Gray free-energy multiphase lattice Boltzmann model with effective transport and wetting properties

Abstract

The paper shows that it is possible to combine the free energy lattice Boltzmann approach to multi-phase modelling of fluids involving both liquid and vapour with the partial bounce back lattice Boltzmann approach to modelling effective media. Effective media models are designed to mimic the properties of porous materials with porosity much finer than the scale of the simulation lattice. In the partial bounce back approach, an effective media parameter or bounce back fraction controls fluid transport. In the combined model, a wetting potential is additionally introduced that controls the wetting properties of the fluid with respect to interfaces between free space (white nodes), effective media (grey nodes) and solids (black nodes). The use of the wetting potential combined with the bounce back parameter gives the model the ability to simulate transport and sorption of a wide range of fluid / material systems. Results for phase separation, permeability, contact angle and wicking in grey media are shown. Sorption is explored in small sections of model multi-scale porous systems to demonstrate two-step desorption, sorption hysteresis and the ink-bottle effect.

Three-dimensional lattice Boltzmann method benchmarks between color-gradient and pseudo-potential immiscible multi-component models

“…For example, Mendoza et al 7 proposed a lattice Boltzmann approach to solve generalized Navier-Stokes equations where the porosity of the medium is taken into account. Similar e®orts are being made for multi-scale multi-phase°ow modeling with the gray LBM based on free-energy 8 and pseudo-potential method. 9 The so-called inter-particle PPM proposed by Shan and Chen, which takes advantage of the molecular/mesoscopical nature of the LBM and executes an interaction between particle distribution functions of di®erent species, has always been a popular alternative to the CGM.…”

Homogenized color-gradient lattice Boltzmann model for immiscible two-phase flow in multiscale porous media

“…3(b). Therefore, to achieve the wettability change in the porous region with adjacent porosities, we correct θ a with the average solid fraction S according to the Cassie-Baxter equation 36,53 cos(θ a ) ¼ S cos(θ r ), (20) where S is a non-local value, representing the joint contribution of all solid fractions around the vicinity node, which can also be obtained from the eighth-order isotropic discretization…”

“…In the following, some tests of droplet scenario, which are also considered in other DBS-LBMs, are implemented to verify physical consistency and numerical stability of the MFCG model. 20,36 As shown in Fig. 8(a), the simulation domain is a fully periodic and homogenized porous medium with the dimension of H = 100 lu, where all lattice nodes have identical porosity ε.…”

“…18,19,[30][31][32][33] Besides, due to the significant advances in conservative phase field models for large-density-ratio fluids modeling, 34,35 some homogenized DBS-LBMs based on such models have gradually developed in recent years. [36][37][38] Although the intrinsic correlation between the grayscale model and the force-adjusted model has been proven numerically, 30 the selection of bounce-back fraction in the former is uncertain, e.g., its relation with structural permeability is not straightforward, making it difficult to correspond with macroscopic parameters. 28 However, model parameters are directly related to macro quantities in force-adjusted LB, which has greater potential for further development to solve multiphase and multiscale flow problems.…”

Homogenized Lattice Boltzmann Model for Simulating Multi-Phase Flows in Heterogeneous Porous Media

“…Although the aforementioned homogenization methods have been heavily discussed and further developed for single-phase fluids [24, 27-29, 32, 33], this is not the case for multi-phase or multi-component fluids. Only a few methods combining GS and multiphase physics [34][35][36] as well as methods combining other homogenization approaches with multi-component physics [37,38] have been reported recently. However, despite the fact that the multi-component Shan-Chen method (MCSC) is most widely used for studying all kinds of immiscible fluids, only one homogenized method has been developed combining GS with MCSC [39].…”