Numerical Simulation on the Onset of Radial Fingering in a Hele-Shaw Cell or a Porous Medium

Numerical simulations on the onset and the growth of viscous fingering during the miscible displacement due to the radial source flow were conducted. With introduction of a new stability criterion, the critical log-viscosity ratio, R-c, was found as a function of the Peclet number, Pe. Similar to the previous linear stability analyses, Pe made the system unstable, i.e., accelerated the onset of instability. For a large Pe system, the present numerical simulation yielded much stable results than the previous theoretical predictions This discrepancy was commonly encountered in the comparison between the theoretical prediction and the experimental finding. Additionally, the difference between the rectilinear system and the present one was also discussed. The present system was found more insensitive to the Peclet number than the rectilinear one.