Forcing term in single-phase and Shan-Chen-type multiphase lattice Boltzmann models

Pore-scale modeling of multiphase reactive transport with phase transitions and dissolution-precipitation processes in closed systems

A pore-scale model based on the lattice Boltzmann (LB) method is developed for multiphase reactive transport with phase transitions and dissolution-precipitation processes. The model combines the single-component multiphase Shan-Chen LB model [X. Shan and H. Chen, Phys. Rev. E 47, 1815 (1993)], the mass transport LB model [S. P. Sullivan et al., Chem. Eng. Sci. 60, 3405 (2005)], and the dissolution-precipitation model [Q. Kang et al., J. Geophys. Res. 111, B05203 (2006)]. Care is taken to handle information on computational nodes undergoing solid-liquid or liquid-vapor phase changes to guarantee mass and momentum conservation. A general LB concentration boundary condition is proposed that can handle various concentration boundaries including reactive and moving boundaries with complex geometries. The pore-scale model can capture coupled nonlinear multiple physicochemical processes including multiphase flow with phase separations, mass transport, chemical reactions, dissolution-precipitation processes, and dynamic evolution of the pore geometries. The model is validated using several multiphase flow and reactive transport problems and then used to study the thermal migration of a brine inclusion in a salt crystal. Multiphase reactive transport phenomena with phase transitions between liquid-vapor phases and dissolution-precipitation processes of the salt in the closed inclusion are simulated and the effects of the initial inclusion size and temperature gradient on the thermal migration are investigated.

Forcing scheme in pseudopotential lattice Boltzmann model for multiphase flows

The pseudopotential lattice Boltzmann (LB) model is a widely used multiphase model in the LB community. In this model, an interaction force, which is usually implemented via a forcing scheme, is employed to mimic the molecular interactions that cause phase segregation. The forcing scheme is therefore expected to play an important role in the pseudoepotential LB model. In this paper, we aim to address some key issues about forcing schemes in the pseudopotential LB model. First, theoretical and numerical analyses will be made for Shan-Chen's forcing scheme [Shan and Chen, Phys. Rev. E 47, 1815 (1993)] and the exact-difference-method forcing scheme [Kupershtokh et al., Comput. Math. Appl. 58, 965 (2009)]. The nature of these two schemes and their recovered macroscopic equations will be shown. Second, through a theoretical analysis, we will reveal the physics behind the phenomenon that different forcing schemes exhibit different performances in the pseudopotential LB model. Moreover, based on the analysis, we will present an improved forcing scheme and numerically demonstrate that the improved scheme can be treated as an alternative approach to achieving thermodynamic consistency in the pseudopotential LB model.