An exponential decay function for polymer degradation in turbulent drag reduction

doi:10.1016/S0141-3910(00)00080-X

Polymer Degradation and Stability

Volume 69, Issue 3, 1 September 2000, Pages 341-346

https://doi.org/10.1016/S0141-3910(00)00080-X Get rights and content

Abstract

The mechanical degradation of high molecular weight polymers under turbulent flow conditions was investigated using a rotating disk apparatus. The validity of the empirical exponential decay function, which has been used to represent the degradation phenomenon in polymer induced turbulent drag reduction in a pipe flow, has been investigated. Results show that the single exponential decay model is not universally suitable for all polymeric drag reducers, but it effectively represents shear resistant, drag reducing agents, including the various polysaccharides, and is also applicable in describing short time degradation behavior.

Introduction

The frictional resistance in turbulent flow can be drastically reduced by the injection of minute amounts of polymeric additive [1]. This phenomenon implies that polymer solutions undergoing flow in a pipe require a lower pressure drop to maintain the same flow rate. This drag reduction is potentially beneficial to many industrial applications, including oil well operations, fire fighting, heating and cooling water circuits, and biomedical systems [2]. Thereby, drag reduction behavior has been the subject of intensive theoretical and experimental research [3], [4], [5], [6]. However, since the drag reduction effect decreases as the additives degrade (e.g. mechanical shear and high turbulent intensity), drag reduction has been limited to relatively short-term industrial applications. Minimizing degradation is thereby a key issue in taking advantage of this technology.

In turbulent flow, polymeric additives are exposed to elongational strain as well as to strong shear stresses, and this mechanical energy causes scission of the polymer chains occurs, decreasing the drag reduction effectiveness [7]. This mechanical degradation in turbulent flow is known to be affected by various properties, including polymer molecular weight (MW), molecular weight distribution (MWD), temperature, polymer–solvent interactions, polymer concentration, turbulent intensity, method of preparation and storage, and flow geometry. Most studies on degradation equilibrium and kinetics were performed in nonuniform, ill defined shear fields, such as high-speed mixers, turbulent pipe flow, or laminar capillary flows with entrance effects, which enhance degradation [8]. While comparative results can be obtained in these experiments, it is necessary to perform degradation experiments in a well defined, uniform shear field to understand the fundamental mechanism of degradation. Fisher and Rodriguez [9] examined degradation in burette-type, pipe flow of poly(ethylene oxide) (PEO) and polyacrylamide (PAAM) solutions by observing molecular weight dependence on the frictional reduction for each polymer due to degradation processes taking place outside of the tube, such as entrance effects, end effects, and splashing.

Hunston and Zakin [7] performed turbulent flow experiments with extremely dilute polymer solutions. Since it is very difficult to measure changes in the MWD for extremely dilute solutions, they used drag reduction measurements to study polymer degradation. This is possible since the drag reduction effectiveness for polymers is strongly dependent on MW [10]. They observed that the MWD for polystyrene (PS) shifted to a lower MW with very little change to the shape of the curve and that drag reduction studies measure changes to the higher MWs of the MWD.

Furthermore, Horn and Merrill [11] reported that midpoint scission of macromolecules occurs in turbulent flow, which strongly suggests that the polymer chains can indeed be fully extended by turbulent flow, as well as by laminar extensional flow. This hypothesis concurs with some proposed drag reduction theories, which propose that drag reduction is caused by the suppression of the extensional portion of the turbulent flow by increasing the extensional viscosity and causing a shear viscosity change. Several theories have indicated that extreme extension of polymer chains causes the polymer molecules to degrade [12]. An interesting aspect of polymer degradation in dilute solution is the effect of polymer–solvent interactions. Recently, Kim et al. [13] studied the mechanical degradation of high molecular weight PS under turbulent flow using a rotating disk apparatus (RDA) for three different solvent systems, and found that the extent of the degradation depended on the solubility parameter of the solvents.

The RDA investigated in this study is descriptive for the external flow, which includes flow over flat plates as well as the flow around submerged objects. One can study the total drag (friction plus form drag) for an external flow [14]. Using an RDA, we have been working on polymer induced turbulent drag reduction with various polymeric additives.

In this paper, several factors on polymer degradation, including molecular structure, MW, and concentration, are studied. We then compare our RDA results with those generated by previous investigators for pipe flow, which give an exponential decay in time-dependent drag reduction.

Section snippets

Experimental

The polymers used in this experiment are water-soluble PEO and xanthan gum (XG). PEO samples are acquired from Scientific Polymer Products (Ontario, NY, USA) in powder form with weight average molecular weights ( $M ̄_{w}$ ) ranging from 4.0×l0⁵ to 5.0×10⁶ [PEO136E ( $M ̄_{w}$ =4.0×10⁵), PEO343 ( $M ̄_{w}$ =9.0×10⁵), PEO344 ( $M ̄_{w} =4.0×10^{6}$ ) and PEO345 ( $M ̄_{w} =5.0×10^{6}$ )], and the natural polysaccharide XG is obtained from the Sigma Chemical Co. (St. Louis, MO, USA). Since only a single molecular weight of XG is commercially

Results and discussion

Drag reduction behavior of PEO has been extensively studied in deionized water, since PEO is the most widely-used, water-soluble drag-reducing additive. We performed drag reduction and degradation experiments for PEO using seawater as a solvent in an RDA, which measures changes in drag reduction as a function of time and the stability of polymers in a strong turbulent flow [16], [19]. Fig. 1(a) represents degradation profiles of PEO solutions for different MWs of PEO in seawater at a fixed

Conclusion

The degradation phenomenon of both our experimental data and literature data was investigated via a single exponential decay model. It is found that the exponential decay equation [Eq. (2)] describes the degradation mode very well for shear resistant polymers, such as various polysaccharides and PAAM. However, the exponential equation deviates from the experimental data for drag reducers such as flexible PEO. Therefore, it can be concluded that the single exponential decay model is not

Acknowledgements

This work was partially supported by Hallym Academy of Sciences, Hallym University, Korea (1999).

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View full text

An exponential decay function for polymer degradation in turbulent drag reduction

Abstract

Introduction

Section snippets

Experimental

Results and discussion

Conclusion

Acknowledgements

Polymer

Polymer

Drag reduction phenomenon with special emphasis on homogeneous polymer solutions

Adv Polym Sci.

The effect of drag-reducing additives on liquid flows and their industrial applications part 1: basic aspects

J. Hydraulic Res.

A self-consistent theoretical approach to polymer induced turbulent drag reduction

Chem. Eng. Commun.

Turbulence induced change in the conformation of polymer molecules

J. Chem. Phys.

Turbulent drag reduction in closed flow system: boundary layer versus bulk effects

Phys Fluids

Drag reduction characteristics of polysaccharide xanthan gum

Macromol Rapid Commun.

Flow-assisted degradation in dilute polystyrene solutions

Polym Eng Sci.

Mechanical degradation of high molecular weight polymers in dilute solution

J. Appl. Polym. Sci.

Degradation of drag-reducing polymers

J. Appl. Polym. Sci.