Shear-induced structure formation in solutions of drag reducing polymers
Introduction
The addition of small amounts of polymers, fibers or surfactants to a liquid can lead to dramatic reductions in the wall shear stress in turbulent flow. This phenomenon, known as drag reduction, is seen experimentally as an increased flow rate through the system for a given pressure drop. Despite decades of research in the area, however, no universally accepted mechanism for drag reduction has been agreed upon.
High molecular weight, flexible chain polymers have been found to be particularly effective as drag reducing agents in aqueous and organic liquids at concentrations as low as a few parts per million by weight [1]. The review by Virk [2] identified the main experimental features of drag reduction and suggested possible mechanisms related to the shear and extensional flow dynamics of the macromolecules. More recent studies have focused on coupling molecular models for both isolated polymer molecules and complex network structures, with direct numerical simulations of the turbulence [3], [4], [5], [6], [7], [8]. Calculations based on the FENE-P bead-spring model have been successful in predicting large drag reductions [6], [7] and illustrating the importance of the macromolecule in dissipating eddies in the buffer layer. However, because of its assumption of infinite dilution, the FENE-P model is incapable of addressing the potential role of molecular interactions in drag reduction. A number of experimental and theoretical works have suggested that chain entanglements or aggregated, gel-like structures exist in typical drag reducing solutions and that these structures can be an important contributing factor to the drag reduction (see [3], [9], [10]). Recent studies in a channel flow facility at the University of Illinois have related the presence of macroscopic, thread-like structures in aqueous polyacrylamide solutions to large drag reductions for a range of turbulent flows [11]. An important issue in all of these studies is whether such structures reflect incomplete dissolution of the polymer or are the result of a flow-induced agglomeration.
Although flow-induced structuring and phase separation have been studied in polymer solutions for decades [12], [13], [14], the phenomenon has received relatively little attention in the drag reduction literature. Shear-thickening, typically associated with structuring, has mainly been found for solutions of drag reducing polymers in water/glycerin solvents with high glycerin content and added salt [15], [16], [17]. Transient experiments with these same systems also show rheopectic behavior, i.e. stress increases with time. Although viscosity sweeps have been performed for aqueous solutions of poly(ethylene oxide) (PEO) and polyacrylamide (PAM), usually used in drag reduction measurements [18], [19], [20], transient stress and torque measurements on these systems have not been reported.
Demonstrations of phase separation and structure formation under flow of dilute and semi-dilute solutions of high molecular weight polymers are ubiquitous. A recent review of the literature has been given by Larson [14]. Initial studies focused on observations of shifts in the cloud point of polystyrene solutions under steady shear and correlations of these with stored free energy arguments though the composition dependence of the first normal stress difference [21]. Studies using in situ optical techniques, particularly rheo-optics, provide strong evidence for structure formation under flow. For example, Kishbaugh and McHugh [13] have shown the relationship between the formation of flow-induced structures in dilute and semi-dilute polystyrene solutions and their shear-thickening behavior at high shear rates. Studies by Yanase et al. [22] have also used birefringence and dichroism to demonstrate the growth of flow-induced concentration fluctuations in more concentrated polystyrene solutions.
A more complete study of structure formation in drag reducing polymer solutions under shear rates and compositions typical of those used in turbulent drag reduction is needed. The object of the present work has been to address this issue. Our experiments focused on evaluating the roles of polymer concentration, solution composition, and shear flow history on the rheological and rheo-optical responses of several drag reducing systems. This paper presents the principal results of our findings. A longer-term goal of our studies is to combine these results with ongoing studies on the drag reduction characteristics in a test facility [11] to determine whether and how much flow-induced structuring occurs in these systems and the possible relation this has to turbulent drag reduction. The results of those studies will be the subject of a later paper.
Section snippets
Materials
Three drag reducing polymers were used in these studies: partially hydrolyzed polyacrylamide (HPAM), polyacrylamide, and poly(ethylene oxide). Details on their relevant properties are listed in Table 1. The PEO and PAM were both manufactured by Polysciences Inc. and the HPAM (Magnafloc 1011) was a commercial grade polymer produced by CIBA Specialty Chemicals. The percent hydrolysis of the HPAM was estimated from CHN experiments to be 12% (i.e. the random co-polymer consists of 12 mol% acrylic
Rheology of HPAM solutions
Fig. 1 shows the steady-state shear viscosity of the HPAM solutions in deionized water at 25 °C for concentrations from 10 to 4000 ppm. In these experiments, the solutions were sheared at the indicated rates for times less than 1 min, during which the torque reached a steady-state value from which the viscosity was determined. Overall, these data exhibit expected patterns for high molecular weight polymer solutions. At higher concentrations (c>75 ppm), the beginnings of a low shear rate Newtonian
Comparison to large-scale drag reduction experiments
To our knowledge, there have been few, if any, studies in which drag reduction phenomena in a large-scale turbulence flow loop have been directly compared with rheological and rheo-optical studies of the same polymer solutions. Our collaboration with ongoing turbulent drag reduction studies at the University of Illinois has produced interesting results for both homogeneous and heterogeneous drag reduction [11].
Polymer solutions prepared for the drag reduction experiments were made in a large
Conclusions
Rheological and rheo-optical characterization of the drag reducing polymers investigated in this study have clearly demonstrated that these systems exhibit structure formation under strong shear flow. Depending on the concentration and shear rate, the structure formation is either pseudo-reversible or irreversible. In all cases, the structure formation process eventually led to large-scale precipitation. This structuring is also related to the occurrence of rheopexy in these solutions.
Acknowledgements
This work was supported by the DARPA Friction Drag Reduction Program under grant MDA 972-01-C-0029.
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