Elongational rheology by different methods and orientation number

Abstract

ABSTRACT:The elongational rheology of polymer melts was measured by the authors using the hyperbolic convergent die technique and the results were compared with the same samples measured using a Meissner type device or an Instron tensile tester. Polyethylene and polystyrene samples were tested at Eidgenö ssische Technische Hochschule-Zü rich or Virginia Polytechnic Institute, and the polyisobutylene was part of a world wide ''Round Robin'' comparison. A modified Weissenberg number, i.e., an Orientation number, is suggested to explain the agreement between techniques for some samples and lack of agreement for others. The Orientation number is the product of Hencky strain, elongational strain rate, and average relaxation time. When it is less than one a relaxation dominant regime results, when greater than one an orientation dominant regime results, and near one a transition occurs. For the hyperbolic convergent die technique, in which the polymers are transversely constrained by the walls, the extrudates in the transition regime have slight surface defects and the pressure fluctuates more than in the other regimes. If the transition occurs after significant time, i.e., lower elongational strain rates, in the free boundary Meissner and Instron devices, the samples apparently experience more relaxation since unconstrained transversely (and perhaps differential thinning) leading to disagreement with the hyperbolic die measurements. The orientation related body forces are magnitudes larger than the shearing forces and cause slip at the wall in the hyperbolic dies in the orientation dominant regime. Even in the relaxation dominant regime, shear near the wall is a minor contributor to the necessary pressure force.

Non‐Darcian flow experiments of shear‐thinning fluids through rough‐walled rock fractures

“…This was attributed to the formation of transient entanglements of polymer molecules due to the action of the extensional component of the flow. Measurement of extensional viscosity is tricky and several methods have been proposed for its determination [ Schunk et al ., ; Petrie , ; Collier et al ., ]. One of the simplest methods consists in the use of an opposed‐jet device [ Willenbacher and Hingmann , ; González et al ., ].…”

Orientation of carbon fiber precursors from 1‐butyl‐3‐metylimidazoluim chloride cellulose solutions

“…(5) below: where N OR is the orientation number, λ is a characteristic relaxation time, ε H is the Hencky strain, and $ {\rm{\dot \varepsilon }} $ is the elongational strain rate. Because of the proportional relations between these parameters, it is expected that imposed orientation should increase as any one of the terms in the product increase as the others are held constant 5. The proper processing conditions result when the orientation number, N OR , is greater than one.…”

“…The proper processing conditions result when the orientation number, N OR , is greater than one. The orientation number proposed represents the amount of orientation occurring in a solution or melt as well as whether or not slip occurs at the die wall 5. Several studies have recently determined that the elongational rheology was dependent on both the elongational strain rate and time 6, 7.…”

“…However, an orientation value less than about one suggests the flow is relaxation dominated and for values greater than about one, the flow is orientation dominated with a transition region between. In the semi‐hyperbolic die, an orientation number greater than one suggests that slip at the wall is occurring 5. The level and distribution of orientation in a fiber should also be dependent on the orientation number because as the orientation number increases the effect of relaxation will decrease in significance in relation to the simultaneously imposed orientation.…”

“…The level and distribution of orientation in a fiber should also be dependent on the orientation number because as the orientation number increases the effect of relaxation will decrease in significance in relation to the simultaneously imposed orientation. As the orientation number approaches one from a lower value, the orientation effect is still strong and significant orientation should still be developing in the majority of the fluid 5. The major resistance to flow through the semi‐hyperbolic die is due to the body forces of the polymer molecules resisting orientation.…”