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Pattern formation and interface pinch-off in rotating Hele-Shaw flows: A phase-field approach

R. Folch1, E. Alvarez-Lacalle2, J. Ortín3, and J. Casademunt3

  • 1Departament d’Enginyeria Química, Universitat Rovira i Virgili, Av. dels Països Catalans 26, E-43007 Tarragona, Spain
  • 2Departament de Física Aplicada, Universitat Politècnica de Catalunya, Av. Dr. Gregorio Marañón 50, E-08028 Barcelona, Spain
  • 3Departament ECM, Universitat de Barcelona, Av. Diagonal 647, E-08028 Barcelona, Spain

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Phys. Rev. E 80, 056305 – Published 16 November, 2009

DOI: https://doi.org/10.1103/PhysRevE.80.056305

Abstract

Viscous fingering dynamics driven by centrifugal forcing is studied for arbitrary viscosity contrast. Theoretical methods, including exact solutions, and numerics based on a phase-field approach are used. Both confirm that pinch-off singularities in patterns originated from the centrifugally driven instability may occur spontaneously and be inherent to the two-dimensional Hele-Shaw dynamics. They are systematically more frequent for lower viscosity contrasts consistently with experimental evidence. The analytical insights provide an interpretation of this fact in terms of the asymptotic matching of the different regions of the fingering patterns. The phase-field numerical scheme is shown to be particularly adequate to elucidate the existence of finite-time singularities through the dependence of the singularity time on the interface thickness, in particular for varying viscosity contrast.

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Pinch-off singularities in rotating Hele-Shaw flows at high viscosity contrast

E. Alvarez-Lacalle, J. Casademunt, and J. Eggers
Phys. Rev. E 80, 056306 (2009)

Article Text

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Phys. Rev. E 80, 056305– Published 16 November, 2009
  • Received 17 February 2009

© 2009 American Physical Society

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