Rheological Theories · Measuring Techniques in Rheology Test Methods in Rheology · Fractures Rheological Properties of Materials · Rheo-Optics · Biorheology pp 1367-1371 | Cite as

# Pressure variation and flow birefringence of polymer melts in flows through straight ducts with approaching channel

## Abstract

*Aoyama*put forward a paper on the interrelation between

*Barus*effect and tube length correction term coefficient (1). Here the cause of the die swell was attributed to the mechanical energy. The principal defect of the paper is that the effect was conclusively directed to the shear strain of the polymer melt flowing through a nozzle. In 1966, at the International Symposium on Macromolecular Chemistry held in Kyoto, a paper on the revision of the forgoing concept was presented where the cause of the die swell was attributed mainly to tensile strains of the flowing melt from a new experimental result on the die exit pressure (2, 3). In 1967, at the 5th International Congress on Rheology in Kyoto, the author presented further experimental results on the interrelations between die swell and die exit pressure (4, 5). The present paper deals with the experimental results so-far obtained in his laboratory within the last 4 years on the elastic responses of melts in steady and in pulsatile flow conditions. For the clarification of the responses, experiments were carried out by the following three different resorts:

- (1)
Investigations on the interrelation between the pressure distribution along the length of circular duct with a contraction portion and the

*Barus*Effect Index ᾱ given by the ratio of the cross-sectional area of the extrudate to that of the nozzle. - (2)
Measurements of the pressure propagation along the length of flow direction in the pulsatile flow through a circular duct with an approaching channel.

- (3)
Measurements on the flow birefringence of polymer melt passing through a slit duct, and the application of photoelasticity analysis for the elastic solid to the flow of the liquid.

## Notation

*D*_{noz}nozzle diameter

*L**D*_{res}reservoir diameter

*L**H*slit clearance

*L**L*_{noz}nozzle length

*L**P*pressure

*ML*^{−1}*T*^{−2}*P*^{ent}driving pressure calculated by

*ML*^{−1}*T*^{−2}linear extrapolation of the pressure gradient curve in the reservoir to the nozzle inlet plane- Δ
*P*_{ent} pressure drop at the nozzle inlet

*ML*^{−1}*T*^{−2}- Δ
*P*_{ent} residual pressure at the nozzle

*ML*^{−1}*T*^{−2}exit*Q*volumetric flow rate

*L*^{3}*T*^{−1}*R*_{ent}nozzle radius

*L**T*slit width

*L**z*coordinate parallel to the axis of

*L*nozzle or slit in flow direction- ᾱ
*Barus*Effect Index dimensionless- y h/2
apparent shear rate at the slit

*T*^{−1}wall- γ ̇′
*R*-noz apparent shear rate at the wall

*T*^{−1}of nozzle- θ
temperature (degree in Centi- θ grade)

*v*nozzle length correction term dimensionless coefficient

*v*_{ent}coefficient of the entrance cor- dimensionless rection term

*v*_{exit}coefficient of the exit correction dimensionless term

- ξ
pressure gradient

*ML*^{−2}*T*^{−2}- ξ
_{η} pressure gradient due to viscos-

*ML*^{−2}*T*^{−2}ity resistance- ξ
_{noz} duct contraction ratio at the dimensionless nozzle entrance

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## References

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*Aral, T., I. Suzuki*, and*N. Akino*, “Pressure Determinations along Die Axis in a Round Tube Extrusion”, paper presented at the International Symposium on Macromolecular Chemistry, Sept. 28, 1966, Kyoto.Google Scholar - 3).
*Arai, T., I. Suzuki, and N. Akino*, Proceedings of the Fujihara Memorial Faculty of Engineering, Keio Univ., Vol.**20**, No. 77, 39 (1967).Google Scholar *Arai, T., I. Suzuki, and N. Akino*, Repts. Progr. Polym. Phys. Japan**10**, p. 127 (1967).Google Scholar- 4).
*Ami, T. and H. Toyota*, Proc. 5th Int. Congr. Rheology, Vol.**4**, pp. 461–470 (Tokyo 1970).Google Scholar - 5).
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