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SUMMARY:Fast flow of an Oldroyd-B fluid through a slowly varying contracti
 on - Professor John Hinch\, DAMTP
DTSTART:20250228T160000Z
DTEND:20250228T170000Z
UID:TALK227077@talks.cam.ac.uk
CONTACT:Professor Grae Worster
DESCRIPTION:Lubrication theory is adapted to incorporate the large normal 
 stresses that occur for order-one Deborah numbers\, $De$\, the ratio of th
 e relaxation time to the residence time.\n\nComparing with the pressure dr
 op for a Newtonian viscous fluid with a viscosity equal to that of an Oldr
 oyd-B fluid in steady simple shear\, we find numerically a reduced pressur
 e drop through a contraction and an increased pressure drop through an exp
 ansion\, both changing linearly with $De$ at high $De$. For a constriction
  there is a smaller pressure drop that plateaus at high $De$. Much of the 
 change in pressure drop occurs in the stress relaxation in a long exit cha
 nnel.\n\nAn asymptotic analysis for high $De$\, based on the idea that nor
 mal stresses are stretched by an accelerating flow in proportion to the sq
 uare of the velocity\, reveals that the large linear changes in pressure d
 rop are due to higher normal stresses pulling the fluid through the narrow
 est gap. A secondary cause of the reduction is that the elastic shear stre
 sses do not have time to build up to their steady state equilibrium value 
 while they accelerate through a contraction.\n\nAnd experiments find diffe
 rently!\n
LOCATION:MR2
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