On the Stability of Elongational Flow of Viscoelastic Liquids. I. The Rubberlike Liquid with a Single-Exponential Memory Function.

Abstract

The report involves the 'spinnability' of high polymers. A new, simple method of analyzing the stability of elongational flow of a cylindrical liquid filament is presented. At time t, the filament is assumed to be composed of two uniform cylinders, of unequal cross-sectional areas A(1)(t), A(2)(t), connected end to end. A constant, uniform tensile force F is suddenly applied at t = 0. Using the 'rubberlike liquid' constitutive equations, the area ratio A(1)(t)/A(2)(t) can be obtained from solutions of a non-linear Volterra integral equation. Numerical solutions are obtained by two independent methods: a step-by-step integration of the Volterra equation, and a Runge-Kutta solution of the non-linear second-order ordinary differential equation to which the Volterra equation can be reduced.

Document Details

Document Type
Technical Report
Publication Date
Nov 01, 1972
Accession Number
AD0755065

Entities

People

  • A. S. Lodge
  • Hui Chang
  • J. B. Mcleod

Organizations

  • University of Wisconsin–Madison

Tags

DTIC Thesaurus Topics

  • Constitutive Equations
  • Cooperation
  • Differential Equations
  • Equations
  • Filaments
  • Integral Equations
  • Integrals
  • Mathematical Analysis
  • Mathematics
  • Partial Differential Equations
  • Rheology
  • Volterra Equations

Fields of Study

  • Mathematics

Readers

  • Calculus or Mathematical Analysis
  • Fluid Dynamics.
  • Reinforced Composite Materials