Roles of Molecular Structure and Solvation on Drag Reduction in

Chapter 21

Roles of Molecular Structure and Solvation on Drag Reduction in Aqueous Solutions

Downloaded by UNIV OF ROCHESTER on November 5, 2014 | http://pubs.acs.org Publication Date: July 18, 1991 | doi: 10.1021/bk-1991-0467.ch021

Charles L. McCormick, Sarah E. Morgan, and Roger D. Hester Department of Polymer Science, The University of Southern Mississippi, Hattiesburg, MS 39406-0076

Drag reduction performance of water-soluble copolymers tailored with specific structural features has been examined. These copolymers including polyelectrolytes, polyampholytes, and hydrophobically-modified polymers respond to changes i n ionic strength as indicated by changes i n hydrodynamic volume i n aqueous solution. Drag reduction performance is greatly affected by polymer microstructure and by solvation. A new method of data representation i n which drag reduction efficiency is shown as a function of volume fraction allows comparison of a large number of polymer types. Further normalization utilizing an empirical shift factor allows all data to fall on a single efficiency curve. Results of this study suggest that predictive dynamic extensional models might be improved by inclusion of parameters reflective of solvent and associative interactions as well as hydrodynamic volume. The phenomenon of drag reduction (DR) was first reported by Toms four decades ago (1). Frictional resistance i n turbulent flow can be reduced to as little as one-quarter of that of pure solvent by the addition of certain flow modifiers. Numerous studies of various polymers i n both aqueous and organic solvents have shown that DR is affected by molecular weight, concentration, chain flexibility, and a number of other parameters. However, a quantitative understanding of the phenomenon has still eluded investigators; a number of conflicting theories and experimental results exist throughout the extensive literature on this subject. Most theories suggest that polymer molecules interfere with production, growth, and transport of turbulent disturbances. Recent evidence points to the importance of molecular extension i n energy dissipation. D R models may be classified somewhat arbitrarily into length scale, time scale and energy theories. Length scale models such as those of Virk (2,3) and Hlavacek (4,5) correlate with polymer chain length or radius of gyration. Time scale models of Lumley (6-8) and Ryskin (9,10) can be related to polymer relaxation time. Energy models generally deal with the ability of polymers to alter the energy balance in turbulent flow with major contributions from Virk (3), Walsh (11), Kohn (12), 0097-6156/91/0467-0320$06.00/0 © 1991 American Chemical Society

In Water-Soluble Polymers; Shalaby, S., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1991.


21. McCORMICK ET AL.

Drag Reduction in Aqueous Solutions

321

and de Gennes (13). Berman (14) has suggested the operation of multiple mechanisms. Despite conflicting explanations of DR, the direct correlation of coil size (or changes therein) to DR efficiency has been repeatedly demonstrated. However, it is not clear whether the parameter providing the best correlation is molecular weight, degree of polymerization, radius of gyration, or hydrodynamic volume. Correlations are complicated by solvent interactions and draining characteristics, molecular weight distribution, and substitutional patterns governing effective segment lengths. Recent reviews of molecular parameters i n DR are found i n references 15 and 16. The purpose of our continuing research (16-19; McCormick, C. L. et al., Macromolecules. two articles i n press; Safieddine, A. M . , Ph.D. Thesis, University of Southern Mississippi, i n press) is to systematically examine the interrelationships between structure and drag reduction performance of structurally tailored water-soluble copolymers. The effects of molecular parameters are examined i n this work utilizing copolymer models whose dimensions rely on specific polymer/polymer or polymer/solvent interactions under given conditions of ionic strength. Copolymers include uncharged, hydrophilic macromolecules, polyampholytes, polyelectrolytes, and hydrophobically associating systems. Extensive studies of dilute solution properties including viscosity, hydrodynamic volume, rheology, and phase behavior have accompanied DR measurements. Experimental Materials. Three molecular weight grades of poly(ethylene oxide) (PEO) were purchased from Union Carbide Corporation. Acrylamide (AM) and acrylic acid (AA) from Aldrich, diacetone acrylamide (DAAM) and 2-acrylamido-2methylpropane sulfonic acid (AMPS) from Polysciences were purified by three recrystallizations from acetone or methanol. The monomer 3-acrylamido-3methyl butanoic acid (AMBA) was synthesized via a Ritter reaction using a previously published procedure (20). 2-Aci^lamido-2-methylpropanedimethylammonium chloride (AMPDAC) synthesis was also reported previously (21). Model copolymers and terpolymers utilized i n drag reduction studies were synthesized and thoroughly characterized previously i n our research group. These include: uncharged homopolyacrylamide and D A A M copolymers with A M (22); polyelectrolytes of A M with A M P S or A M B A (23); polyampholytes containing A M P S and A M P D A C (24.25). Polymer Characterization. Polymer compositions were determined from elemental analyses (M-H-W Laboratories, Phoenix) and C - N M R . Intrinsic viscosities were determined on a Contraves Low Shear 30 Rheometer. Classical light scattering studies were performed using a Chromatix K M X - 6 low angle laser light scattering spectrophotometer utilizing a 2mW He-Ne laser operating at 633 nm to obtain weight average molecular weights. Specific refractive index increment was determined with a Chromatix KMX-16 laser differential refractometer. Quasielastic light scattering studies, yielding the translational diffusion coefficient were performed with the KMX-6 i n conjunction with a Langley-Ford Model LFI-64 channel digital correlator. Hydrodynamic diameter was calculated from the diffusional coefficient using the Stokes-Einstein relationship. 13

Drag Reduction Measurements. Polymer solutions were prepared by dissolving the required mass of polymer with 0.01% N a N biocide i n solvent i n one liter 3


322

WATER-SOLUBLE P O L Y M E R S

flasks by gentle room temperature stirring for 48 hours. Solutions were then transferred to polypropylene tanks and diluted with solvent (deionized water or 0.514 M aqueous NaCI) to twenty liters, and gently stirred for an additional 24 hours before drag reduction measurements were made at 25 C. Polymeric solutions were tested for drag reduction performance i n both a rotating disk and a tube flow apparatus. The first system consisted of a modified Haake, Model RV3, rheometer equipped with a rotating disk. The stainless steel disk was 9 cm i n radius, 2mm in thickness, and was machined to insure flatness and smoothness. The disk was centered i n a chamber with the depth i n the fluid being adjustable by changing the length of a stainless steel shaft to which the disk was attached. The chamber was a Pyrex jar 305 mm i n diameter by 457 mm i n height with a capacity of 33.4 liters. The disk was driven by a variable speed motor. The motor drive and torque sensing unit are components from a Haake RV3 rotoviscometer. The torque applied to the rotating disk was determined using the stress measuring head which was calibrated using the method described by the manufacturer (26). The data acquisition system for recording the torque consisted of a Hewlett-Packard 41C calculator connected to an ADC 41 (Interface Instruments, Corvallis, OR) analog to digital interface. The experimental data, torque (x ) and disk angular velocity (ω), were converted to Reynolds number (Re) and friction factor (f) using Equations 1 and 2 which were developed for a disk of radius (R) rotating i n an unbounded fluid of viscosity μ and density ρ (27.28).


e

q

f = τ^τφατΈ ) 5

(1)

Re = ρΚ ω/μ

(2)

2

The tube flow apparatus consisted of a smooth stainless steel tube 102 cm i n length, L , with a diameter, D, of 0.210 cm. This single pass testing system was driven by a high pressure nitrogen gas source. Pressure taps were placed at 150 L/D and 350 L/D downstream from the tube entrance to determine pressure drop. Pressure was measured by a Validyne DP 15 differential pressure transducer. Flow rate was monitored by a load cell with strain gauges connected to a Hewlett-Packard plotter where weight was plotted as a function of time. From measured pressure drop and flow rate, friction factor and Reynolds number were calculated (27). Results and Discussion Tailored Copolymers. Synthetic copolymers (Table I) were prepared with structural features of particular interest when examining the drag reduction phenomenon. Acrylamide (AM) is a neutral, hydrophilic monomer with a high rate of propagation i n aqueous solution. Copolymers of A M with sodium acrylate (NaA), sodium-2-acrylamido-2-methylpropane sulfonate (NaAMPS) and sodîum-3-acrylamido-3-methylbutanoate (NaAMB) are anionic polyelectrolytes. The latter polymers are more electrolyte tolerant than the N a A copolymers due to the somewhat more hydrophobic character introduced by the geminal dimethyl groups and apparent intramolecular chain stiffening (29.30). The uncharged diacetone acrylamide monomer (DAAM) is more hydrophobic than acrylamide. A M / D A A M copolymers have unusual intermolecular associations which increase at certain copolymer compositions with addition of electrolytes (22). High concentrations of D A A M result i n intramolecular associations with micelle-like structures.



323


The polyampholytes of this study, the ADAS (24) and A DASA M (25), have unusual properties i n that viscosity increases upon addition of simple electrolytes to the respective aqueous solutions. This "antipolyelectrolyte" behavior is due to disruption of strong ionic interactions between adjacent or closely spaced mers. It should be noted that unbalanced compositions of cationic and anionic units leads to traditional polyelectrolyte behavior. Additionally, the A D A S A M terpolymers or low charge density ampholytes are much larger than the high charge density A D A S copolymers. A number of solution parameters of the model copolymers of this study are listed i n Table I along with structural data. Zero shear intrinsic viscosity [η] from low shear rheometry, weight average molecular weights M and second virial coefficients Aa from low angle laser light scattering, and translational diffusion coefficients D from quasielastic light scattering are given for each sample. Hydrodynamic diameter d,, was calculated from D using the StokesEinstein relationship. w


0

0

Drag Reduction Studies. We continue to use a method of data reduction previously reported by our group (McCormick, C. L. et al., Macromolecules. two articles i n press) which is quite instructive when examining the role of molecular parameters and solvation. Percent drag reduction is defined by Equation (1) in which f, and f represent the friction factors of solvent and polymer solution, respectively. p

% DR = [(f. - f )/fj χ 100 p

(3)

Values of friction factor can be obtained from plots of the type shown i n Figure 1 at a given Reynolds number above the laminar/turbulent transition. Normalized DR is then plotted vs [nJC, a dimensionless parameter related to polymer volume fraction. Figure 2 is representative of this relationship, which we call an efficiency plot, for selected polymer models (Table I) tested i n either tube flow or rotating disk geometries. Normalization procedures allow direct comparison of diverse polymer types with different degrees of polymerization and solvation. Each branch of the family of curves represents a particular polymer type (symbols for legends are found in Table II). The most efficient have high values of % DR/[nJC at low volume fractions. In each case a maximum i n DR efficiency is obtained beyond which increasing values of [nJC only serve to reduce efficiency. A t particular abscissa values for each polymer type, a common slope is reached; eventually at high values of [nJC, the curves merge into a single line. Effects of Composition. Close examination of Figure 2 reveals that the polymers of our study with the greatest drag reduction efficiency (%DR/[T]]C) at the lowest volume fraction are the diacetone acrylamide copolymers (DAAM). The uncharged homopolyacrylamide (PAM) and polyethylene oxide (PEO) yield moderate values; the homopolyelectrolytes are the least efficient. Figure 3 is a plot of DR efficiency curves for the N a A M B copolyelectrolytes in 0.514 Ν NaCI. Those copolymers with the lowest mole percentages of the charged N a A M B comonomer exhibit the highest efficiencies. The N a A M B homopolymer is the least efficient. These trends parallel the hydrodynamic volume as measured by intrinsic viscosity and light scattering (Table I). The D A A M copolymers, on the other hand, show increasing DR efficiency with increasing incorporation of the hydrophobic comonomer (Figure 4); this trend does not parallel hydrodynamic volume or molecular weight. It



NaAMB NaAMB NaAMB NaAMB NaAMB NaAMB NaAMB NaAMB

5 10 10* 25 25* 40 40* 100

PAM-MC

PAM-4

WSR-N-12K

WSR-N-60K

WSR-301

Sample [100]

NH,

[95] [90] [90] [78] [76] [66] [64] [0]

NH,

4-CH,_CH->C=0

··

[5] [10] [10] [22] [24] [34] [36] [100]

COO-Na*

ÇH,

NH CHr-O-CH,

fo

-^-CH^-CH^-

[100]

[100]

-4-CH,--CH4-

fo

[100]

[100]

-

40-CHr-CHr)-

Repeating Units [mole %']

— — — — — — —

9.6

35.0

— — —

H,0

22.0 47.0 1.8 52.0 6.3 40.0 9.0 8.4

9.3

34.0

6.4

13.0

16.0

0.514 M NaCI w

6

4

— — — — — — —

—

— — — 5.3*

— 4.5

— 3.6

2.9

—

2.7

—

— 3.8

— 22.0

— 2.5

— 3.9

— 25.0

4.2

1.3

— — —

1.9 1.4

3.0

3.0

— — —

2.4 3.2

24.0 28.0

6.0

24.0

1.7*

4.0*

2

Light Scattering e

d

M χ 10 Α. χ 10* D. χ 10 1 M Urea (g/mol) (mol cmVg)* (cmVsec)

Intrinsic Viscosity [η] (dl/g)

Table I Structure and Solution Properties of Copolymer Models


1600

—

2000

2200

—

2900 3300

1600

3300

— — —

Α·

M


325


Si

IS

888
CO

©i oi ci

ιβ CO Oi Tf ΙΟ OS OS Χ ίθ t> Q06O5N

Ο Ο ΙΟ i l CO 00* II

M M

îî is il

Ό

I

qo^o-o; 00 O 00 Ci H N

>ooc

, -φ-) at constant copolymer volume fraction, [n]C = 0.0015.



334

WATER-SOLUBLE P O L Y M E R S

Effect of Associations and Solvent Ordering. Associations of the relatively hydrophobic diacetone acrylamide units i n the D A A M / A M copolymers appear to be responsible for the enhanced drag reduction efficiency observed for these systems (Figure 1). To further study such effects, viscosity, light scattering, and drag reduction experiments were conducted on each copolymer i n the D A A M series utilizing three solvents which strongly affect the nature of interand intramolecular hydrophobic association. A comparison of the hydrodynamic volume data i n Table I with the drag reduction studies i n our rotating disk apparatus is quite revealing. Figure 9a is a plot of friction factor vs Reynolds number for a 15 ppm solution of D A A M 35 i n deionized water, 1 M urea, and 0.514 M NaCI, respectively. Friction reduction is greatest i n the saline solution i n which intramolecular associations (and any existing intermolecular associations) would be enhanced and lowest i n urea where hydrophobic associations are virtually eliminated. This behavior is not predicted by most drag reduction theoretical models which normally suggest a parallel between DR behavior and hydrodynamic volume. In this case DR is poorest i n urea despite a 3-fold increase i n intrinsic viscosity over that i n saline solutions (Table I). Universal P R Calibration for Diverse Polymer Types. Our method of plotting drag reduction efficiency clearly indicates that copolymer composition is an important consideration in designing optimal DR fluids. Significantly, a family of curves is generated for specified conditions with a distinct curve for each copolymer type as shown in Figure 2. Additional normalization can be accomplished by introduction of a shift factor Δ which allows all data to fall on a single efficiency curve (Figure 10). The polyethylene oxide curve for WSR301 was chosen as a standard (Δ = 1) to which all other curves were adjusted. Table II lists Δ values for all polymers tested in disk flow. Interestingly, shift factors range over two orders of magnitude with D A A M 35 giving the largest value of Δ and homopolyelectrolytes the lowest. Agreement with Theoretical Models. Recently we applied our experimental results to a number of theoretical models found in the literature (McCormick, C. L. et al., Macromolecules. i n press). One model showing particular promise is that of Ryskin (9,10) which involves polymer extension dynamics i n what is referred to as a yo-yo model. Equation 2 yields the polymer effect on viscosity enhancement ζ : a

w

ίιιΑ

= O.OÔaXaWC/M. N a C Ν

A

= = = =

Avogadro's number length of a repeat unit polymer concentration degree of polymerization

(4)

M , = mol. weight repeat unit α = ratio of chain length to that of a fully extended chain

For each copolymer model, α may be adjusted to yield acceptable correlation with experimental data. We are currently assessing experimental approaches to determine a. We believe that α may be related to our empirical shift factor Δ via the extensibility of an effective segment length or Kuhn segment. We also feel that changes i n coil draining during extension and the related reordering of solvent are important contributions to the drag reduction phenomenon.


21. M c C O R M I C K E T AL.

Drag

Reduction

in Aqueous

335

Solutions

0.0015 π


0.0013 Η

a

a a

0.0011 Η

0.0009 300000

1

1

τ-β

400000

Re

500000

600000

F i g u r e 9. Friction factor vs Reynolds number for D A A M copolymers using various solvents tested by rotating disk. 15 ppm D A A M 35 i n 1 M urea (B), i n deionized water (•), i n 0.514 M NaCI (•).

u

ο ο

10 Η 3

γ 10 ι " η

0.001

0.01 Ah]C

-ι

1

r—τ—ι

1I ι ι

0.1

F i g u r e 10. Polymer solution drag reduction efficiency vs polymer volume fraction employing shift factors. See Table Π for symbol descriptions and shift factor information. Disk flow measurements were made at Re = 520,000.


336

WATER-SOLUBLE POLYMERS


Conclusions The relationship between drag reduction behavior and chemical structure has been investigated for tailored water-soluble copolymers with measured values of intrinsic viscosity, molecular weight, and hydrodynamic volume. Studied were the effects of: structural changes at constant solvent and flow conditions, changes i n molecular weight for constant structure, changes i n hydrodynamic volume at constant molecular weight and structure, and changes i n solvent nature and association for constant structure. Drag reduction studies were conducted both i n a rotating disk and i n a tube flow apparatus. Experimental data were presented by traditional f vs Reynolds number plots and i n normalized %DR vs volume fraction plots at a given Reynolds number under specified conditions of solvent and concentration. Results clearly show the influence of polymer molecular structure on drag reduction efficiency; those polymers with the best efficiencies are polymers with the greatest potential for extension i n turbulent flow. Polyelectrolytes which have often been reported to have the best absolute D R behavior are actually much less efficient than others i n this study. A n empirical shift factor may be introduced to collapse efficiency curves for families of copolymers onto a single universal curve. Initial correlations of experiment and theory utilizing extensional dynamic models such as that proposed by Ryskin have been promising. Of special interest is the possibility of correlating an extensibility factor with our empirical shift factor utilizing an effective segment length concept. Acknowledgments Research support from the Office of Naval Research and the Defense Advanced Research Projects Agency is gratefully acknowledged. References Cited 1.

Toms, B. A. Proceedings of International Congress on Rheology, 1949, Vol. 2, p 135. 2. Virk, P. S. A.I.Ch.E. J. 1975, 21, 625. 3. Virk, P. S. Biotechnology of Marine Polysaccharides; Colwell, R.; Pariser, E. R.; Sinskey, A J., Eds.; Hemisphere: Washington, 1985; p 149. 4. Hlavacek, B.; Rollin, L. Α.; Schreiber, H. P. Polymer 1976, 17, 81. 5. Hlavacek, B.; Sangster, J . Can. J. Chem. Engng. 1976, 54, 115. 6. Lumley, J. L. J . Polym. Sci. Macromolec. Rev. 1973, 7, 263. 7. Fabula, A. G.; Lumley, J . L.; Taylor, W. D. Modern Developments in the Mechanics of Continua; Academic Press: New York, 1966. 8. Lumley, J. L. Phys. Fluids 1977, 20, Part II. 9. Ryskin, G. J . Fluid Mech. 1987, 178, 423. 10. Ryskin, G. Phys. Rev. Lett. 1987, 59, 2059. 11. Walsh, M. Ph.D. Thesis, Cal. Inst. of Technology, Pasadena, CA, 1967. 12. Kohn, M. C. J . Polym. Sci., Polym. Phys. Edn. 1973, 11, 2339. 13. de Gennes, P. G. Physica 1986, 140A, 9. 14. Berman, N. S. The Influence of Polymer Additives on Velocity and Temperature Fields; Gampert, B., Ed.; Springer-Verlag: Berlin, 1985; p 293. 15. Kulicke, W. M.; Kotter, M.; Grager, H. In Advances in Polymer Science; Springer-Verlag: Berlin, 1989; p 1. 16. McCormick, C. L.; Morgan, S. E. Prog. Polym. Sci. 1990, 15(3).


21.

17. 18. 19. 20. 21. 22. Downloaded by UNIV OF ROCHESTER on November 5, 2014 | http://pubs.acs.org Publication Date: July 18, 1991 | doi: 10.1021/bk-1991-0467.ch021

23. 24. 25. 26. 27. 28. 29. 30.

M c C O R M I C K E T AL.

Drag

Reduction

in Aqueous

Solutions

337

Morgan, S. E. Ph.D. Thesis, The University of Southern Mississippi, Hattiesburg, MS, 1988. McCormick, C. L.; Mumick, P. S.; Morgan, S. E. Polymer Preprints 1989, 30(2), 256. McCormick, C. L.; Hester, R. D.; Morgan, S. E.; Mumick, P. S. Pacific Polymer Preprints 1989, 1, 147. McCormick, C. L.; Blackmon, Κ. P. J . Polym. Sci., Polym. Chem. 1986, 24, 2635. Blackmon, K. P. Ph.D. Thesis, The University of Southern Mississippi, Hattiesburg, MS, 1986. McCormick, C. L.; Hutchinson, Β. H.; Morgan, S. E. Makromol. Chem. 1987, 188, 357. McCormick, C. L.; Blackmon, K. P.; Elliott, D. L. J . Polym. Sci., Polym. Chem. 1986, 24, 2619. McCormick, C. L.; Johnson, C. B. Macromolecules 1988, 21, 686. McCormick, C. L.; Johnson, C. B. Macromolecules 1988, 21, 694. Instruction Manual, Model Rotovisco RV3, Haake Instruments: Saddle Brook, NJ. Schlichting, H. Boundary Layer Theory; McGraw-Hill: New York, 1979; p 647. Bird, R. B.; Stewart, W. E.; Lightfoot, Ε. N. Transport Phenomena; John Wiley & Sons: New York, 1980; p 181. McCormick, C. L.; Blackmon, K. P. Macromolecules 1986, 19, 1512. McCormick, C. L.; Blackmon, Κ. P.; Elliott, D. L. Macromolecules 1986, 19, 1516.

RECEIVED June 4, 1990


Roles of Molecular Structure and Solvation on Drag Reduction in

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