Improving the staircase approximation for wettability implementation of phase-field model: Part 2 – Three-component permeation

Abstract

In this study, the displacement dynamics of compound droplet inside porous medium with complex structure is numerically investigated by the newly-proposed wetting boundary treatments in Part 1 [1]. The compound droplet consists of two immiscible fluids surrounded by another fluid forming a three-phase system. To investigate the compound droplet's penetration and spreading in two regimes, the conservative phase-field model is solved via the lattice Boltzmann method (LBM) at different wettability and governing non-dimensional numbers including the Reynolds number (25-100), Weber number (100-1000), and density ratio (7.5-750). Moreover, the permeation and spreading of each droplet, without the presence of the other in the binary system, is compared with those of ternary. It is revealed that the way the penetration is influenced by the variation of surface tension, wettability, and density ratio completely depends on the value of Bond number and the capillary or gravitational-dominant regimes. Furthermore, it appears that in the capillary-dominant regime, the migration pattern of one droplet cannot be evaluated independent of the other, since the factors affecting the capillary pressure and viscous coupling on one, affects the penetration and spreading of the other. Finally, it is identified that ternary penetration is slower than binary and the presence of the other droplet confines the early stage spreading in the ternary system.