Pseudopotential Model Research Articles

A comparative study on surface tension, diffusion coefficient and shear viscosity coefficient of liquid transition metals

Surface tensions of liquid transition metals of the 3d, 4d and 5d series have been calculated using modified Mayer’s formula involving hard sphere (HS) interaction of liquids derived from first and second order approximations of Percus–Yevick (PY) solutions of isothermal compressibility. Effective HS diameter and packing fraction are key ingredients of this study. To determine them, we have used effective pair potential derived from both Bretonnet–Silbert (BS) pseudopotential model and many body potential obtained from embedded atom method (EAM) in conjunction with variational modified hypernetted chain (VMHNC) integral equation theory of liquid structure. Calculated values of surface tension are used to evaluate transport coefficients such as diffusion and shear viscosity coefficients. Comparing with experimental and simulated data, calculated results suggest that expression derived from second order approximation of PY solution with the combination of EAM potential and VMHNC theory works better than any other combinations for the concerned systems.

Lattice Boltzmann modelling of isothermal two-component evaporation in porous media

A mesoscopic lattice Boltzmann model is implemented for modelling isothermal two-component evaporation in porous media. The model is based on the pseudopotential multiphase model with two components to mimic the phase-change component (e.g. water and its vapour) and the non-condensible component (e.g. dry air), and the cascaded collision operator is used to enhance the numerical performance. The model is first analysed based on Chapman–Enskog expansion and then validated by the theoretical solution of an isothermal diffusive evaporation problem. We then discuss in detail the implementation of wettability based on a geometric function scheme and further validate the model with microfluidic evaporation experiments. We apply the method to simulate the convective evaporation of a dual-porosity medium and investigate the effects of inflow vapour concentration ( ${Y_{vapour,in}}$ ) and contact angle ( $\theta$ ) on the evaporation. Simulation results reproduce the typical transition from the constant evaporation regime (CRP) at large liquid saturation (S) to the receding front period (RFP) at small S, with an intermediate falling rate period in between. The dependence of the average evaporation rates on ${Y_{vapour,in}}$ and $\theta$ during CRP and RFP is investigated. A universal scaling formulation for the evaporation rate during CRP is found with respect to the concentration-related mass transfer number $B_Y$ , contact angle $\theta$ and inflow Reynolds number Re, i.e. $E{R_{CRP}} = {k_3}\ln \left ( {1 + {B_Y}} \right ) {\cdot } \left [ {\ln \left ( {1 + {Re}} \right ) + {k_2}} \right ]\left [ {\cos (\theta ) + {k_1}} \right ]$ , where ${k_1}$ , ${k_2}$ and ${k_3}$ are fitting parameters.

Трехмерная ловушка с возбуждением колебаний ионов на границе устойчивости диаграммы Матье

Vibrations of charged particles in compositions of three-dimensional high-frequency quadrupole and static homogeneous electric fields in the stable region and in the vicinity of the stability boundary of the Mathieu diagram are investigated. Using a pseudopotential model of a rapidly oscillating field, it is shown that the motion of charged particles during linear scanning of a secular frequency is described by the Airy differential equation. Based on the properties of solutions of the Airy equation, a method of ion mass separation with resonant excitation of oscillations at the stability boundary of the Mathieu diagram has been developed. To implement the method, the ion-optical system of the three-dimensional trap is supplemented with corrective electrodes. Computer modeling has determined the optimal potentials of the correcting electrodes, at which the errors of the distributions of quadrupole and homogeneous fields do not exceed 10E-4 and 2·10E-3. Keywords: superposition of quadrupole and homogeneous fields, Airy differential equation, mode of resonant excitation of oscillations, three-dimensional ion trap with correcting electrodes.

Generalized relativistic small‐core pseudopotentials accounting for quantum electrodynamic effects: Construction and pilot applications

AbstractA simple procedure to incorporate one‐loop quantum electrodynamic (QED) corrections into the generalized (Gatchina) nonlocal shape‐consistent relativistic pseudopotential model is described. The pseudopotentials for Lu, Tl, and Ra replacing only inner core shells (with principal quantum numbersn ≤ 3 for the two former elements andn ≤ 4 for the latter one) are derived from the solutions of reference atomic SCF problems with the Dirac–Coulomb–Breit Hamiltonian to which the model Lamb shift operator added. QED contributions to atomic valence excitation energies evaluated at the SCF level are demonstrated to exceed the errors introduced by the pseudopotential approximation itself by an order of magnitude. Pilot applications of the new model to calculations of excitation energies of two‐valence‐electron atomic systems using the intermediate‐Hamiltonian relativistic Fock space coupled cluster method reformulated here for incomplete main model spaces are reported. Implications for high‐accuracy molecular excited state calculations are discussed.

Wall wettability effect on process of collapse of single cavitation bubbles in near-wall region using pseudo-potential lattice Boltzmann method

This study investigates the effect of wall wettability on cavitation collapse based on a large-density-ratio lattice Boltzmann method (LBM) pseudo-potential model. The validity and superiority of the proposed model in simulation of cavitation under complex conditions are confirmed by comparing with theories, experiments, and numerical results by other models. Our simulations indicate that wall wettability has a significant influence on near-wall cavitation of an order no less than the effect of the initial bubble distance. A criterial initial distance exists in near-wall cavitation within which the micro-jet will direct toward the wall. This criterial distance is shown to be positively correlated with the contact angle by a cosine function. Within this distance, the lifetime of the bubble decreases by up to 50%, and the increase of the maximum micro-jet velocity and collapse pressure are up to 131% and 65%, respectively, when the contact angle increases from the hydrophilic 53° to the hydrophobic 113°. Without considering the shock-wave mechanism, the impact pressure transmitted to the hydrophilic wall is of the same order as the maximum collapse pressure while the impact velocity is an order smaller than the maximum micro-jet velocity. Wall wettability affects collapse through the Bjerknes force and the pressure around the bubble. Preliminary analysis also suggests that the relation between the pressure difference and the intensity of collapse exhibits more patterns than we have assumed, which fits a logistic curve well, and appears not changing with the contact angle or the initial bubble distance.

Calculation of diffusion coefficient of liquid less simple metals

Diffusion coefficient of liquid less simple metals has been studied using linear trajectory (LT) and small-step (SS) diffusion theories of liquid metals with Carnahan–Stirling (CS) approximation. Friction coefficients, the key ingredients of this study, are calculated using effective pair potentials, v(r), and static structure factors, S(q). For v(r), Brettonet–Silbert pseudopotential model has been chosen whereas for S(q), both variational modified hypernetted chain (VMHNC) integral equation and linearized Weeks–Chandler–Andersen (LWCA) perturbation theory have been employed. Calculated friction coefficients are found comparable to the available simulated data. Inclusion of CS approximation increases the value of friction coefficient obtained from hard part which dominates over rest of the coefficients. Applied LWCA theory provides slightly larger values of diffusion coefficients than those obtained from VMHNC. Comparing with literature values, calculated results suggest that the combination of LWCA theory along with LT and SS theories with CS approximation is excellent for calculation of diffusion coefficient.

An effective pseudo-potential lattice Boltzmann model with extremely large density ratio and adjustable surface tension

The pseudo-potential lattice Boltzmann (LB) model is versatile in modeling multiphase flows since the mesoscopic interaction potential enables it to directly describe the nonideal effect evading the tracking or integrating of phase interface. In this paper, we develop an effective pseudo-potential lattice Boltzmann model to simultaneously realize the thermodynamic consistency, the extremely large density ratio, and the adjustable surface tension. Decoupling the mesh space from the momentum space by a scale factor, denser lattice nodes depict the transition region more accurately. The high-precision explicit finite difference method (EFM) further enhances the calculation accuracy of interaction force. The present model is validated to satisfy thermodynamic even at very low temperature, where the liquid–gas density ratio exceeds 1010. The spurious current can be suppressed to a very low level (<0.0007) despite the density ratio reaching tens of thousands. A modified pressure tension is introduced to tune the surface tension free from the influence of the density ratio. The numerical stability of multiphase simulations is significantly improved, and the droplet splashing is successfully reproduced at Reynolds number 25 000, while the density ratio is more than 10 000.

Hybridization and deconfinement in colloidal quantum dot molecules.

The structural, electronic, and optical properties of CdSe/CdS core-shell colloidal quantum dot molecules, a new class of coupled quantum dot dimers, are explored using atomistic approaches. Unlike the case of dimers grown by molecular beam epitaxy, simulated strain profile maps of free-standing colloidal dimers show negligible additional strain resulting from the attachment. The electronic properties of the relaxed dimers are described within a semiempirical pseudopotential model combined with the Bethe-Salpeter equation within the static screening approximation to account for electron-hole correlations. The interplay of strain, hybridization (tunneling splitting), quantum confinement, and electron-hole binding energies on the optical properties is analyzed and discussed. The effects of the dimensions of the neck connecting the two quantum dot building blocks, as well as the shell thickness, are studied.

Unit conversion in pseudopotential lattice Boltzmann method for liquid–vapor phase change simulations

Pseudopotential lattice Boltzmann (LB) model is an effective mesoscopic method for liquid–vapor phase change simulations. In LB methods, calculations are often carried out in lattice units. Thus, a correct mapping from the lattice unit system to the physical unit system is crucial for accurate simulations of practical problems. The unit conversion for liquid–vapor phase change problems is more complicated than single-phase problems, because an equation of state (EOS) for a nonideal fluid is introduced in the pseudopotential two-phase model. In this work, a novel unit conversion method for the pseudopotential LB model is proposed. The basic strategy is to obtain the conversion relations of fundamental units by mapping the surface tension and EOS parameters related to fluid properties, and thus, the unit conversion relations of other quantities are deduced. Numerical simulations of benchmark problems including the film evaporation and the bubble heterogeneous nucleation from a V-shaped cavity are carried out, and the simulation results are converted to the physical unit system by the proposed method. The numerical results demonstrate that the proposed method is able to recover the physical-unit latent heat of the fluid in the film evaporation problem. In the bubble nucleation from a V-shaped cavity problem, the conventional unit conversion method cannot derive the correct superheat temperature in the physical unit, whereas the proposed method based on the fundamental units recovers the critical superheat temperature which is consistent with the analytical result.

Cavitation bubbles with a tunable-surface-tension thermal lattice Boltzmann model

The effects of surface tension and initial input energy on cavitation properties based on a tunable-surface-tension large-density-ratio thermal lattice Boltzmann method pseudo-potential model are investigated. The validity and superiority of the proposed model in simulating the D2 law, Laplace law, and revised thermal two-dimensional Rayleigh–Plesset equation are demonstrated. Moreover, the lattice Boltzmann method was used to study the effects of varied surface tension on cavitation bubble properties for the first time, and the maximum surface tension-to-minimum surface tension ratio of 25 is utilized, which is highly improved compared with previous numerical simulations (<4) and makes our result more clear. The simulation results indicate that for an infinite liquid, the increase in the surface tension will improve the collapse intensity of cavitation bubbles, increasing the collapse pressure, velocity, and temperature and meanwhile reducing the bubble lifetime. For the cavitation bubbles collapsing near a neutral wall, with an increase in the surface tension, the collapse pressure, temperature, and cavitation bubble lifetime trends are the same as in the infinite liquid. However, the collapse velocity is affected by the neutral wall, and the micro-jet becomes wider and shorter. The maximum cavitation bubble radius in an infinite liquid is nearly linearly proportional to the input initial energy. An increase in the surface energy reduces the maximum radius of the cavitation bubbles, while increasing the pressure energy and thermal energy promotes the maximum radius of the cavitation bubbles. This series of simulations proves the feasibility of the proposed model to investigate the thermodynamic process of the cavitation bubbles with high density ratios, wide viscosity ratios, and various surface tensions.

A unified interaction model for multiphase flows with the lattice Boltzmann method

AbstractThe lattice Boltzmann method (LBM) has been increasingly adopted for modelling multiphase fluid simulations in engineering problems. Although relatively easy to implement, the ubiquitous Shan–Chen pseudopotential model suffers from limitations such as thermodynamic consistency and the formation of spurious currents. In the literature, the Zhang–Chen, Kupershtokh et al., the β‐scheme, and the Yang–He alternative models seek to mitigate these effects. Here, through analytical manipulations, we call attention to a unified model from which these multiphase interaction forces can be recovered. Isothermal phase‐transition simulations of single‐component in stationary and oscillating droplet conditions, as well as spinodal decomposition calculations, validate the model numerically and reinforce that the multiphase forces are essentially equivalent. Parameters are selected based on the vapour densities at low temperatures in the Maxwell coexistence curve, where there is a narrow range of optimal values. We find that expressing the model parameters as functions of the reduced temperature further enhances the thermodynamic consistency without losing stability or increasing spurious velocities.

Three-dimensional study of double droplets impact on a wettability-patterned surface

In this paper, a three-dimensional multi-relaxation-time pseudopotential lattice Boltzmann model is adopted to study the double droplets impact on a wettability-patterned surface. The effects of several factors like the wettability difference, the Weber number and the droplet spacing on the droplet dynamic behavior are studied in detail. The numerical results show that the unbalanced Young’s force caused by the wetting difference will induce the droplets to rebound or migrate laterally toward the region with high-wettability. In addition, there exist three evolutionary phases for the double droplets impact on the wettability-patterned surface: the asymmetric spreading phase, asymmetric retracting phase, and wetting equilibrium phase. Further, when the Weber number is relatively smaller, a secondary spreading behavior could be observed which in turn causes an increase in the contact time. Finally, as far as the influence of the droplet spacing is concerned, we find that the flow patterns for different droplet spacings are largely different, and the presence of a air cavity could reduce the contact time.

Numerical simulation of liquid water transport in perforated cracks of microporous layer

As a kind of clean energy, proton exchange membrane fuel cell (PEMFCs) are expected to become power source of vehicles. Microporous layer (MPL) enhances the output performance of PEMFC by regulating water management. In this study, a 3D lattice Boltzmann method (LBM) pseudopotential multicomponent model is applied to investigate the effects of perforated cracks in MPL on liquid water distribution and flow regime of liquid water. The perforated cracks can not only reduce capillary resistance and water saturation but also promote liquid water from capillary fingering to viscous fingering essentially, which means enhancement of the permeability of liquid water in the through-plane direction and reduction of percolation in the in-plane direction. The liquid water in perforated cracks is insensitive to the wettability of MPL. This study can give guidance for the practical design and application of MPL with artificial pore structure.

Two pressure boundary conditions for multi-component multiphase flow simulations using the pseudo-potential lattice Boltzmann model

In this study, two boundary condition (BC) schemes are proposed for the pseudo-potential (PP) lattice Boltzmann method (LBM). The two BC schemes include a modified Convective Boundary Condition (mCBC) and a modified Non-equilibrium Bounceback (mNEBB), and their development is aimed at treating pressure-driven outflow problems for fluids with similar and different density ratios in multi-component multiphase (MCMP) environments. It is the first attempt to incorporate interaction force at boundaries for MCMP fluids. Key limitations of existing LBM boundary schemes for MCMP flow are alleviated. In particular, the constraint of zero-velocity specification at tangential direction is removed by applying the proposed mCBC scheme. In addition, it is demonstrated that multiphase outflow performance is improved with the application of either scheme, while alleviating the nonphysical distortions introduced by the available BC schemes. Three numerical case studies have been conducted to test the proposed scheme. Results have been validated using uncut-off extended domains. These cases are designed to test the induced distortion to the fluids exiting boundaries, examine the scheme’s capability to treat the pressure boundary condition, and explore whether the model can make physically meaningful predictions when these modified BCs are applied. The mCBC scheme is shown to be more capable to correctly treat such pressure specified boundary conditions.

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.

Lattice Boltzmann simulation of wetting gradient accelerating droplets merging and shedding on a circumferential surface

A lattice Boltzmann method (LBM) based on Shan-Chen pseudo-potential model is used to investigate the process of droplets merging and shedding on a gradient wetting circular surface. The effects of wetting gradient, radius, and radius ratio on droplet merging and shedding were mainly explored. The results show that applying a wetting gradient on the circumferential surface can accelerate the process of droplet merging and shedding. The velocity of droplets merging and shedding increase with the increase of the wetting gradient. The more hydrophilic the original surface, the better the optimization effect of accelerating drainage is by applying a wetting gradient. The radius and radius ratio significantly affect droplets merging and shedding on the gradient wetting surface. The larger the radius and radius ratio, the shorter the droplets merging and shedding time.

Bridging confined phase behavior of CH[formula omitted]-CO[formula omitted] binary systems across scales

Phase behavior of confined fluids may deviate significantly from that of the bulk fluid due to the fluid–wall interactions being a significant portion of all intermolecular interactions under confinement. Despite recent advancements in understanding confined phase behavior of pure fluids, confined phase behavior of mixtures remains an understudied topic. In this work, we examine the confined phase behavior of a CH4-CO2 binary system by combining Monte Carlo (MC) simulations, a cubic equation of state (EoS), and the lattice Boltzmann method (LBM). First, the effects of confinement on density and phase distribution in nano-size pores are established using Gibbs Ensemble MC calculations, which produce precise results of liquid and vapor confined pressures and account for the modification of the phase change location. By comparing the phase envelopes of bulk and confined mixtures at a fixed temperature, it is observed that the phase envelopes shrink with reductions in pore size. Based on this observation, we extend a modified Peng–Robinson EoS, which was originally developed for pure fluids under confinement, to mixtures via van-der-Waals-type mixing rules and by accounting for shifts in the critical properties of confined CH4-CO2. The resulting phase envelopes are in good agreement with the MC data. In addition, a local density model is used in combination with the confined EoS to calculate adsorption isotherms of CH4-CO2 mixtures and to characterize the behavior of confined matter in nanopores. Finally, we incorporate this EoS in a multicomponent multiphase LBM that uses a pseudopotential model to represent intermolecular forces. This workflow utilizes multiscale simulation techniques to bridge the behavior of multicomponent systems across scales and to shed light on the confined phase behavior of CH4-CO2 binary systems.

A mesoscopic model for simulating the physisorption process in nanopores

In this study, we applied the lattice Boltzmann pseudopotential model to systematically simulate the phase behavior of the confined fluids and the physisorption process in nanopores. The simulation results indicated that the pseudopotential model could well describe the thermodynamic and phase behaviors of the confined fluids on the molecular level. By performing numerical adsorption experiments in nanopores, the model accurately captured the essential characteristics of types I and IV physisorption isotherms in micropores and mesopores, respectively, and revealed the underlying mechanisms of adsorption hysteresis induced by adsorption metastability and network effects. The present work shows the potential and advantages of the pseudopotential model to simulate the physisorption process in nano-porous media.

Influence of pressure and composition on electronic properties, phonon frequencies, and sound velocity for the zinc-blende GaAs1-xNx alloy

We investigated the electronic, phonon frequencies, and sound velocity of GaAs1-xNx ternary semiconductor alloys with the zinc-blende crystal structure over the entire nitrogen concentration range (with x from 0 to 1) using the empirical pseudo-potential model within the virtual crystal approximation including the compositional disorder effect. The pressure-dependent electronic, phonon frequencies and sound velocity of GaAs1-xNx ternary alloy have been studied. Our findings and the existing experimental data are found to be in good agreement. According to the dependence on pressure, a rising bandgap is predicted for GaAs1-xNx alloys at high-pressure values. According to the findings of this study, the GaAs1-xNx characteristics could have substantial optoelectronic applications in the infrared and mid-infrared spectral ranges.

Simulating wetting phenomenon on curved surfaces based on the weighted-orthogonal multiple-relaxation-time pseudopotential lattice Boltzmann model

In this work, our recently developed weighted-orthogonal multiple-relaxation-time pseudopotential lattice Boltzmann (PLB) model [J. Tang et al., “Multiphase flow simulation with three-dimensional weighted-orthogonal multiple-relaxation-time pseudopotential lattice Boltzmann model,” Phys. Fluids 33, 123305 (2021)] is further extended to simulate the complex wetting phenomenon on curved surfaces at large density ratios (ρl/ρg∼1000), where a new geometrical formulation scheme is proposed to characterize the wettability of the curved boundary. Compared with the existing geometrical formulation schemes, the significant advantage of the new scheme is that the characteristic vector representing the phase interface is no longer needed, and, thus, the complex calculations induced by the characteristic vector are avoided, which significantly simplifies computations and facilitates the implementation of the geometrical formulation scheme on curved boundaries. Meanwhile, it is applicable to both two-dimensional and three-dimensional (3D) simulations and maintains the feature of setting the contact angle explicitly. Furthermore, the numerical results of four classical wetting phenomenon benchmark cases at large density ratios predicted by the present model agree well with the analytical solutions, numerical results, or experimental results in the literature. It exhibits the capability of the present model coupled with the proposed scheme to simulate the wetting phenomenon involving curved surfaces with good numerical accuracy. Note that, to the author's knowledge, this is the first time that the geometrical formulation scheme has been successfully adopted in the 3D PLB model to simulate the wetting phenomenon on curved surfaces. We believe that this work lays the foundation for further application of the PLB model to the complex wetting phenomenon.