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Radial fingering under arbitrary viscosity and density ratios

Pedro H. A. Anjos, Eduardo O. Dias*, and José A. Miranda†

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

  • *eduardodias@df.ufpe.br
  • †jme@df.ufpe.br
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Phys. Rev. Fluids 2, 084004 – Published 21 August, 2017

DOI: https://doi.org/10.1103/PhysRevFluids.2.084004

Abstract

We study viscous fingering formation in radial Hele-Shaw cell geometry considering the combined action of capillary and inertial effects for arbitrary values of viscosity and density ratios. We tackle the problem by employing a perturbative mode-coupling approach and focus our attention on weakly nonlinear stages of the dynamics. If inertial effects are neglected, our theoretical results indicate that the shape of the resulting interfacial patterns is significantly affected by changes in the viscosity ratio. Under such conditions, the growing fingers tend to proliferate through a repeated ramification process (e.g., by finger bifurcation, quadrifurcation, etc.) as the capillary number is increased. Nevertheless, we find that this scenario is dramatically altered when inertia is taken into account. When inertia is relevant, the conventional finger splitting morphologies are replaced by three-lobed structures, characterized by the occurrence of sidebranching phenomena. We verify that slightly different types of sidebranched patterns arise, presenting either wide or sharp fingertips, for a range of capillary numbers and density ratios.

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Phys. Rev. Fluids 2, 084004– Published 21 August, 2017
  • Received 25 April 2017

©2017 American Physical Society

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