Lattice Boltzmann simulation of immiscible displacement in the complex micro-channel

The immiscible displacement process in micro-channel, which widely existes in daily life and industrial production, is an important research subject. This subject is a typical contact line problem involving complicated fluid-fluid interactions and fluid-solid interactions which have attracted the interest of many scholars. Although the immiscible displacement in micro-channels has been studied by some researches, the problem is still not fully understood because the mechanism of the immiscible displacement is very complex. In order to further explain the physical mechanism of immiscible displacement process in micro-channels, detailed numerical simulations are carried out in a complex micro-channel containing a semicircular cavity and a semicircular by bulge using an improved pseudo-potential lattice Boltzmann method (LBM). This model overcomes the drawback of the dependence of the fluid properties on the grid size, which exists in the original pseudo-potential LBM. Initially, the cavity is filled with the liquid and the rest of the area is filled with its vapour. The semicircular bulge represents the roughness of the micro-channel. The approach is first validated by the Laplace law. The results show that the numerical results are in good agreement with the theoretical predictions. Then the model is employed to study the immiscible displacement process in the micro-channel. The effects of the surface wettability, the surface roughness, the viscosity ratio between the liquid phase and the gas phase, and the distance between the semicircular cavity and the semicircular bulge are studied. The simulation results show that the influence of the surface wettability on the displacement process is a decisive factor compared with other factors. With the increase of the contact angle, the displacement efficiency increases and the displacement time decreases. When the contact〉is larger than a certain value, all of the liquid can be displaced from the cavity. At that time, the displacement efficiency is equal to 1. The above results are consistent with the theoretical prediction that with the increase of the contact angle, the liquid is easily driven out of the cavity because the adhesion force of the liquid in the cavity decreases. On the other hand, the influence of the surface roughness on the displacement process is more complex. The displacement efficiency increases with the radius of the semicircle bulge increasing in a certain range. When the radius is larger than a certain value, the liquid cannot be ejected from the cavity due to the velocity around the cavity is too small. Furthermore, the liquid cannot be displaced from the cavity at a small viscosity ratio. As the viscosity ratio increases, the displacement efficiency increases and the displacement time decreases. As for the distance between the semicircular bulge and the semicircular cavity, it promotes the displacement process at an early stage. When the distance exceeds a certain value, it has little effect on the displacement process.