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 $\tilde{\lambda }$ controls all elastic effects. For small values of $\tilde{\lambda }$, Newtonian behavior dominates, while for higher values of $\tilde{\lambda }$ viscoelastic effects appear. We show that the linear growth rate of a small initial perturbation diverges for a critical value $\tilde{\lambda }=\widetilde{{\lambda }_{\mathbf{c}}}\simeq \mathbf{1}\mathbf{0}$. 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.

• Received 23 June 2009

DOI:https://doi.org/10.1103/PhysRevE.81.026305