Extensional viscosity measurements of drag-reducing polymer solutions using a Capillary Break-up Extensional Rheometer

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Extensional viscosity measurements of
drag-reducing polymer solutions using a Capillary
Break-up Extensional Rheometer Robert J Poole ,
Adam Swift and Marcel P Escudier Department of
Engineering, University of Liverpool, UK
ESR 2nd Annual European Rheology Conference,
April 21-23, Grenoble-France
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Outline

• Introduction Drag reduction and extensional
  viscosity
• Fluid shear and oscillatory shear rheology
• Capillary Break-up technique
• Extensional viscosity data
• Conclusions

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Introduction

• (Turbulent) drag reduction by polymer additives
  first discovered by Toms (1948) (or Mysels
  (1949)).
• Small additions (as little as a few p.p.m) of a
  polymer additive to a Newtonian solvent can
  reduce friction factor by up to 80.

• Major reviews by
• Lumley (1969) 185 cites
• Virk (1975) 310 cites
• Nieuwstadt and den Toonder (2001)

Still significant interest (gt50 papers in 2004
and 15 papers already in 2005).
Turbulence structure and Modulation, (ed. A.
Soldati and R. Monti) Springer
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Introduction
0.4 CMC
0.2 XG
0.09 XG / 0.09 CMC
0.2 PAA
A keyword in most attempts to explain the
mechanism of drag reduction is extensional (or
elongational) viscosity
Escudier, Presti and Smith (1999) JnNFM
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Extensional viscosity
Why is extensional viscosity thought to play a
major role in turbulent drag reduction?
Counter-rotating eddy-pairs
Fluid element
Direction of flow
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Fluid shear rheology

• Polymers studied (water as solvent for all)
• Polyacrylamide (PAA 0.2, 0.02 and 0.01)
  Separan AP 273 E from Floreger Very flexible
  polymer, high molecular weight (2 x 106 g/mol)
• 0.2 Xanthan gum (XG) Keltrol TF from Kelco.
  Semi-rigid polymer, high molecular weight (5 x
  106 g/mol)
• 0.4 Sodium carboxymethylcellulose (CMC) Aldrich
  Grade 9004-32-4 molecular weight (7 x 105
  g/mol)
• (d) 0.09 XG / 0.09 CMC blend same grades as
  unblended polymers.

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Fluid shear rheology
0.4 CMC
0.2 XG
0.09 XG / 0.09 CMC
PAA
? 0.2
? 0.02
? 0.01
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G (open symbols), G (closed symbols)
0.09 XG / 0.09 CMC
0.4 CMC
? 2.1 s
? 5.8 s
? 0.2 PAA
0.2 XG
? 0.02
? 0.01
? 25 s
? 30 s
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Capillary Break-up technique
D 4 mm
h0 2 mm
t - 50 ms
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Capillary Break-up technique
Surface tension drives pinch off of liquid
thread ? resisted by extensional stresses
hf ? 8 mm
? hf / h0
DMID (t)
Laser micrometer measures DMID (t)
D 4 mm
h0 2 mm
t - 50 ms
t gt 0
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Capillary Break-up technique
Single relaxation time Maxwell model gives
alternatively you may calculate a Hencky strain
at the midpoint
DMID (t)
and estimate an apparent extensional viscosity
t gt 0
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Thinning of filament diameter
0.2 XG
0.2 PAA
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Thinning of filament diameter
0.2 XG
0.2 PAA
Effects of inertia
Finite extensionability effects?
intermediate times
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Extensional viscosity
0.2 XG
0.2 PAA
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Extensional viscosity data
Fluid DR () (Pa.s)
0.2 PAA 48 1600 67 178000 1660
0.2 XG 46 1.5 0.086 465 89
0.4 CMC 39 6 8.2 6000 65
CMC/XG blend 36 1 0.81 264 44
DR at Re 5000
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Conclusions

• Capillary-thinning behaviour of PAA significantly
  different to XG, CMC and a XG/CMC blend
• Extensional viscosity of PAA two orders of
  magnitude greater than XG (despite very similar
  levels of DR)

• Biaxial not uniaxial extensional flows which are
  created by streamwise vortical structures?
• (Shaqfeh et al (2004) ICR)