Abstract
The flow of a viscoelastic fluid in a co-rotating two-roll mill is studied using a modified Chilcott-Rallison constitutive model, which includes the Hinch-DeGennes formulation of a conformation-dependent friction coefficient. One well known feature of this model, for homogeneous flows, is that there is a hysteresis loop in the dependence of the steady-state configuration on the strain-rate. However, for inhomogeneous flows, at finite polymer concentrations, there is a strong coupling between the velocity and configuration fields, which is shown by present calculations to mask the hysteresis loop, and the associated non-uniqueness of the steady-state configuration. This is a consequence of the reduction in extensional strength of the velocity field with increasing polymeric contribution to the stress field. For small polymer concentrations the transition from the coiled-state to the stretched-state is abrupt in time and the transitional Deborah number range is relatively narrow. However, with increasing polymer concentration, both the time taken to reach the steady-state and the transitional Deborah number range increase significantly. For relatively large values of c, L and De a birefringent pipe-like structure emerges along the outflow axis of the two-roll mill. This and the overall spatial distribution of the configuration qualitatively agree with birefringence photographs for real polymeric liquids.
Original language | English (US) |
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Pages (from-to) | 137-178 |
Number of pages | 42 |
Journal | Journal of Non-Newtonian Fluid Mechanics |
Volume | 67 |
Issue number | 1-3 |
DOIs | |
State | Published - Nov 1996 |
Externally published | Yes |
All Science Journal Classification (ASJC) codes
- General Chemical Engineering
- General Materials Science
- Condensed Matter Physics
- Mechanical Engineering
- Applied Mathematics
Keywords
- Co-rotating two-roll mill
- Conformation-dependent friction
- FENE dumbbell model