1. 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

2. Outline Introduction: Drag reduction and extensional viscosity
Fluid shear and oscillatory shear rheology
Capillary Break-up technique
Extensional viscosity data
Conclusions

3. 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 (>50 papers in 2004 and 15 papers already
in 2005).
*Turbulence structure and Modulation, (ed. A. Soldati and R. Monti) Springer

4. 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

5. 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

6. 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 ] molecular weight (7 x 105 g/mol)
(d) 0.09% XG / 0.09% CMC blend [same grades as unblended polymers].

7. Fluid shear rheology 0.4% CMC 0.2% XG 0.09% XG / 0.09% CMC PAA  0.2%
 0.2%
 0.02%
 0.01%

8. 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

9. Capillary Break-up technique
D = 4 mm
h0 = 2 mm
t =- 50 ms

10. 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 > 0

11. Single relaxation time Maxwell model gives:
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 > 0

12. Thinning of filament diameter
0.2% XG
0.2% PAA

13. Thinning of filament diameter
0.2% XG
0.2% PAA
Effects of inertia
‘intermediate times’
Finite extensionability effects?

14. Extensional viscosity
0.2% XG
0.2% PAA

15. 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

16. 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)