Linear stability analysis on the onset of the viscous fingering of a miscible slice in a porous medium

The onset of miscible viscous fingering of a miscible high viscosity slice analyzed theoretically in connection with the spreading of a contaminant in groundwater. Considering the effects of a finite extent of the high viscosity region, new stability equations were derived in a similar domain and attempted to solve them with and without quasi-steady state approximation. The initial growth rate analysis showed that initially the system was unconditionally stable regardless of the width of the high viscosity slice. The effects of the finite extension and the viscosity contrast on the stability characteristics are systematically studied and compared with the previous theoretical results. This study has found that there is a critical time for the disturbance to start to grow and also there is a critical width for the growth rate to become always negative, i.e. the system is unconditionally stable under critical time and critical width.