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Nonlinear Saffman-Taylor instability.

E Alvarez-Lacalle1, J Ortín, J Casademunt

  • 1Departament ECM, Universitat de Barcelona, Avinguda Diagonal 647, E-08028, Barcelona, Spain. enric@ecm.ub.es

Physical Review Letters
|March 6, 2004
PubMed
Summary
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The interface between two viscous fluids in a Hele-Shaw cell can become unstable before predicted linear instability points. This study identifies elastica solutions as the cause, leading to interface pinchoff.

Area of Science:

  • Fluid dynamics
  • Nonlinear physics
  • Interface phenomena

Background:

  • The Saffman-Taylor instability describes fluid interface behavior in Hele-Shaw cells.
  • Previous models primarily focused on linear instability points.

Purpose of the Study:

  • To investigate nonlinear instability in viscous fluid interfaces before the Saffman-Taylor linear instability point.
  • To identify the underlying physical mechanisms and mathematical solutions governing this pre-instability behavior.
  • To experimentally validate the proposed theoretical framework.

Main Methods:

  • Theoretical analysis using elastica solutions.
  • Experimental investigation in a Hele-Shaw cell.
  • Development of a procedure for preparing arbitrary initial conditions.

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Main Results:

  • Demonstrated nonlinear instability occurring before the linear Saffman-Taylor instability point.
  • Identified elastica solutions as the unstable branch of a subcritical bifurcation.
  • Observed interface pinchoff as a topological singularity.
  • Experimental validation of the theoretical bifurcation scenario.

Conclusions:

  • The study reveals a previously uncharacterized nonlinear instability in Hele-Shaw cells.
  • Elastica solutions play a crucial role in pre-instability dynamics and interface pinchoff.
  • The findings have implications for understanding and controlling fluid interfaces in various applications.