Saffman-Taylor instability of viscoelastic fluids: From viscous fingering to elastic fractures

Abstract

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.