Analysis of Spurt Phenomena for a Non-Newtonian Fluid
Abstract
This document discusses novel phenomena in dynamic shearing flows of non-Newtonian fluids of importance for polymer processing. A striking example is spurt which was observed experimentally in the flow of monodispersive polyisoprenes through capillaries; the volumetric flow rate increased dramatically at a critical stress independent of molecular weight. The authors show that satisfactory explanation of spurt requires studying the full dynamics of the equations of motion and constitutive relations characterized by a non- monotonic relation between the steady shear stress and strain rate. The increase in volumetric flow rate is shown to correspond to jumps in the strain rate when the driving pressure gradient exceeds a critical value. Motivated by scaling suggested by accurate numerical computations of the governing dynamic problem that yielded qualitative and quantitative agreement with experiment, we introduce a system of ordinary differential equation that approximates dynamic behavior of highly elastic and very viscous fluids. The complete dynamics of the system of ode's determined by phase plane analysis. These results are then used to explain not only spurt but also shape memory, hysteresis, latency, and other effects that have also been observed in numerical simulations.
Document Details
- Document Type
- Technical Report
- Publication Date
- Mar 01, 1989
- Accession Number
- ADA210560
Entities
People
- Bradley J. Plohr
- David S. Malkus
- John A. Nohel
Organizations
- University of Wisconsin–Madison