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Physical Review E: Statistical, Nonlinear, and Soft Matter Physics 81 (2010) 026305
Saffman-Taylor instability of viscoelastic fluids: From viscous fingering to elastic fractures
Serge Mora1, M. Manna2
(2010)

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 approximate to controls all elastic effects. For small values of lambda approximate to, Newtonian behavior dominates, while for higher values of lambda approximate to viscoelastic effects appear. We show that the linear growth rate of a small initial perturbation diverges for a critical value lambda approximate to=lambda(c)approximate to similar or equal to 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.
1 :  LCVN - Laboratoire des colloïdes, verres et nanomatériaux
2 :  LPTA - Laboratoire de Physique Théorique et Astroparticules
Physique/Physique/Physique Générale
HELE-SHAW CELL – TRANSIENT NETWORK – RHEOLOGY – POLYMERS – LIQUID – PERCOLATION – SCATTERING – MICELLES – GROWTH – FLOWS