Numerical simulations of miscible displacement in an inclined channel by lattice Boltzmann method

Abstract

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 RaC<105, 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 t1+RaC/106. When considering the effect of the viscosity ratio in the K–H instability region, the displacement efficiency scales as η∼t1+RaC/106R0.1. 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.