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Introduction: This study investigates the displacement of two miscible fluids within an inclined porous medium at the pore scale, highlighting how the pore-scale microstructure, inclination angle, and viscosity ratio affect the interfacial instability between two fluids during displacement processes. Methods: The lattice Boltzmann Method (LBM) is employed to solve the governing equations. Two distribution functions are used to simulate the velocity field and the concentration field, respectively. Results and discussion: An increase in inclination angle exacerbates the interfacial instability between fluids and the viscous fingering phenomenon. This viscous fingering expands the sweep range of displacing fluids, which improves the displacement efficiency. When θ≥ 50°, further increase in inclination angle will not cause significant changes in displacement efficiency. In addition, the viscosity ratio is a key factor affecting displacement efficiency. The larger the viscosity ratio, the greater the displacement efficiency. Furthermore, the critical viscosity ratio has been found, and any increase in the viscosity ratio above the critical value will not affect the displacement efficiency. [ABSTRACT FROM AUTHOR]

The interfacial instability between miscible fluids in a channel is determined by many factors, such as viscosity contrast and the inclination angle. Considering the effect of the gravity field, we investigate the displacement phenomenon between two miscible fluids with different viscosities in an inclined channel. The results show that when the concentration Rayleigh number Ra C < 10 5 , the inclination angle θ ranges from 0 ° to 90 ° , and the natural logarithm of the viscosity ratio R > 0; there are three fluid–fluid interfacial instability regions, namely, viscous fingering, "Kelvin–Helmholtz" (K–H) instability, and "Rayleigh–Taylor" (R–T) instability. A scaling analysis is developed to describe the time evolution of the displacement as described by the displacement efficiency at a fixed viscous ratio. Our analysis indicates that in the viscous fingering region, the time evolution of the displacement efficiency gradually increases with t scaling due to fingering formations; in the K–H and R–T regions, the displacement efficiency rapidly increases with t 1 + Ra C / 10 6 . When considering the effect of the viscosity ratio in the K–H instability region, the displacement efficiency scales as η ∼ t 1 + Ra C / 10 6 R 0.1 . In addition, when the inclination angle is negative or R < 0, the instability phenomenon is not obvious, and the displacement efficiency decreases as the inclination angle or R decreases. [ABSTRACT FROM AUTHOR]

The solid particles with different sizes exist widely, like cell separation, food processing, water treatment, thus, investigating the motion of the solid particles with different sizes is important. This study investigates the motion of a pair of neutrally buoyant circular particles with different sizes in a lid-driven square cavity using the lattice Boltzmann method. The motion of the circular particles with different sizes and that of the circular particles with identical sizes are quite different. The steady trajectories of the circular particles with identical sizes are identical, which is not affected by the Reynolds number. Differently, the circular particles with different sizes orbit along different steady trajectories, namely, the steady trajectory of the small particle is closer to the walls of the square cavity, while that of the large particle shrinks toward the center of the square cavity, which may provide us a possible method to separate them. However, it is not always effective, if the Reynolds number is low, the velocity difference between the circular particles with different sizes is small, which may fail to separate them completely. [ABSTRACT FROM AUTHOR]