Characteristics and design procedure of hyperbolic dies

Abstract

SYNOPSISNozzle profiles capable of generating constant extensional strain rates are termed hyperbolic dies. When used in polymer extrusion, they exhibit greater potential in inducing and retaining polymer molecular orientation than conventional capillary dies. Most mathematical expressions found in the literature involve several processing variables in describing and designing such nozzle profiles. This report reveals that a hyperbolic die profile, although rather complicated, can be expressed with equations in terms of two ordinary geometrical parameters-the exit diameter and the hyperbolic length. This finding greatly simplifies the design procedure of hyperbolic dies. The extensional strain rate of a hyperbolic die can be related to the length-to-diameter ratio for any given exit diameter. Examples of various types of die profiles are presented and their constant extensional strain-rate characteristics are discussed.Keywords: extrusion from hyperbolic dies, characteristics and design procedures in strain rate in extrusion procedures, hyperbolic die design and filament production with constant extensional strain rate with hyperbolic dies

Simulation of Flow in the Silk Gland

“…From the extension rate profile (Figure ), it is immediately obvious that neither silk gland is shaped as a constant extension rate funnel, as has been previously suggested for the spider MA gland. , Constant extension rate funnels have been under investigation in the fiber spinning community because they are believed to minimize the pressure drop required for flow as well as induce and maintain the highest degree of molecular alignment in a solution. − The spider MA gland actually acts as an increasing extension rate funnel, perhaps in order to maintain extension despite the strain hardening character of highly strained silk dope …”

“…1,9 Constant extension rate funnels have been under investigation in the fiber spinning community because they are believed to minimize the pressure drop required for flow as well as induce and maintain the highest degree of molecular alignment in a solution. [38][39][40] The spider MA gland actually acts as an increasing extension rate funnel, perhaps in order to maintain extension despite the strain hardening character of highly strained silk dope. 16 The maximum extension rate in the spider silk MA gland rises to an order of magnitude higher than that in the silkworm gland.…”

Liquid crystals and flow elongation in a spider's silk production line

“…The hyperbolic geometry of the S-shaped duct described above is of interest. Man-made extrusion dies sometimes use this geometry as it reduces disorientation by maintaining a constant elongational £ow rate throughout the entire length of the die (Chen et al 1992). The slow reduction in diameter of the lumen in the spider's ampulla and S-shaped duct are thought to produce a slow elongational £ow rate which may prevent premature crystallization of the feedstock until high shear rates (Kerkam et al 1991;Kaplan et al 1994;Willcox et al 1996) are produced in the draw down taper.…”