Control of viscous fingering: From the perspective of energy evolution

Improving the ability to control viscous fingering instabilities plays an essential role in a wide variety of scientific and engineering fields. Based on linear stability analysis, we present an energy model characterized by the viscous dissipation rate, which can reflect the evolution process of the fluid-fluid interface, and predictions of control schemes are obtained from the model. One type of scheme is to control the morphological patterns of instability through initial disturbances. Another series of schemes is to control whether the viscous fingering instability is suppressed or continues to develop by different scaling laws of injection rate versus time based on the variational method. Furthermore, a stable and continual forward movement of the interface is achieved by a periodic suppression scheme, which is significant in practical applications. The effectiveness of the energy model and all control schemes are well verified by experiments.