Self-similar jet breakup for a generalized PTT model

Abstract

Listen

Translate article

We discuss self-similar solutions for jet breakup for a family of models of non-Newtonian fluids which includes the Phan-Thien Tanner (PTT) model. The constitutive law is given by (1) T t+( v·∇) T−(∇ v) T− T(∇ v) T +κ T+ν( tr T) a−1 T=μ(∇ v+(∇ v) T ), 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.