Self-similar jet breakup for a generalized PTT model

We discuss self-similar solutions for jet breakup for a family of models of nonNewtonian fluids which includes the Phan-Thien Tanner model. The constitutive law is given by Tt + (v · ∇)T− (∇v)T−T(∇v)T + κT +ν(trT)a−1T = μ(∇v + (∇v)T ), (1) where a > 1. For a = 2, a recent paper establishes the existence of a similarity solution for surface tension driven jet breakup. In this paper, we show that analogous similarity solutions exist for a < 7/3. If, on the other hand a > 7/3, then surface tension plays no role in the breakup, and a different type of similarity solution exists.