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Inertia-induced dendriticlike patterns in lifting Hele-Shaw flows

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, 014003 – Published 20 January, 2017

DOI: https://doi.org/10.1103/PhysRevFluids.2.014003

Abstract

The lifting Hele-Shaw cell problem is a variant of the classical constant-gap Hele-Shaw situation in which the cell gap width is time dependent. Experiments on Newtonian fluid flows in lifting Hele-Shaw cells with large lifting velocities reveal the development of dendriticlike fingered structures that compete among themselves. The usual Darcy law description of the problem, where inertial effects are neglected, has not been able to explain the origin of these competing sidebranched patterns. In this work we use a generalized Darcy law and a perturbative mode-coupling theory to investigate the impact of inertia on the pattern-forming dynamics of the system. Two main results are deduced: Inertia induces a mechanism for finger sidebranching formation and favors the intensification of finger competition events.

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Phys. Rev. Fluids 2, 014003– Published 20 January, 2017
  • Received 15 July 2016

©2017 American Physical Society

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