Viscous fluid fingering on a negatively curved surface

Rodolfo Brandão and José A. Miranda
Phys. Rev. E 92, 013018 – Published 27 July 2015

Abstract

Viscous fingering formation in flat Hele-Shaw cells is a classical and widely studied fluid mechanical problem. We examine the development of viscous fluid fingering on a two-dimensional surface of constant negative Gaussian curvature, the hyperbolic plane H2. A perturbative mode-coupling formalism is applied to study the influence of the negative surface curvature on the two most important pattern formation mechanisms of the system: fingertip splitting and finger competition. We also report on a time-dependent control strategy placed on the injection rate, which is able to minimize viscous fingering growth on H2.

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  • Received 11 June 2015

DOI:https://doi.org/10.1103/PhysRevE.92.013018

©2015 American Physical Society

Authors & Affiliations

Rodolfo Brandão and José A. Miranda*

  • Departamento de Física, Universidade Federal de Pernambuco, Recife, Pernambuco 50670-901, Brazil

  • *jme@df.ufpe.br

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Vol. 92, Iss. 1 — July 2015

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