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Fluctuations in viscous fingering.

Mitchell G Moore1, Anne Juel, John M Burgess

  • 1Center for Nonlinear Dynamics and Department of Physics, The University of Texas at Austin, Texas 78712, USA. mgmoore@chaos.ph.utexas.edu

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|March 23, 2002
PubMed
Summary
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Viscous fingering in Hele-Shaw channels shows intermittent width fluctuations, unlike prior studies. The fluctuation magnitude follows a power law, Ca(-0.64), and mean finger width shows unexpected behavior at large aspect ratios.

Area of Science:

  • Fluid dynamics
  • Complex fluid behavior
  • Pattern formation

Background:

  • The Saffman-Taylor instability describes viscous fingering in Hele-Shaw cells.
  • Previous studies observed stable finger widths, often at lower capillary numbers (Ca) and aspect ratios.

Purpose of the Study:

  • Investigate viscous fingering dynamics in Hele-Shaw channels with varying aspect ratios.
  • Characterize previously unobserved finger width fluctuations and their dependence on capillary number (Ca).

Main Methods:

  • Experimental study of viscous fingering in Hele-Shaw channels.
  • Systematic variation of aspect ratios and capillary numbers (Ca).
  • Quantitative analysis of finger width fluctuations and mean finger width.

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Main Results:

  • Observed intermittent finger width fluctuations, not seen in lower aspect ratio or higher Ca experiments.
  • Quantified fluctuation magnitude with a power law: Ca(-0.64), applicable up to tip instabilities.
  • Discovered that for large aspect ratios, mean finger width peaks as Ca decreases, contradicting monotonic predictions.

Conclusions:

  • Finger width fluctuations are a key feature of viscous fingering, dependent on experimental conditions.
  • The observed power law provides a new quantitative description of these fluctuations.
  • Results challenge existing models for mean finger width behavior, particularly at high aspect ratios.