Different Diffusivity Effects on the Radial Viscous Fingering in a Porous Medium: Theoretical Analyses and Numerical Simulations
摘要
The effects of the different diffusivities of the displacing and displaced components on the growth of miscible viscous fingering in a radial porous medium are analyzed theoretically and numerically. By considering viscosity profiles determined by the diffusivity ratio and the log-viscosity parameters, six stability regimes are identified. For each regime, the influences of physical parameters on the onset and the growth of the radial viscous fingering are examined using linear stability analysis (LSA) and numerical simulations. In the present regime IVU, where viscosity decreases monotonically with an inflection point, a new dynamic stability criterion is proposed to explain the instabilities without viscosity mismatch, and its validity is demonstrated through linear stability analysis (LSA) and numerical simulations. Although the system is initially stable, double-diffusive effects render it unstable in the present regime V. Unlike a system with identical diffusivities, the Péclet number delays the onset and suppresses the growth of fingering motion in regimes IVU and V. Because of the differences in the spatio-temporal domains between the linear stability analysis (LSA) and the numerical simulations, visible motion is not observed in the present simulations, particularly for instabilities that grow slowly.