Observation of a Finite-Time Singularity in Needle Propagation in Hele-Shaw Cells
- 2 November 1998
- journal article
- research article
- Published by American Physical Society (APS) in Physical Review Letters
- Vol. 81 (18) , 3860-3863
- https://doi.org/10.1103/physrevlett.81.3860
Abstract
Very narrow fingers or needles are observed in viscous fingering experiments using lyotropic lamellar phases as the viscous liquid and air as the less viscous fluid. The highly anisotropic flow-induced texture of the lamellar phase is strongly correlated with the onset of needle formation. The needles are observed to have a width which decreases to zero while the velocity of the tip increases dramatically with time, reminiscent of a finite-time singularity.This publication has 25 references indexed in Scilit:
- A Cascade of Structure in a Drop Falling from a FaucetScience, 1994
- Finite-time singularity formation in Hele-Shaw systemsPhysical Review E, 1993
- Topology transitions and singularities in viscous flowsPhysical Review Letters, 1993
- Finite-time singularities in the axisymmetric three-dimension Euler equationsPhysical Review Letters, 1992
- An experimental study of the Saffman-Taylor instabilityJournal of Fluid Mechanics, 1987
- Narrow fingers in the Saffman-Taylor instabilityPhysical Review A, 1986
- Shape Selection of Saffman-Taylor FingersPhysical Review Letters, 1986
- Analytic Theory of the Selection Mechanism in the Saffman-Taylor ProblemPhysical Review Letters, 1986
- Velocity Selection and the Saffman-Taylor ProblemPhysical Review Letters, 1986
- The penetration of a fluid into a porous medium or Hele-Shaw cell containing a more viscous liquidProceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences, 1958