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

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

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

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

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

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].

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

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

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

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

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

Thinning of filament diameter 0.2% XG 0.2% PAA

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

Extensional viscosity 0.2% XG 0.2% PAA

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

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)