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SUMMARY:On bounds of conformation tensor space in planar flows of the Oldr
 oyd B model - Robert Poole\, University of Liverpool
DTSTART:20251128T160000Z
DTEND:20251128T170000Z
UID:TALK237979@talks.cam.ac.uk
CONTACT:Duncan Hewitt
DESCRIPTION:The response of the polymeric stress in the Oldroyd-B model to
  various planar flow kinematics is probed. By focusing on the two invarian
 ts of the conformation tensor (C)\, namely the trace (tr) and determinant 
 (det)\, (or\, equivalently\, the sum and the product of the two eigenvalue
 s) the domain of realisable stress states are mapped. Previous theoretical
  bounds have been (re)proposed for 2D flows\, viz det C  1 and therefore t
 r C  2 (det C)1/2 ((Hulsen (1988)\, Hu & Lelièvre (2007)\, Yerasi et al (
 2024)). \n\nFor all steady homogeneous 2D flows\, including flows tending 
 to solid body rotation\, steady shearing\, planar extension (and all flows
  in between these bounds)\, plus fully developed channel flow (i.e. inhomo
 geneous shearing) and flows next to all continuous walls without sharp cor
 ners\, we show that tr C = 2 det C. Start-up shearing and planar extension
  are seen to approach the steady flow relationship in a differing manner\,
  whilst large amplitude oscillatory shearing (LAOS) and extension (LAOE) e
 xhibit rich kinematics.  We find the lower theoretical bound (tr C  2 (det
  C)1/2) is only approached for strongly time varying extensional kinematic
 s (LAOE with De~O(0.1)) and many other flows appear bound by tr C = 1 + de
 t C (start up extension\, LAOS). \n\nLimited results from more complex ben
 chmark flows involving mixed shear and extension (steady in a Eulerian sen
 se)\, including flow past a confined cylinder in a channel\, the cross slo
 t and flow in a 4:1 contraction fall within the bounds of those “simpler
 ” kinematics.   Extensions of the approach to more complicated models\, 
 such as the simplified Phan-Thien and Tanner and the FENE-P models\, will 
 also briefly be discussed.  The results here may be useful in determining 
 bounds for numerical computations or providing information regarding what 
 rheological tests produce similar stress state responses to more complex f
 lows.       \n
LOCATION:MR2
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