Saffman-Taylor instability of viscoelastic fluids: from viscous fingering to elastic fractures.
We study the linear stability of an air front pushing on a viscoelastic upper convected Mawxell fluid inside a Hele-Shaw cell. Both theory and experiments involving several viscoelastic fluids prove that a unique dimensionless time parameter lambda[over] controls all elastic effects. For small values of lambda[over], Newtonian behavior dominates, while for higher values of lambda[over] viscoelastic effects appear. We show that the linear growth rate of a small initial perturbation diverges for a critical value lambda[over]=lambda(c)[over] approximately 10. Experiments prove that this divergence is associated to a fracturelike pattern instability of the interface. We conclude that the observed fractures come from the Saffman-Taylor instability and that they directly emerge from the linear regime of it.
Mora
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Laboratoire des Colloïdes, Verres et Nanomatériaux, UMR 5587, Université Montpellier 2 and CNRS, Place Eugène Bataillon, F-34095 Montpellier Cedex, France. smora@univ-montp2.fr
Manna
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