Break-up and no break-up in a family of models for the evolution of viscoelastic jets

The goal of this paper is to study the conditions under which break-up of a thin viscoelastic jet is inhibited or, oppositely, to provide families of self-similar break-up solutions emerging in the evolution. The fluid is a polymeric solution and the constitutive relation we consider is of the Johnson-Segalman type which contains one parameter. The models under consideration are the limits of the well know one-dimensional model when the viscosity of the solvent goes to zero or to infinity and when the Deborah number is very large. Some considerations on the stationary and travelling wave solutions of the models are also presented.