Control of instability by injection rate oscillations in a radial Hele-Shaw cell

Small spatial perturbations grow into fingers along the unstable interface of a fluid displacing a more viscous fluid in a porous medium, reducing the efficiency of fluid displacement applications. For analogous flow in a radial Hele-Shaw cell, a combined analytical and experimental study reveals that linear instability of the interface is mildly mitigated by adding to the base injection low-frequency oscillations of small magnitude and, to a lesser extent, high-frequency oscillations of large amplitude. This is due to selective suppression of the growth of large wave numbers in the linear regime. By contrast, adding oscillations of an intermediate frequency significantly destabilizes the interface.