Control of viscous fingering: From the perspective of energy evolution

An energy model is developed to describe the linear viscous fingering (VF) phenomena from the perspective of evolution paths of energy dissipation rate. By means of the variational method, rate-altering control schemes with different scaling laws are constructed in the energy model to control whether the VF instability develops or is suppressed. Furthermore, a stable and continuous forward movement of the fluid-fluid interface is achieved through a periodic suppression scheme. The effectiveness of the energy model and all control schemes are well verified by our experiments.