Instability of a free boundary in a Hele-Shaw cell with sink/source and its parameter dependence

• Tani Hisasi

  Meiji University Keio University

• Yazaki Shigetoshi

  Meiji University

Abstract

We carry out a linear stability analysis for a free boundary between two fluids in a Hele-Shaw cell, which is driven by the Darcy's law and an injection or suction at the center. In general, stability of an interface is determined by the well-known Saffman-Taylor instability condition. The linear growth rate of the perturbation depends on two parameters; the rate of the injection/suction and the viscosity contrast of the two fluids. In this paper, we numerically find a parameter region, in which the interface can be stable (resp. unstable) even though it has been considered to be unstable (resp. stable) due to the Saffman-Taylor instability. For the case of the injection, it is suggested that such parameter region vanishes as time increases to infinity. However, the destabilization can be retarded for a sufficiently long time, as one tunes the viscosity and the injection rate of the injecting fluid.

Journal

• JSIAM Letters

  JSIAM Letters 9 (0), 37-40, 2017

  The Japan Society for Industrial and Applied Mathematics

Keywords

• Hele-Shaw cell with sink/source
• Saffman--Taylor instability
• linear stability analysis
• two phase Hele-Shaw problem
• free boundary

Details

• CRID: 1390001205301462784
• NII Article ID: 130006900379
• DOI: 10.14495/jsiaml.9.37
• ISSN: 18830617
• ISSN: 18830609
• Web Site: https://www.jstage.jst.go.jp/article/jsiaml/9/0/9_37/_pdf
• Text Lang: en
• Data Source:
  • JaLC
  • Crossref
  • CiNii Articles
  • KAKEN
• Abstract License Flag: Disallowed