IMMISCIBLE VISCOUS FINGERING IN AN ANNULAR HELE-SHAW CELL WITH A SOURCE

The displacement of a viscous fluid from an annular Hele-Shaw cell with a source of finite radius by a less viscous one is studied. The fluids are considered immiscible, so that surface tension forces are acting on the interface. Linear analysis shows a stabilizing effect of surface tension and the presence of a critical interfacial mode with the highest rate of growth. The number of the critical mode is strongly dependent on the capillary number and is virtually independent of the viscosity ratio. The consistency with experimental data is acceptable for small capillary numbers. Numerical simulation of the displacement process is conducted using the continuum surface force (CSF) model. A stabilizing effect of surface tension clearly appears at the initial stage of displacement. The number of generated viscous fingers turns out to be in satisfactory agreement with linear theory and experimental data. However, the lateral surface of viscous fingers can lose stability at the subsequent (nonlinear) stage of displacement.