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The original Shan-Chen’s pseudopotential Lattice Boltzmann Model (LBM) has continuously evolved during the past two decades. However, despite its capability to simulate multiphase flows, the model still faces challenges when applied to multicomponent-multiphase flows in complex geometries with a moderately high-density ratio. Furthermore, classical cubic equations of state usually incorporated into the model cannot accurately predict fluid thermodynamics in the near-critical region. This paper addresses these issues by incorporating a crossover Peng–Robinson equation of state into LBM and further improving the model to consider the density and the critical temperature differences between the CO2 and water during the injection of the CO2 in a water-saturated 2D homogeneous porous medium. The numerical model is first validated by analyzing the supercritical CO2 penetration into a single narrow channel initially filled with H2O, depicting the fundamental role of the driving pressure gradient to overcome the capillary resistance in near one and higher density ratios. Significant differences are observed by extending the model to the injection of CO2 into a 2D homogeneous porous medium when using a flat versus a curved inlet velocity profile.

Abstract Pseudopotential lattice Boltzmann model (LBM) for multiphase flow has been widely studied due to its conceptual simplicity and computational efficiency. Additional interaction force terms are proposed to adjust mechanical stability condition for thermodynamic consistency in pseudopotential force. However, the additional force terms introduce a new non-physical effect in fourth-order macroscopic equation, which causes a variation of density ratio with different relaxation times in the multiphase-relaxation-time (MRT) LBM. In this work, a fourth-order analysis of force term in MRT LBM is presented to identify the fourth-order terms in recovered Navier–Stokes equations. Through the higher-order analysis, two methods are proposed to eliminate this effect. A series of numerical tests of planar interface and droplet are conducted to validate the analyses. [ABSTRACT FROM AUTHOR]

In this paper, an improved lattice Boltzmann Shan‒Chen model coupled with Carnahan-Starling equation of state (C-S EOS) and the exact differential method (EDM) force scheme is used to simulate the cavitation bubble collapse in the near-wall region. First, the collapse of a single cavitation bubble in the near-wall region was simulated; the results were in good agreement with the physical experiment and the stability of the model was verified. Then the simulated model was used to simulate the collapse of two cavitation bubbles in the near-wall region. The main connection between the two cavitation bubble centre lines and the wall surface had a 45° angle and parallel and the evolution law of cavitation bubbles in the near-wall region is obtained. Finally, the effects of a single cavitation bubble and double cavitation bubble on the wall surface in the near-wall region are compared, which can be used to study the method to reduce the influence of cavitation on solid materials in practical engineering. The cavitation bubble collapse process under a two-dimensional pressure field is visualized, and the flow field is used to describe the morphological changes of cavitation bubble collapse in the near-wall region. The improved lattice Boltzmann Method (LBM) Shan‒Chen model has many advantages in simulating cavitation problems, and will provide a reference for further simulations.

• Substrate heating destabilizes contact angle schemes in pseudopotential LB model. • Fluid density variation near wall deforms the simulated droplet interface shape. • Spurious current causes inaccurate Marangoni vortex and temperature distribution. • A special ghost fluid layer is proposed to improve numerical stability and accuracy. The PP scheme (primitive pseudopotential-based scheme), the MP scheme (modified pseudopotential-based scheme) and the IVD scheme (improved virtual-density scheme) are the three most widely used contact angle schemes in pseudopotential lattice Boltzmann (LB) models to simulate wetting characteristics of multiphase flow over solid surfaces under isothermal conditions. In this paper, we apply these schemes to simulate the problem of sessile droplet evaporation on a heated substrate, which is an example of non-isothermal phase-change heat transfer process. It is found that the substrate heating effect destabilizes algorithms of these schemes in certain ranges of contact angles of a heated substrate. The droplet interface shapes simulated by the PP scheme and the MP scheme are inaccurate at obtuse contact angles due to large fluid density variations near the wall. The spurious currents near the droplet triple-phase contact line are very large in the MP scheme, causing the deformation of the Marangoni vortex shape inside the droplet and the erroneous droplet interface temperature distribution near the triple-phase contact line. The addition of a special ghost fluid layer on the wall proposed in this study can improve numerical stability of the PP and the MP schemes for application under non-isothermal conditions as well as under high saturated liquid/vapor density ratios. Although the IVD Scheme (with the nearest fluid layer temperatures above the heated wall chosen for calculating the effective mass of wall nodes) is also stable at low liquid/vapor density ratios, its numerical stability at high density ratios is not as robust as those of the PP and the MP schemes if a special ghost fluid layer is added in these schemes. It is shown that by adding such a special ghost fluid layer on the wall, large near-wall fluid density variations diminish in the PP and MP schemes and accurate droplet interface shapes can be recovered at obtuse contact angles. The spurious current in the MP schemes can be also reduced and accurate Marangoni vortex shapes in the droplet and droplet interface temperature distribution near the triple-phase contact line can be predicted. [ABSTRACT FROM AUTHOR]

In this work, a third-order Chapman–Enskog analysis of the multiple-relaxation-time (MRT) pseudopotential lattice Boltzmann (LB) model for multiphase flow is performed for the first time. The leading terms on the interaction force, consisting of an anisotropic and an isotropic term, are successfully identified in the third-order macroscopic equation recovered by the lattice Boltzmann equation (LBE), and then new mathematical insights into the pseudopotential LB model are provided. For the third-order anisotropic term, numerical tests show that it can cause the stationary droplet to become out-of-round, which suggests the isotropic property of the LBE needs to be seriously considered in the pseudopotential LB model. By adopting the classical equilibrium moment or setting the so-called “magic” parameter to 1/12, the anisotropic term can be eliminated, which is found from the present third-order analysis and also validated numerically. As for the third-order isotropic term, when and only when it is considered, accurate continuum form pressure tensor can be definitely obtained, by which the predicted coexistence densities always agree well with the numerical results. Compared with this continuum form pressure tensor, the classical discrete form pressure tensor is accurate only when the isotropic term is a specific one. At last, in the framework of the present third-order analysis, a consistent scheme for third-order additional term is proposed, which can be used to independently adjust the coexistence densities and surface tension. Numerical tests are subsequently carried out to validate the present scheme. [ABSTRACT FROM AUTHOR]

The original Shan-Chen's pseudopotential Lattice Boltzmann Model (LBM) has continuously evolved during the past two decades. However, despite its capability to simulate multiphase flows, the model still faces challenges when applied to multicomponent-multiphase flows in complex geometries with a moderately high-density ratio. Furthermore, classical cubic equations of state usually incorporated into the model cannot accurately predict fluid thermodynamics in the near-critical region. This paper addresses these issues by incorporating a crossover Peng–Robinson equation of state into LBM and further improving the model to consider the density and the critical temperature differences between the CO2 and water during the injection of the CO2 in a water-saturated 2D homogeneous porous medium. The numerical model is first validated by analyzing the supercritical CO2 penetration into a single narrow channel initially filled with H2O, depicting the fundamental role of the driving pressure gradient to overcome the capillary resistance in near one and higher density ratios. Significant differences are observed by extending the model to the injection of CO2 into a 2D homogeneous porous medium when using a flat versus a curved inlet velocity profile. [ABSTRACT FROM AUTHOR]

• Thermodynamic phase transition in nanopores is directly modeled by using a molecular-level approach. • Effects of adsorption and capillary pressure on phase equilibrium in nanoscale are evaluated. • Vapor-liquid contact angle is used to characterize molecular scale fluid–solid interaction. • Phase behavior in a nanoporous medium with chemical heterogeneity is presented. Owing to the strong interaction between fluid molecules and solid surface, thermodynamic phase behavior of fluids in nanopores deviates from that at bulk condition. In this work, a pseudopotential lattice Boltzmann method is employed to directly model phase equilibrium of methane in nanopores. The effects of adsorption and fluid–solid force on confined phase behavior are studied. In the absence of solid walls, our simulation of nanoscale droplets is consistent with prediction from thermodynamic model coupling Peng-Robinson equation of state and capillary pressure. The shifted phase equilibrium is compared with Kelvin equation. When the pore space is confined by solid walls, heterogeneous density distributions in nanopores are developed by adsorption. It is observed that the apparent critical temperature and critical pressure decrease whereas critical density increases in nanopores from the simulated co-existence curves. In addition, it is found that a larger fluid–solid force leads to a more heterogeneous density distribution in nanopores. However, the average liquid/vapor density and apparent critical temperature in confined space are not significantly affected by the strength of fluid–solid force. Density of gas in equilibrium with condensed liquid, on the other hand, is significantly decreased with increasing fluid–solid force. We propose that the phase equilibrium in nanopores under different fluid–solid forces can be characterized by using contact angle. In the end, we extend this method to model the phase equilibrium in a nanoporous medium with chemical heterogeneity. [ABSTRACT FROM AUTHOR]

In this paper, an improved lattice Boltzmann Shan‒Chen model coupled with Carnahan-Starling equation of state (C-S EOS) and the exact differential method (EDM) force scheme is used to simulate the cavitation bubble collapse in the near-wall region. First, the collapse of a single cavitation bubble in the near-wall region was simulated; the results were in good agreement with the physical experiment and the stability of the model was verified. Then the simulated model was used to simulate the collapse of two cavitation bubbles in the near-wall region. The main connection between the two cavitation bubble centre lines and the wall surface had a 45° angle and parallel and the evolution law of cavitation bubbles in the near-wall region is obtained. Finally, the effects of a single cavitation bubble and double cavitation bubble on the wall surface in the near-wall region are compared, which can be used to study the method to reduce the influence of cavitation on solid materials in practical engineering. The cavitation bubble collapse process under a two-dimensional pressure field is visualized, and the flow field is used to describe the morphological changes of cavitation bubble collapse in the near-wall region. The improved lattice Boltzmann Method (LBM) Shan‒Chen model has many advantages in simulating cavitation problems, and will provide a reference for further simulations. [ABSTRACT FROM AUTHOR]