1. EPSRC Portfolio Partnership in Complex Fluids and Complex Flows Single eXtended Pom-Pom model: planar contractions PRIFYSGOL CYMRU ABERTAWE UNIVERSITY OF WALES SWANSEA Dynamics of Polymer Melts 0b Relaxation time for orientation of backbone 0s Relaxation time for stretch qNumber of arms at each end of molecule Length of backbone/value at equilibrium (L/L 0 )  Anisotropy parameter Increasing SS EE  =  s /  T Declining of thinning level value of the second plateau increases Major drop in level of softening value of the second plateau increases  = 0s/ 0b Slight increase in thinning region Visible effect in hardening region, not as significant as for q qNo significant effect Strong increase in the hardening level Single eXtended Pom-Pom (SXPP): non-dimensional equations Extra-stress evolution (  ) Extra function f (,  ) Double eq model ( 2 XPP) – Stretch ( ) Backbone stretch ( ) Bautista-Manero model Viscoelastic stress evolution Kinetic equation Structural relaxation time kKinetic constant for structure breakdown  Viscosity 00 Viscosity at zero shear rate  Viscosity at very high shear rates EPTT and SXPP material functions (  S,  E, Tr)  = 1/9,  PTT = 0,  SXPP = 0  PTT = 0.02  PTT = 0.25 SXPP, Poiseuille flow planar channel- We  Re = 1,  = 1/9,  = 1/3,  = 0.15, q = 2 Increasing Comments We Initially blunter velocity profiles (shear- thinning fluid); as We increases, there is recovery of parabolic-shape velocity profile Molecular stretch increases  (More diluted systems) velocity profiles approach to parabolic-shape Polymeric stress contribution declines  Small effect on velocity profile; increase in this parameter yields higher polymeric stress q No significant differences Remarks: Influence of Model Parameters – Channel SXPP model parameters fitting EPTT (  PTT =0.02,  =0)  = 0.999…, q = 8  = 0.5, q = 5 m a t c h i n g Tr matching Ematching E  = 1/3, q = 2  = 0.075, q = 2 m a t c h i n g Tr matching Ematching E SXPP model parameters fitting EPTT (  PTT =0.25  =0) Re = 0  = 1/9,  = 0 EPTT in contraction flows (shear-thinning, strain-hardening/softening) We crit ~ 30 We crit ~ 0(10 2 )  PTT = 0.25 (moderate hardening)  PTT = 0.02 (extreme hardening)  PTT = 0.02  PTT = 0.25 We = 30 L = 2.9 X = 3.3  sal = 129.19  10 -4 We = 20 L = 2.8 X = 2.7  sal = 89.76  10 -4 We = 20 L = 1.7 X = 1.6  sal = 4.48  10 -4 We = 100 L = 1.4 X = 1.3  sal = 1.01  10 -4 Re = 0  = 1/9  = 0.15 Re = 0  = 1/9  = 0.15 Re = 0  = 1/9  = 0.15 Re = 0  = 1/9  = 0.15 Re = 0  = 1/9,  = 0 We = 1 L = 1.5 X = 1.3  sal = 4.82  10 -4 We = 5 L = 1.4 X = 1.1  sal = 4.27  10 -4 We = 10 L = 2.3 X = 1.4  sal = 19.73  10 -4 We = 15 L = 2.7 X = 2.1  sal = 67.36  10 -4 We = 1 L = 2.0 X = 1.4  sal = 6.64  10 -4 We = 5 L = 1.9 X = 1.6  sal = 12.64  10 -4 We = 10 L = 1.8 X = 1.6  sal = 5.77  10 -4 We = 15 L = 1.8 X = 1.6  sal = 6.13  10 -4 EPTT and SXPP Vortex Behaviour LPTT in Contraction Flows (shear-thinning, strain-hardening) We crit ~ 24 We crit ~ 50  PTT = 0.25 (moderate hardening)  PTT = 0.02 (extreme hardening) We = 1 L = 1.6 X = 1.3  sal = 5.34  10 -4 We = 5 L = 2.2 X = 1.6  sal = 12.06  10 -4 We = 10 L = 2.2 X = 1.6  sal = 12.57  10 -4 We = 15 L = 2.2 X = 1.9  sal = 14.09  10 -4 We = 1 L = 1.5 X = 1.2  sal = 4.82  10 -4 We = 5 L = 1.3 X = 1.1  sal = 3.70  10 -4 We = 10 L = 1.8 X = 1.1  sal =8.39  10 -4 We = 15 L = 2.3 X = 1.3  sal = 16.75  10 -4 We = 20 L = 2.3 X = 1.9  sal = 16.60  10 -4 We = 50 L = 2.6 X = 2.4  sal = 20.35  10 -4 We = 24 L = 2.8 X = 1.6  sal = 28.82  10 -4 EPTT in Axisymmetric flows (shear-thinning, strain-hardening/softening)  PTT = 0.25 (moderate hardening)  PTT = 0.02 (extreme hardening) We = 1 L = 1.9 X = 1.3  sal = 12.76  10 -4 We = 10 L = 2.9 X = 3.3  sal = 614.01  10 -4 We = 1 L = 1.9 X = 1.3  sal = 11.92  10 -4 We = 10 L = 1.7 X = 1.5  sal = 13.06  10 -4 We = 20 L = 2.9 X = 3.9  sal = 549.94  10 -4 We = 30 L = 2.8 X = 4.4  sal = 364.34  10 -4 We = 20 L = 0.9 X = 0.9  sal = 0.93  10 -4 We = 100 L = 0.6 X = 0.6  sal = 0.13  10 -4 We crit ~ 30We crit ~ 100 Re = 0  = 1/9,  = 0 Re = 0  = 1/9,  = 0 Re = 0  = 1/9,  = 0 Re = 0  = 1/9,  = 0