Extensional-flow theory with application to fibre drawing

Abstract

Extensional or elongational flows are most commonly associated with the study of rheology following the work of Trouton (1906). In this paper we outline an asymptotic method for the derivation of an extensional-flow model for the drawing of fibres. We obtain ODEs describing the change in area of the cross-section and the temperature from preform to fibre. In general, these are coupled with a 2D transverse-flow problem describing the evolution of the geometry in the cross-section due to surface tension and pressure. The accuracy of the model is demonstrated by comparison with experiments and finite-element simulations, and its computational efficiency is briefly discussed. Models may be obtained for other extensional flows using similar methods.