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Published on: February 3, 2014
Pattern formation and interface pinch-off in rotating Hele-Shaw flows: a phase-field approach
R Folch1, E Alvarez-Lacalle, J Ortín
1Departament d'Enginyeria Química, Universitat Rovira i Virgili, Av. dels Països Catalans 26, E-43007 Tarragona, Spain.
Summary
Centrifugal forcing in viscous fingering can cause spontaneous pinch-off singularities in Hele-Shaw dynamics, especially with lower viscosity contrasts. This study confirms these inherent singularities using theoretical and phase-field methods.
Area of Science:
- Fluid dynamics
- Nonlinear dynamics
- Complex systems
Background:
- Viscous fingering is a classic instability in fluid dynamics.
- Centrifugal forces can introduce unique dynamics not seen in standard Hele-Shaw cells.
- Understanding pattern formation and singularities is crucial for fluid behavior prediction.
Purpose of the Study:
- To investigate viscous fingering dynamics under centrifugal forcing.
- To analyze the occurrence and characteristics of pinch-off singularities.
- To explore the influence of viscosity contrast on instability patterns.
Main Methods:
- Theoretical analysis, including exact solutions.
- Numerical simulations using a phase-field approach.
- Asymptotic matching for analytical insights.
Main Results:
- Spontaneous pinch-off singularities are inherent to centrifugally driven Hele-Shaw dynamics.
- Singularities are more frequent with lower viscosity contrasts, aligning with experimental data.
- The phase-field method effectively reveals finite-time singularities and their dependence on interface thickness and viscosity contrast.
Conclusions:
- Centrifugal forcing in viscous fingering leads to inherent pinch-off singularities.
- Viscosity contrast significantly influences the frequency of these singularities.
- Phase-field simulations offer a robust method for studying complex fluid instabilities.
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