Analysis of the String Structure Near Break-up of A Slender Jet of An Upper Convected Maxwell Liquid

In this paper, we study local dynamics for the break-up of a slender jet of a viscoelastic liquid surrounded by a vacuum. The governing equations are derived from the conservation laws of mass and momentum, and the rheological equation of the jet. The rheological equation of the jet is assumed to satisfy an Upper Convected Maxwell (UCM) model. Introducing a stretch variable and then applying a transformation, we obtain a coupled system of nonlinear differential equations. Via these equations, we then show that the UCM jet does not break up in finite time.