Title: Extensional viscosity measurements of drag-reducing polymer solutions using a Capillary Break-up Extensional Rheometer
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
2Outline
- Introduction Drag reduction and extensional
viscosity - Fluid shear and oscillatory shear rheology
- Capillary Break-up technique
- Extensional viscosity data
- Conclusions
3Introduction
- (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
4Introduction
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
5Extensional viscosity
Why is extensional viscosity thought to play a
major role in turbulent drag reduction?
Counter-rotating eddy-pairs
Fluid element
Direction of flow
6Fluid 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. -
7Fluid shear rheology
0.4 CMC
0.2 XG
0.09 XG / 0.09 CMC
PAA
? 0.2
? 0.02
? 0.01
8G (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
9Capillary Break-up technique
D 4 mm
h0 2 mm
t - 50 ms
10Capillary 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
11Capillary 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
12Thinning of filament diameter
0.2 XG
0.2 PAA
13Thinning of filament diameter
0.2 XG
0.2 PAA
Effects of inertia
Finite extensionability effects?
intermediate times
14Extensional viscosity
0.2 XG
0.2 PAA
15Extensional 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
16Conclusions
- 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)