Optimal control of viscous fingers in radial Hele-Shaw cell

Abstract

This work considers the displacement of a resident fluid in a radial Hele-Shaw cell by an invading low viscosity fluid driven by time-dependent injection rates. Finger formation in the circular interface through a sequence of bifurcations may be minimized by the optimal choice of a time-dependent injection rate. Approximate solutions of fluid equations predict how bifurcations can be suppressed or strongly reduced. Based on a computational fluid-dynamic approach, the magnitude of the fluctuations of invading interface is numerically evaluated, leading to the identification of the optimal parameter choice for any injection rate family. The combination of two time-dependent injection rates is investigated, where one decreases as a power-law and the second increases linearly. Results for a well tuned change between the two regimes reduce the injection time as compared to those based on a single rate whole process, with similar or reduced effects on interface fluctuations.