Some remarks on the stability of extensional flows

Tube theory of entangled polymer dynamics

“…For example, branched entangled polymers (see below) may be strain-hardening in extension (the e ective`viscosity' de®ned as stress/strain-rate increases with strain), but strain-softening in shear. The existence of molecular e ects that appear rheologically only in extensional¯ows, as well as the central role played by extensional¯ows in processing [131] have motivated the re®nement of two designs of extensional rheometer. In`®lament rheometers', the material is stretched between two plates which separate at an exponential rate [132± 135].…”

Simple indicator of draw resonance instability in melt spinning processes

“…[1][2][3][4][5][6][7][8][9][10][11][12] However, there are still unsettled issues about draw resonance, many of them expounded by Petrie. 13 In fiber spinning of Newtonian or viscoelastic liquids, the onset of draw resonance is an oscillatory instability or overstability, as termed by Eddington, 14 or a stable supercritical Hopf bifurcation, as used in the singularity theory. In an analysis by means of the method of infinitesimal disturbances -linear stability analysis -Schultz et al 6 showed that as the drawdown ratio is raised just beyond the Hopf bifurcation, the frequency of oscillation falls, and, thus, the period of the nascent limit cycle grows.…”

One hundred years of extensional flow

“…An earlier review by Denn [11] is also well worth reading, particularly on the subject of the effect of multiple relaxation times. Instabilities in extensional flow have received much attention with reviews from 1976 [12][13][14] and more recently [15][16][17]. Books by Middleman [18] and Yarin [19] discuss, among other things, the stability and breakup of an axisymmetric Newtonian jet and offer a link to literature on much high quality experimental and theoretical work on Newtonian liquid jets.…”