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

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 9004-32-4] 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% 0.02%  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. 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 *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)