Temporal instability of a viscoelastic liquid thread in the presence of a surrounding viscoelastic fluid

This paper is concerned with the temporal stability analysis of an infinitely long thread of a viscoelastic fluid surrounded by another immiscible viscoelastic fluid. The study provides an extension of the dispersion relation derived by Tomotika that captures the effects of elasticity on the fastest growing mode. The general case of two Jeffreys fluids is presented first, from which limiting cases, such as the Maxwell model or the Newtonian model, are discussed. We show that the presence of elasticity in the constitutive equation of the external medium decreases the value of the growth rate correspondent to the fastest growing mode. This implies a more stable fluid thread, thus longer breakup lengths. When both fluids have similar elastic properties, the dispersion relation reduces to the Newtonian limit and the interface behaves as if the fluids were purely viscous.