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

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...

Full description

Saved in:
Bibliographic Details
Published inPhysical review. E, Statistical, nonlinear, and soft matter physics Vol. 80; no. 5 Pt 2; p. 056305
Main Authors Folch, R, Alvarez-Lacalle, E, Ortín, J, Casademunt, J
Format Journal Article
LanguageEnglish
Published United States 01.11.2009
Subjects
Algorithms
Computer Simulation
Models, Theoretical
Physics - methods
Rheology
Surface Properties
Surface Tension
Viscosity
Online AccessGet more information

Cover

More Information
Summary: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.
ISSN:1550-2376
DOI:10.1103/PhysRevE.80.056305