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Suppressing viscous fingering with rotation: Linear predictions and nonlinear simulations
Írio M Coutinho1, José A Miranda1
1Universidade Federal de Pernambuco, Departamento de Física, CCEN, Recife, Pernambuco 50670-901, Brazil.
Physical Review. E
|April 18, 2026
Summary
Centrifugal forces can suppress viscous fingering instabilities in Hele-Shaw cells. A criterion based on maximum interfacial perturbation amplitude accurately predicts the critical rotation speed needed for stabilization.
Area of Science:
- Fluid dynamics
- Instability phenomena
- Hele-Shaw flow
Background:
- Viscous fingering instabilities arise during fluid injection in Hele-Shaw cells.
- Centrifugal forces from cell rotation offer a potential method for instability suppression.
Purpose of the Study:
- Investigate centrifugal force effects on injection-driven viscous fingering.
- Determine critical rotation speeds for interface stabilization.
- Compare linear stability criteria for predicting stabilization.
Main Methods:
- Developed two linear stability criteria: wavelength selection and maximum perturbation amplitude.
- Employed fully numerical simulations using the level set method.
- Analyzed nonlinear dynamics of fluid injection and rotation.
Main Results:
- The maximum perturbation amplitude criterion accurately predicted stabilization.
- The conventional growth-rate (wavelength selection) criterion failed to predict critical angular velocity.
- Numerical simulations validated the amplitude-based criterion for suppressing viscous fingering.
Conclusions:
- Centrifugal forces effectively suppress viscous fingering in radial Hele-Shaw cells.
- The maximum interfacial perturbation amplitude criterion is a robust predictor of stabilization.
- Nonlinear simulations confirm the analytical predictions for controlling interface dynamics.
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