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.

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.

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.

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.

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.

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.