Drawing of Weakly Viscoelastic Fluid Tubes

TL;DR

This paper investigates how weakly viscoelastic effects influence the drawing process of fluid tubes, revealing that elasticity can both promote and hinder hole closure depending on conditions, and affects process stability.

Contribution

It derives asymptotic equations for weakly viscoelastic tubes and uncovers the complex role of elastic stresses in hole closure and stability during drawing.

Findings

Elastic effects generally enhance hole closure at the outlet.

Elasticity destabilizes the drawing process when inertia is negligible.

Elastic effects can either stabilize or destabilize depending on inertia and parameters.

Abstract

We explore the drawing of an axisymmetric viscoelastic tube subject to inertial and surface tension effects. We adopt the Giesekus constitutive model and derive asymptotic long-wave equations for weakly viscoelastic effects. Intuitively, one might imagine that the elastic stresses should act to prevent hole closure during the drawing process. Surprisingly, our results show that the hole closure at the outlet is enhanced by elastic effects for most parameter values. However, the opposite is true if the tube has a very large hole size at the inlet of the device or if the axial stretching is very weak. We explain the physical mechanism underlying this phenomenon by examining how the second normal stress difference induced by elastic effects modifies the hole evolution process. We also determine how viscoelasticity affects the stability of the drawing process and show that elastic effects are always destabilizing for negligible inertia. This is in direct contrast to the case of a thread without a hole for which elastic effects are always stabilizing. On the other hand, our results show that if the inertia is non-zero, elastic effects can be either stabilizing or destabilizing depending on the parameters.