PMID: 11308768Apr 20, 2001Paper

Saffman-Taylor problem on a sphere

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
F ParisioMichael Widom

Abstract

The Saffman-Taylor problem addresses the morphological instability of an interface separating two immiscible, viscous fluids when they move in a narrow gap between two flat parallel plates (Hele-Shaw cell). In this work, we extend the classic Saffman-Taylor situation, by considering the flow between two curved, closely spaced, concentric spheres (spherical Hele-Shaw cell). We derive the mode-coupling differential equation for the interface perturbation amplitudes and study both linear and nonlinear flow regimes. The effect of the spherical cell (positive) spatial curvature on the shape of the interfacial patterns is investigated. We show that stability properties of the fluid-fluid interface are sensitive to the curvature of the surface. In particular, it is found that positive spatial curvature inhibits finger tip-splitting. Hele-Shaw flow on weakly negative, curved surfaces is briefly discussed.

References

Nov 15, 1989·Physical Review A: General Physics·M J Gingras, Z Rácz
Nov 15, 1990·Physical Review. a·H Zhao, J V Maher
Dec 1, 1993·Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics·P PeczakD Levine
Jul 6, 1992·Physical Review Letters·J E Avron, D Levine
Apr 17, 2001·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·J A MirandaM Widom
Apr 24, 2002·Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics·C VareaR A Barrio

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Citations

Apr 19, 2017·Physical Review. E·Rodolfo Brandão, José A Miranda
Dec 7, 2019·Physical Review Letters·Roiy Sayag
Aug 15, 2015·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Rodolfo Brandão, José A Miranda
Feb 28, 2002·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·José A Miranda
Feb 7, 2012·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Luciano dos Reis, José A Miranda
Dec 11, 2014·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Rodolfo BrandãoJosé A Miranda
Aug 11, 2005·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Ching-Yao ChenJosé A Miranda
Mar 23, 2002·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·José A Miranda

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