖于剪切率,润滑油的减阻特性与传统超疏水壁面的减阻特性有相似性。

Total Energy and Electronic States of CdSe Nanoparticles

The authors fulfilled calculations of the total energy and electronic states of Cd_(n)Se_(n) nanoparticle:“wurzite”,“sphalerite”and“rock-salt”types of the structure.It was shown that at n≤72 the“rock-salt”type is the most favorable energetically.However the extrapolation of the behavior of the energy per Cd-Se atomic pair shows that for n>130(corresponding to a size of about 2 nm),particles with a“wurtzite”structure can be more advantageous.Particles of the“wurtzite”and“rock-salt”types have an electronic structure with an energy gap.For particles with the“wurtzite”structure,the gap width decreases with increasing particle size:from 3.3 eV to 2.2 eV as the particle increases from 0.5 nm to 1.5 nm.For particles of the“rock-salt”type,the gap width grows slightly,remaining about 3 eV.“Sphalerite”-type particles have a metal-like electronic structure.

Electronic Structure of CdS Nanoparticles and CdSe/CdS Nanosystems

The electronic states of“wurtzite”CdS nanoparticles and CdSe/CdS nanosystems with up to 80 pairs of Cd-Se or CdS atoms were calculated.The results for CdS particles were compared with the results obtained earlier for CdSe particles of the same size and with published calculations of other authors.The calculated gap values in the range of 2.84 eV~3.78 eV are typical for CdS particles of studied sizes in accordance with results of published data.The CdSe/CdS nanosystems were considered as layered ones and as quantum dots.The layered CdSe/CdS systems with two-layer CdS coverings can be interpreted in terms of combinations of two semiconductors with different energy band gaps(2.6 eV and 3.3 eV),while analogous systems with single-layer CdS coverings do not demonstrate a two-gap electron structure.Simulation of a CdSe/CdS quantum dot shows that the single-layer CdS shell demonstrates a tendency for the formation of the electronic structure with two energy gaps:approximately of 2.5 eV and 3.0 eV.

基于格子玻尔兹曼方法的双空化泡溃灭相互作用过程数值模拟研究

文章利用格子玻尔兹曼多相流伪势模型模拟了近壁区垂向并排双空化泡溃灭过程,结果表明上部空化泡溃灭时间小于下部空化泡;同时上部空化泡在下部空化泡的影响下均朝向壁面发生溃灭,但溃灭时冲击波与微射流均作用在下部空化泡上,并不直接作用于壁面;当下部空化泡位于壁面影响区外时,其溃灭产生的微射流朝向上部空化泡,而当下部空化泡位于壁面影响区内时,下方空化泡溃灭前横向压缩大于纵向压缩。格子玻尔兹曼伪势模型与边界积分法模拟结果和实验结果吻合一致,表明格子玻尔兹曼伪势模型可有效模拟近壁区多空化泡溃灭时的相互作用过程。