Ind. Eng. Chem. Res. 1997, 36, 5483-5487
5483
Differences in the Flow Behaviors of Polymeric and Cationic Surfactant Drag-Reducing Additives Jiri Myska Institute of Hydrodynamics, Prague, Czech Republic
Jacques L. Zakin* Department of Chemical Engineering, The Ohio State University, Columbus, Ohio 43210
Research on cationic surfactant drag-reducing additives has grown in recent years because of their repairability after shear degradation, making them suitable for potential applications in recirculation flows such as district heating and district cooling systems. Substantial differences between their flow behaviors and those of high-polymer, drag-reducing additives have been found. These include the influence of preshearing, the effect of mechanical shear on degradation, the influence of tube diameter, maximum drag-reduction effectiveness, and the shape of their mean velocity profiles. Examples of these different flow behaviors are described. The differences suggest that the mechanisms for causing drag reduction may be different for the two types of additives. Introduction Drag reduction by additives is a flow phenomenon in which small amounts of an additive in a fluid cause a reduction in the turbulent friction compared with that of the pure fluid at the same flow rate. The dragreduced flow remains turbulent, however, with a modified turbulent structure. A reduction in energy loss in turbulent pipe flow of wood pulp fiber suspensions in water was reported by Forrest and Grierson (1931) more than 65 years ago. This first report of drag reduction went largely unnoticed (Radin, 1974; Nadolink and Haigh, 1995). Mysels and his associates (Mysels, 1949; Agoston et al., 1954; Mysels, 1971) found that the pressure drop in pipe flow for gasoline thickened by aluminum disoaps was lower than that of pure gasoline at the same flow rate. Because of war-time secrecy requirements, their results were not released until 1949 when a patent was issued listing a 1945 application date. At the First International Rheological Congress in 1948, Toms (1949, 1977) reported drag-reduction results on dilute solutions of high-molecular-weight poly(methyl methacrylate) in monochlorobenzene. He observed that, at constant pressure gradient, the flow rate could be increased by the addition of the polymer. Drag reduction is sometimes called the “Toms Effect”. The Mysels and Toms results were the first in which drag reduction was recognized. Since the first reports of drag reduction, a large number of researchers have worked in this area. Nadolink and Haigh (1995) compiled a bibliography on drag reduction by polymers and other additives. There are over 4900 references dating from 1931 to 1994. The potential use of drag-reducing additives in recirculating turbulent flow systems such as district heating or district cooling systems has generated interest in finding suitable additives for recirculating systems. Such applications would require additives which either do not degrade with mechanical shear or extensional flows or will repair after degradation. Since effective high-polymer, drag-reducing additives are sensitive to * Author to whom correspondence should be addressed. E-mail:
[email protected]. S0888-5885(97)00324-2 CCC: $14.00
mechanical degradation, there has been a great deal of interest in aqueous surfactant drag-reducing systems in the last decade as these additives are “repairable” after mechanical degradation. These and other differences suggest that there may be differences in their drag-reduction mechanisms. The differences range from the form of their viscosity-shear rate curves, their response to shear-degrading conditions, tube diameter effects, limiting drag-reduction asymptotes, and limiting mean velocity profile asymptotes. This paper will illustrate these differences from our own results and from data in the literature and will relate them to the differences in the nature of the two types of additives. Experimental Section Rheological measurements were made with rotational rheometers (Rotovisco RV 20 and CV 20 of Haake) using procedures recommended by Haake which provide for necessary corrections. The steady shear-flow curves were measured with a coaxial cylinder fixture (Figure 1), and the first normal stress differences were measured with a cone-plate system (Figure 2). Mean velocity profiles were measured with a laser Doppler anemometry (LDA) system which was assembled from standard Dantec components and a Carl Zeiss argon-ion laser. With the use of LDA, there is always an uncertainty in the location of the light beam’s cross section, which is not a point but a rhombus-like plane with side lengths of the order of several tenths of millimeters but well below 1 mm. The distance of the rhombus center from the tube wall has an uncertainty of about 0.1 mm. Surfactants used were Habon G (hexadecyldimethyl(hydroxyethyl)ammonium 3-hydroxy-2-naphthoate supplied by Hoechst AG) and Ethoquad T/13-50 (tallow tris(hydroxyethyl)ammonium acetate supplied by AkzoNobel) with sodium salicylate counterion. At very low concentrations, the amount of drag reduction increases with concentration, but it levels off at some concentration which depends on the surfactant chemical composition (Chara et al., 1993). All drag-reduction data shown here are at or near this saturation level. © 1997 American Chemical Society
5484 Ind. Eng. Chem. Res., Vol. 36, No. 12, 1997
Figure 1. Apparent viscosity (η) vs shear rate (D) for Ethoquad T/13-50-sodium salicylate system (1.5 mM/3.9 mM).
Figure 2. First normal stress difference (N1) vs shear rate (D) for Habon G solution (2 mM).
In all pipe flow experiments, pipes with smooth walls were used. Results and Discussion A. Viscosity and Normal Stress vs Shear Rate Behavior. Dilute polymer solutions such as those effective as drag reducers typically are shear thinning. Generally, they can be described by a power law equation with power law index less than unity. Dragreducing surfactant solutions, whose micelles are rodlike in shape, are also shear thinning at low shear rate but generally show a rise in viscosity at higher shear rates after preshearing. This is shown in Figure 1 for Ethoquad T/13-50 with sodium salicylate (NaSal) counterion. Above 120 s-1, there is a steep rise in viscosity in the lower (before preshearing) curve (see Figure 1). This is believed to be caused by formation of a shearinduced structure (SIS). After further shearing by pumping around the flow loop, viscosity increases still more. The variety of shear effects on viscosity for dragreducing polymer and surfactant solutions indicates that shear-viscosity effects are not in themselves relevant for predicting drag-reduction behavior. However, microstructure changes, which manifest themselves in SIS, are probably relevant. The increased viscosity is often accompanied by the occurrence of an enhanced first normal stress difference (N1) and flow birefringence indicating that the rod-like micelles are aligned in some form of supramolecular structure (Hoffman and Hofmann, 1993). At very high
Figure 3. Percent drag reduction vs solvent Reynolds number for Ethoquad T/13-50-sodium salicylate system (3.75 mM/5.63 mM) showing effect of time of shearing (Chou, 1991).
shear rates, the SIS becomes shear thinning again. The SIS structure will relax to its original structure if shear is removed. The relaxation time varies with the nature of the surfactant-counterion system, the concentrations, the level of shear imposed, and the temperature. Figure 2 shows N1 vs shear rate data for 2 mM Habon G. The increase in N1 for the unsheared solution is modest and drops off at high shear rates. A similar solution that was presheared in the Couette apparatus for 2 h at a shear rate of 1180 s-1 showed much larger N1 values (measured in the cone and plate apparatus). The N1 values increase rapidly until about 200 s-1 and then increase more gradually. The SIS formed is stable to much higher shear rates than the structure in the unsheared solution. While relatively large first normal stress differences are generally found in drag-reducing polymer and surfactant solutions, they are not always present. For example, Lu et al. (1997) showed an example of a drag-reducing surfactant solution which had zero first normal stress differences. Also, Myska et al. (1996) showed a non-drag-reducing surfactant system with significant first normal stress differences. Dilute high-polymer solution behavior in these types of experiments would be different. Unsheared polymer solutions are generally shear thinning. If high-molecular weight polymer solutions were sheared like the solutions in Figures 1 and 2, the polymer molecular weight would be reduced and viscosity and normal stress differences would diminish to near water-like behavior. B. Degradation by Shear. The supramolecular structures of surfactant solutions are broken up in very high shear regions. Figure 3 shows percent drag reduction vs solvent Reynolds number in a 6.2-mm tube (Chou, 1991). The solution was investigated in a recirculation system driven by a pump. At high Reynolds number (high wall shear stress) a critical wall shear stress is reached, and above this an abrupt loss in drag reduction occurs. At higher Reynolds numbers, all drag reduction is lost. What is unusual about these systems, however, is that if the degraded fluid enters a region of low shear (for example if the flow rate is reduced), the structure is “repaired” and the solution completely regains its drag-reduction capabilities. This reversible effect can be repeated many times, and drag reduction of the same magnitude is always regained. This par-
Ind. Eng. Chem. Res., Vol. 36, No. 12, 1997 5485
Figure 4. Fanning friction factor vs solvent Reynolds number for 1000 ppm polyisobutylene (MW ) 800 000) in cyclohexane at 30 °C (Hershey, 1965).
ticular solution was recirculated at high and low Reynolds numbers for 8 days with no loss of effectiveness for Reynolds numbers below 80 000. The reason these systems can do this is that the surfactant micelles and the supramolecular structures formed are thermodynamically stable. They are held together by secondary forces which are always present. If they are broken up in regions of very high shear, the equilibrium structures tend to reform if shear stresses are reduced. This occurs rapidly, in the order of 1 s or less. Polymer solutions also degrade mechanically when subjected to high shear. The high-molecular-weight polymer molecules break down to molecules of lower molecular weight which contribute not at all to drag reduction and only modestly to viscosity. For this reason, high polymers are not used in recirculation flows. In fact, they need to be replenished each time they pass through a pump in the Alyeska and other pipelines (Burger et al., 1982). High-polymer molecules cannot be “repaired” as the mechanical shear breaks primary chemical bonds and the probabilities of the free ends remating in dilute solution are nil. C. Diameter Effect. Figure 4 shows the effect of tube diameter on the onset of drag reduction for a 1000 ppm polyisobutylene polymer (800 000 molecular weight) in cyclohexane (Hershey, 1965). This polymer is not as effective a drag reducer as many others, but the data illustrate the influence of tube diameter on the onset of drag reduction. The friction factor-Reynolds number data lie close to the von Karman equation until a critical shear rate is reached at which the onset of drag reduction begins. The critical shear rate is reached at decreasing Reynolds numbers as diameter decreases. For the 0.032- and 0.046-in. diameter tubes, it is reached before the transition friction factor data reach the von
Figure 5. Blasius friction factor (λ) vs solvent Reynolds number for 500 ppm Habon G solution showing effect of tube diameter (Pollert et al., 1993).
Karman curve. While the velocity profiles in the smallest tubes may be affected by the viscous wall layer being a substantial fraction of the total cross sectional area, the trend of onset with diameter is clear. For surfactant solutions, the critical onset shear rate is reached at low Reynolds numbers, and turbulent friction factor data generally appear as gradual departures from the laminar curve in these types of plots. Drag reduction increases until a critical wall shear stress is reached, above which the surfactant microstructure is mechanically degraded and the friction factor abruptly approaches the von Karman line and drag reduction is lost (as seen in Figure 3). Figure 5 shows that for a 500 ppm Habon G solution, loss of drag reduction occurs at low solvent Reynolds numbers for the 4- and 6-mm tubes as the critical wall shear stress is exceeded and the SIS is broken up (Pollert et al.,
5486 Ind. Eng. Chem. Res., Vol. 36, No. 12, 1997
1993). The critical shear stress is not reached until higher Reynolds numbers for the larger tubes. Note the steep rises for the 10- and 20-mm tubes. For the 39.4mm tube, the critical wall shear stress is not exceeded at solvent Reynolds numbers exceeding 105. D. Maximum Drag Reduction Asymptote. Virk et al. (1970) examined drag-reduction data for a large number of “concentrated” polymer solutions and proposed a maximum drag-reduction asymptote (MDRA). This defined the lower limit of friction factor achievable with polymer drag-reducing additives. The equation for the MDRA is
1 ) 19.0 log Rexf - 32.4 xf
(1)
f ) 0.58Re-0.58
(2)
or
for Reynolds numbers 4000-40000. Examination of data in Figure 5 for the 39.4-mm tube and those of several authors (Pollert et al., 1993; Fankha¨nel, 1991; Weber, 1990; Althaus, 1991; Ohlendorf and Schwarz, 1984; Myska and Vlasak, 1988; Myska and Vocel, 1977; Sylvester and Smith, 1979; McMillan et al., 1971; Chara et al., 1993) who reported drag-reducing data for a variety of surfactants and two aluminum disoaps indicates that friction factors significantly lower than those predicted by the MDRA for high-polymer solutions can be observed. A proposed envelope curve to represent the minimum achievable friction factors (maximum drag reduction) represents an MDRA for surfactants and aluminum disoaps which lies significantly below eqs 1 and 2. The equation (Zakin et al., 1996) is
while that of Virk et al. (1970) for the elastic sublayer region for high polymer solutions is
f ≈ 0.32Re-0.55
u+ ) 26.9 log y+ - 17
(
0.1108 e0.4u - 1 - 0.4u+ +
u+ ) 53.9 log y+ - 65
(3)
The data for the two aluminum disoaps in hydrocarbon solvent (McMillan et al., 1971; Sylvester and Smith, 1979) lie close to the aqueous surfactants. These soaps form inverse micelles in the hydrocarbon solutions with structures and flow behaviors more like those of surfactant solutions than those of high-polymer solutions. E. Mean Velocity Profiles. Figure 6 shows mean velocity profile (u+ vs y+) data for Habon G in water. Habon G is an excellent drag-reducing additive, and friction factor data for Habon G which lie below the MDRA of eqs 1 and 2 were cited above. The measured points for water in the mean velocity profile in Figure 6 generally follow the Spalding (1961) correction (eq 4) for the data of Laufer (1954). The points at the lowest values of y+ lie about 4% below the Spalding equation (dashed curve). The correction has the equation
y+ ) u+ +
Figure 6. Mean velocity profiles (u+ vs y+) for 500 ppm Habon G solutions at different solvent Reynolds numbers.
)
(0.4u+)2 (0.4u+)3 (4) 2 6
The measured points for water at high values of y+ lie above the theoretical line as well as do similar measurements of other authors. This is ascribed to the “wake” effect. The high Reynolds number velocity profile data for Habon G in Figure 6 fit the equation of Chara et al. (1993)
(5)
(6)
The slope of eq 5 is significantly steeper than that of eq 6. The steeper slope of eq 5 gives a mixing length constant of 0.02, much lower than the value of 0.04 for eq 6. Bewersdorff and Thiel (1993) and Bewersdorff and Ohlendorf (1988) observed even steeper velocity profiles with surfactant drag-reducing additives, suggesting that the ultimate slope may be even steeper than predicted by eq 5. While we do not have a mechanistic explanation for the lower limiting friction factors and steeper velocity profiles obtained with surfactant solutions, a threedimensional intertwined (thread-like network) structure is formed in the surfactant solution (Lu et al., 1996). This pervasive network should be more effective in inhibiting eddy formation and turbulence production than polymers, some of which reach maximum dragreduction at concentrations 1 or 2 orders of magnitude lower. The 3-dimensional networks may account for the higher ultimate effectiveness and steeper velocity profiles of surfactant solutions compared with drag-reducing polymer solutions. Conclusions Polymer solutions are generally shear thinning while cationic surfactants show increases in viscosity when sheared, indicating the formation of a shear-induced structure (SIS). Polymer solutions degrade irreversibly when sheared and lose their drag-reduction behavior. Cationic sur-
Ind. Eng. Chem. Res., Vol. 36, No. 12, 1997 5487
factants degrade under high shear, but the structures are “repairable” and they regain their drag-reducing ability when shear is reduced. Dilute polymer solutions become drag reducing when a critical shear rate is exceeded. Surfactant solutions generally show a gradual departure from the laminar flow curve and are drag reducing until a critical shear rate is reached. Friction factors significantly below those predicted by the maximum drag-reduction asymptote for high polymers can be reached in cationic surfactant and aluminum disoap systems. Turbulent mean velocity profiles for cationic surfactants can be significantly steeper than the limit predicted by the elastic sublayer model for high polymers. A three-dimensional intertwined thread-like network formed in surfactant solutions may cause a different drag-reduction mechanism from that for high-polymer solutions. Acknowledgment This research was supported in part under Grant 12.074E, Program in Science and Technology Cooperation, Office of Science Advisor, U.S. Agency for International Development. Financial support by the Czech Agency of the Czech Republic, Praha, is also gratefully acknowledged. Literature Cited Agoston, G. A.; Harte, W. H.; Hottel, H. C.; Klemm, W. A.; Mysels, K. J.; Pomeroy, H. H.; Thompson, J. M. Flow of Gasoline Thickened by Napalm. Ind. Eng. Chem. 1954, 46, 1017-1019. Althaus, W. Anwendung Widerstandsvermindernder Additive in Fernwa¨rmesystemen. (Use of Drag-Reducing Additives in District Heating Systems.) Ph.D. Dissertation, Universita¨t Dortmund, Dortmund, Germany, 1991. Bewersdorff, H. W.; Ohlendorf, D. The Behavior of Drag-Reducing Cationic Surfactant Solutions. Colloid Polym. Sci. 1988, 266, 941-953. Bewersdorff, H. W.; Thiel, S. Turbulence Structure of Dilute Polymer and Surfactant Solutions in Artificially Roughened Pipes. Appl. Sci. Res. 1993, 50, 347-368. Burger, E. D.; Munk, W. R.; Wahl, H. A. Flow Increase in the Trans Alaska Pipeline Through Use of a Polymeric DragReducing Additive. J. Pet. Technol. 1982, Feb, 377-386. Chara, Z.; Zakin, J. L.; Severa, M.; Myska, J. Turbulence Measurements of Drag-Reducing Surfactant Systems. Exp. Fluids 1993, 16, 36-41. Chou. L. C. Drag Reducing Cationic Surfactant Solutions for District Heating and Cooling Systems. Ph.D. Dissertation, The Ohio State University, Columbus, Ohio, 1991. Fankha¨nel, M. Durchverlust and Wa¨rmeu¨bergang in Fernwa¨rmesystemen bei Einsatz von Mizzellasen Widerstandsverminderen. (Pressure Loss and Heat Transfer in District Heating Systems by Use of Micellar Drag-Reducing Additives.) Ph.D. Dissertation, Universita¨t Dortmund, Dortmund, Germany, 1991. Forrest, F.; Grierson, G. A. Friction Losses in Cast Iron Pipe Carrying Paper Stock. Pap. Trade J. 1931, 92 (22), 39-41. Hershey, H. C. Drag Reduction in Newtonian Polymer Solutions. Ph.D. Dissertation, University of MissourisRolla, Rolla, MO, 1965. Hoffman, H.; Hofmann, S. Surfactant Solutions Under Shear. Proc. Fluid Mechanics and Hydrodynamical Aspects of Biosphere, Castle Liblice, Academy of Sciences of the Czech Republic, pp 5-13, Sept 1993. Laufer, J. The Structure of Turbulence in Fully Developed Pipe Flow. National Advisory Committee for Aeronautics Tech. Rep. 11, U.S. Government Printing Office: Washington, DC, 1954.
Lu, B.; Li, X.; Talmon, Y.; Zakin, J. L. Influence of Chemical Structures of Cationic Surfactants on Their Drag Reduction and Rheological Behaviors. presented at XIIth International Congress on Rheology, Quebec, Canada, August 18-23, 1996, pp 373-374. Lu, B.; Li, X.; Zakin, J. L.; Talmon, Y. A Non-Viscoelastic Drag Reducing Cationic Surfactant System. J. Non-Newtonian Fluid Mech. 1997, 71, 59-72. McMillan, M. L.; Hershey, H. C.; Baxter, R. Effects of Aging, Concentration, Temperature, Method of Preparation, and Other Variables on the Drag Reduction of Aluminum Disoaps in Toluene. Chem. Eng. Prog. Symp. Ser. 1971, 67, 27-44. Mysels, K. J. Flow of Thickened Fluids, U.S. Patent No. 2,492,173, 1949. Mysels, K. J. Early Experiences with Viscous Drag Reduction. Chem. Eng. Prog. Symp. Ser. 1971, 67, 45-49. Myska, J.; Vocel, S. The Flow of Model Suspension with Complex Soap in a Tube. Vodohospod. Cas. 1977, 25, 74-94. Myska, J.; Vlasak, J. Flow of Capsules in a Drag Reducing Liquid. Commun. Inst. Hydrodyn. (Praha), 1988, 16, 57-71. Myska, J.; Zakin, J. L.; Chara, Z. Viscoelasticity of a Surfactant and Its Drag-Reducing Ability. Appl. Sci. Res. 1996, 55, 297310. Nadolink, R. H.; Haigh, W. W. Bibliography on the Skin Friction Reduction with Polymers and other Boundary-Layer Additives. Appl. Mech. Rev. 1995, 48 (7), 351-460. Ohlendorf, D.; Schwarz, G. M. Minderung von Rohrreibungsverlusten durch langzeitstabile Additive. (Reduction of Pressure Drop in Pipes by Long-Time Stable Additives.) Report for Hoechst AG and EBV-Fernwa¨rme GmbH, 1984. Pollert, J.; Komrzy, P.; Vozenilek, A.; Zakin, J. L. Influence of Pipe Diameter and Temperature on Efficiency of Drag Reducing Surfactants. Proc. Fluid Mechanics and Hydrodynamical Aspects of Biosphere, Castle Liblice, Academy of Sciences of the Czech Republic, pp 61-67, Sept 1993. Radin, I. Solid-Fluid Drag Reduction. Ph.D. Dissertation, Univ. of MissourisRolla, Rolla, MO, 1974. Spalding, D. B.; A Single Formula for the ‘Law of the Wall’. Trans. ASME, J. Appl. Mech. 1961, 455-458. Sylvester, N. D.; Smith, P. S. The Concentration and Friction Velocity Effects on Drag Reduction of Dowell-APE in Kerosene. Ind. Eng. Chem. Prod. Res. Dev. 1979, 18, 47-49. Toms, B. A. Some Observations on the Flow of Linear Polymer Solutions Through Straight Tubes at Large Reynolds Numbers. Proc. 1st Int. Rheological Congress, II, Part 2. North-Holland: Amsterdam, The Netherlands, 1949; 135-142. Toms, B. A. On the Early Experiments on Drag Reduction by Polymers. Phys. Fluids 1977, 20 (10), 53-55. Virk, P. S.; Mickley, H. S.; Smith, K. A. The Ultimate Asymptote and Shear Flow Structures in Toms’ Phenomenon. ASME, J. Appl. Mech. 1970, 37, 488-493. Weber, M. Wa¨rmeu¨bergang und Druckverlust wasseriger Tensidlosungen in Rohren und Rohrwendeln. (Heat Transfer and Pressure Loss of Aqueous Surfactant Solutions in Pipes and Coils.) Ph.D. Dissertation, Universita¨t Dortmund, Dortmund, Germany, 1990. Zakin, J. L.; Myska , J.; Chara, Z. New Limiting Drag Reduction and Velocity Profile Asymptotes for Nonpolymeric Additives Systems. AIChE J. 1996, 42, 3544-46.
Received for review May 7, 1997 Revised manuscript received August 25, 1997 Accepted August 29, 1997X IE9703245
X Abstract published in Advance ACS Abstracts, November 1, 1997.
