Color-gradient lattice Boltzmann modeling of immiscible two-phase flows on partially wetting surfaces

Abstract

A zero-interfacial-force condition is derived and implemented to improve the wetting boundary scheme for a lattice Boltzmann color-gradient model. This new wetting boundary scheme is validated by two static problems, i.e. a droplet resting on a flat surface and a cylindrical surface, and one dynamic problem, i.e. the capillary filling in a two-dimensional channel. In these simulations, we observe that non-physical mass transfer is suppressed and spurious velocities become smaller. Meanwhile, accurate results including dynamic contact line movement are achieved for a broad range of contact angles. The model is then applied to study the displacement of immiscible fluids in a two-dimensional channel. Both the displacement velocity and the change rate of finger length are found to exhibit a linear dependence on the contact angle at the viscosity ratio of unity. The displacement velocity decreases but the change rate of finger length increases with increasing capillary number, while the displacement velocity tends to be constant, i.e. two-thirds of the maximum inlet velocity, at high viscosity ratios or low capillary numbers. In contrast to the displacement velocity, the change rate of finger length is negligible at high viscosity ratios or low capillary numbers, where the finger length is in an equilibrium state, while the equilibrium finger length itself is smaller at a higher viscosity ratio or a lower capillary number.

Inertial Effects During the Process of Supercritical CO2 Displacing Brine in a Sandstone: Lattice Boltzmann Simulations Based on the Continuum‐Surface‐Force and Geometrical Wetting Models

“…However, with the introduction of the geometrical wetting models, the value of the order parameters on the solid boundary nodes are extrapolated from nearby fluid boundary nodes (Leclaire et al, 2017) instead of having a preassigned value in the FD wetting model; thus, the color gradients between fluid and solid nodes are minimized. Furthermore, a zero-interfacial-force scheme (Yu et al, 2018) can be applied to the CSF-based model to further reduce the unbalanced forces near the three-phase contact line minimizing the spurious currents, which is particularly important for geometrical wetting models at contact angle far away from 90 • , as mentioned in section 2.2.…”

“…The first step is the extrapolation of to solid boundary nodes (Leclaire et al, 2017), so that the color gradient at fluid boundary nodes is minimized according to equation ( 5), thus guaranteeing that there are no strong interactions between the fluid nodes and solid nodes. The second step is to apply the zero-interfacial-force scheme (Yu et al, 2018) by extrapolating the normal direction vector n of the fluid interface to solid boundary nodes as the calculation of interface curvature in equation ( 14) at the three-phase contact line requires the value of n at solid boundary nodes. In such case, the force F in equation ( 8) is minimized at the three-phase contact line which significantly reduces the spurious currents.…”

Pore-scale study of counter-current imbibition in strongly water-wet fractured porous media using lattice Boltzmann method

“…The LB color-gradient model is employed to solve the counter-current spontaneous imbibition processes in this work. It is based on the work of Halliday et al [34][35][36] and incorporates the improvements given by Xu et al 24 and Yu et al 37 . The indicator or color function ρ N is used to distinguish one fluid from the other, and it is defined as…”

Lattice Boltzmann Simulation of Immiscible Two-Phase Displacement in Two-Dimensional Berea Sandstone

“…On the contrary, pore-scale simulation can provide local detailed information about the flow field. The previous works on pore-scale simulation of immiscible two-phase flows in porous media [5][6][7][8][9][10] have been shown to be capable of capturing the effects of various factors, e.g., capillary number, viscosity ratio, surface wettability, and media heterogeneity. However, due to the inherent complexity related to interface evolution, heterogeneous geometry, dominant capillarity, and moving contact line, the computational simulation of multiphase displacement in realistic porous media still remains a research challenge.…”

“…The colour gradient LBM was first proposed by Rothman and Keller [13], and has been widely used for the simulation of immiscible fluids [9,12,[23][24][25][26]. To obtain an accurate and detailed understanding of the pore-scale mechanisms within porous media, Xu et al [25] proposed a new algorithm for imposing the contact angle on the solid surface in the colour gradient LBM.…”