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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.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics

|April 7, 2010

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.

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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.