Control of viscous fingering patterns in a radial Hele-Shaw cell.
We study numerically and experimentally the dynamics and control of viscous fingering patterns in a circular Hele-Shaw cell. The nonlocality and nonlinearity of the system, especially interactions among developing fingers, make the emergent pattern difficult to predict and control. By controlling the injection rate of the less viscous fluid, we can precisely suppress the evolving interfacial instabilities. There exist denumerable attractive, self-similarly evolving symmetric, universal shapes. Experiments confirm the feasibility of the control strategy, which is summarized in a morphology diagram.
Li
Shuwang
S
Department of Applied Mathematics, Illinois Institute of Technology, Chicago, Illinois 60616, USA. sli@math.iit.edu
Lowengrub
John S
JS
Fontana
Jake
J
Palffy-Muhoray
Peter
P