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Parisio F, Moraes F, Miranda JA, et al. Saffman-Taylor problem on a sphere. Phys Rev E Stat Nonlin Soft Matter Phys. 2001;63(3):036307doi: 10.1103/PhysRevE.63.036307.
Parisio, F., Moraes, F., Miranda, J. A., & Widom, M. (2001). Saffman-Taylor problem on a sphere. Physical review. E, Statistical, nonlinear, and soft matter physics, 63(3), 036307. https://doi.org/10.1103/PhysRevE.63.036307
Parisio, F, et al. "Saffman-Taylor problem on a sphere." Physical review. E, Statistical, nonlinear, and soft matter physics vol. 63,3 (2001): 036307. doi: https://doi.org/10.1103/PhysRevE.63.036307
Parisio F, Moraes F, Miranda JA, Widom M. Saffman-Taylor problem on a sphere. Phys Rev E Stat Nonlin Soft Matter Phys. 2001 Mar;63(3):036307. doi: 10.1103/PhysRevE.63.036307. Epub 2001 Feb 27. PMID: 11308768.
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Phys Rev E Stat Nonlin Soft Matter Phys. 2001 Mar;63(3):036307. doi: 10.1103/PhysRevE.63.036307. Epub 2001 Feb 27.

Saffman-Taylor problem on a sphere.

Physical review. E, Statistical, nonlinear, and soft matter physics

F Parisio, F Moraes, J A Miranda, M Widom

Affiliations

  1. Laboratório de Física Teórica e Computacional, Departamento de Física, Universidade Federal de Pernambuco, Recife, PE 50670-901, Brazil.

PMID: 11308768 DOI: 10.1103/PhysRevE.63.036307

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.

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