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APS » Journals » Phys. Rev. Lett. » Volume 102 » Issue 17
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Phys. Rev. Lett. 102, 174501 (2009) [4 pages]

Control of Viscous Fingering Patterns in a Radial Hele-Shaw Cell

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Shuwang Li*
Department of Applied Mathematics, Illinois Institute of Technology, Chicago, Illinois 60616, USA

John S. Lowengrub†
Department of Mathematics, University of California, Irvine, California 92697, USA

Jake Fontana‡
Liquid Crystal Institute, Kent State University, Kent, Ohio 44242, USA

Peter Palffy-Muhoray§
Liquid Crystal Institute, Kent State University, Kent, Ohio 44242, USA

Received 25 November 2008; published 30 April 2009

We study numerically and experimentally the dynamics and control of viscous fingering patterns in a circular Hele-Shaw cell. The nonlocality and nonlinearity of the system, especially interactions among developing fingers, make the emergent pattern difficult to predict and control. By controlling the injection rate of the less viscous fluid, we can precisely suppress the evolving interfacial instabilities. There exist denumerable attractive, self-similarly evolving symmetric, universal shapes. Experiments confirm the feasibility of the control strategy, which is summarized in a morphology diagram.

© 2009 The American Physical Society

URL:
http://link.aps.org/doi/10.1103/PhysRevLett.102.174501
DOI:
10.1103/PhysRevLett.102.174501
PACS:
47.15.gp, 47.20.Hw, 47.54.−r, 47.55.N−

*sli@math.iit.edu

†lowengrb@math.uci.edu

‡jfontana@lci.kent.edu

§mpalffy@cpip.kent.edu

 
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