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Articles Effects of Congo Red on the Drag Reduction Properties of Poly(ethylene oxide) in Aqueous Solution Based on Drop Impact Images Melissa I. Alkschbirs, Vanessa C. Bizotto, Marcelo G. de Oliveira, and Edvaldo Sabadini* Instituto de Quı´mica, Universidade Estadual de Campinas, Caixa Postal 6154, CEP 13084-862, Campinas, SP, Brazil Received May 4, 2004. In Final Form: August 9, 2004 The presence of very small amounts (ppm) of high-MW polymers in solution produces high levels of drag reduction in a turbulent flow. This phenomenon, often termed as the Toms effect, is highly dependent not only on MW, but also on the flexibility of the macromolecular chain. The Toms effect can be studied through the images of the structures produced after the drop impact against shallow solution surfaces. The splash structures composed of crown, cavity, and Rayleigh jet are highly dependent on the elongational properties of the solution. This work presents the effects of Congo red on the drag reduction properties of poly(ethylene oxide) in aqueous solutions through the analysis of splash structures. Results obtained in this analysis indicate that Congo red molecules act as physical cross-linking agents, decreasing the polymer elasticity and its drag reduction capacity. It was observed that the maximum height of the Rayleigh jet can be used as a sensitive parameter to the complexation between the dye and the polymer molecules.
Introduction Frictional drag results in dissipation of energy, and, for many years, scientists and technologists have attempted to devise methods to minimize this effect. In 1946, B. A. Toms found that a very dilute high-MW polymeric solution in a turbulent flow required a lower pipe flow-pressure gradient than the pure solvent to produce the same flow rate.1 The phenomenon, often termed “Toms effect”, has become of considerable engineering interest, mainly in pumping processes.2-5 Substances such as synthetic polymers, biopolymers, or aggregates of surfactants can produce the phenomenon described above.2,3,6,7 However, poly(ethylene oxide) (PEO), a flexible polymer, is the most effective drag reducing agent in aqueous systems.3 The drag reduction (DR) phenomenon is necessarily complex, as both turbulence effects and the extremely dilute nature of the solutions involved have to be taken into account,2,8 and an understanding of the role of polymers in DR processes at the molecular level is still * Corresponding author. E-mail:
[email protected]. (1) Virk, P. S.; Merrill, E. W.; Mickley, H. S.; Smith, K. A.; MolloChristensen, E. L. J. Fluid Mech. 1967, 30, 305. (2) McCormick, C. L.; Hester, R. D.; Morgan, S. E.; Safieddine, A. M. Macromolecules 1990, 23, 2132. (3) Bailey, F. E., Koleske, V. J., Eds. Poly(ethylene oxide); Academic Press: New York, 1976. (4) Figueredo, R. C. R; Sabadini, E. Collids Surf., A: Physicochem. Eng. Asp. 2003, 215, 77. (5) Kulicke, W. M.; Gra¨gem, H.; Ko¨tter, M. Drag reduction phenomenon with special emphasis on homogeneous polymer solutions - Polymer Characterization/Polymer Solutions; Springer-Verlag: Berlin, 1989. (6) Sellin, R. H. J.; Hoyt, J. W.; Scrivener, O. J. Hydraul. Res. 1982, 20, 29. (7) Lin Z. Q.; Lu, B.; Zakin, J. L.; Talmon, Y.; Zheng, Y.; Davis, H. T.; Scriven, L. E. J. Colloid Interface Sci. 2001, 239, 543. (8) Bonn, D.; Couder, Y.; van Dam, P. H.; Douady, S. Phys. Rev. E 1993, 47, 28.
primitive.9 One theory assumes that the added macromolecules, under high shear, undergo a dynamic chain elongation, absorbing the energy of the eddies in the flow. This energy is then dissipated as elastic shear waves.10-12 Therefore, the DR phenomenon depends strongly on the intrinsic polymer flexibility. Chain elongation occurs when the shear rate in a turbulent flow is greater than the reciprocal of the molecular relaxation time, 1/τ.12,13 The relaxation time for a polymer in solution can be estimated from the Rouse14 and Zimm15 theories, in which both the MW and the concentration of a polymer (C) are contributing factors, as shown in eq 1:
τ)
Mv(ηsp/C)η0 0.586RTλi
(1)
where Mv, ηsp, η0, R, T, and λi are the viscosity-averaged MW, the specific viscosity, the solvent viscosity, the gas constant, the absolute temperature, and the eigenvalues of Zimm theory, respectively. Each λi is associated with one specific linear normal mode due to the cooperative motion of the polymer segments. A range of relaxation time is possible, but the longest τ, where λ ) 1, is the most important for DR.10-12 Experimentally, the studies involving this phenomenon are generally performed during pipe flow. Recently, studies (9) Kim, O.-K.; Choi, L.-S.; Long, T.; Yoon, T. H. Polym. Commun. 1988, 29, 168. (10) Lumley, J. L. Appl. Mech. 1967, 20, 1139. (11) Peterlin, A. Nature 1970, 227, 598. (12) Kim, O.-K.; Choi, L. S.; Long, T.; McGrath, K.; Armistead, J. P.; Yoon, T. H. Macromolecules 1993, 26, 379. (13) Shenoy, A. V. Colloids Polym. Sci. 1984, 262, 319. (14) Rouse, P. E. J. Chem. Phys. 1953, 21, 1272. (15) Zimm, B. H. J. Chem. Phys. 1956, 24, 269.
10.1021/la0489007 CCC: $27.50 © 2004 American Chemical Society Published on Web 11/25/2004
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Figure 1. Molecular structure of Congo red.
of DR have been focused on the visualization of splash structures produced by the impact of a droplet against a shallow aqueous PEO solution.16,17 Splash is a term used for the formation of a crownlike structure, produced by the impact of a droplet on a liquid surface (the target liquid).18,19 In the milliseconds after droplet impact, the gravitational potential energy of the droplet provokes the formation of a “crown” on the liquid-air surface, and a cavity in the target liquid. During the splash evolution, both the collapse of the crown and the closing of the cavity force the liquid upward, forming a column called the Rayleigh jet.20-22 The amplitude of the Rayleigh jet depends on the elongational viscosity of the solution and can be used to estimate the stored impact energy.17 We have already shown that the structures of the splash are sensitive to PEO MW, concentration, and chain flexibility.23 Splash investigations on the restrictions in PEO chain elongation induced by intramolecular chain complexation may add new information on this phenomenon. The addition of very small quantities of Congo Red, CR (Figure 1), to a PEO aqueous solution greatly affects the polymer chain elongation, and therefore DR. A dipoletype cross-coupling formed between the two -NH2groups of CR and the oxygen atoms of the PEO units produces a restriction in the free stretching of the polymer chain.24 This work presents the effects of CR on the DR properties of PEO in aqueous solutions, using “frozen images” of the splash captured with a high-speed CCD camera. The complex formed between CR and PEO was also investigated using electronic fluorescence spectroscopy. Experimental Section Materials and Methods. Aqueous PEO solutions were prepared by an adaptation of the procedure suggested by Little and Wiegard.25 Briefly, samples of PEO 1, 6, 9, 20, and 40 × 105 gmol-1 (Aldrich), weighted within (1 mg, were sprinkled over a large area of water to avoid clumping of the particles. At 3 h intervals, the solutions were gently stirred using a glass rod, to avoid polymer degradation, and this procedure was also repeated on the following day. The final solutions were then prepared in volumetric flasks. For experiments involving polymeric solutions, the same concentration of PEO was used in both the droplet and the target solutions. Congo red (Carlo Erba) was used as received. All of the experiments were carried out using analytical grade water from a Millipore Milli-Q Gradient filtration system. Apparatus Used To Produce the Splash. A complete description of the experimental procedure used to produce and to capture controlled splash images was described elsewhere.23 Droplets (with mass ) 25 ( 2 mg) were released from 184 cm above the surface of the target liquid. The liquid film thickness (0.31 cm) was adjusted in each experiment. The drop impact (16) Sabadini, S.; Alkschbirs, M. I. Journal Visualization 2001, 4, 217. (17) Sabadini, E.; Alkschbirs, M. I. Exp. Fluids 2002, 33, 242. (18) Worthingon, A. M. Proc. R. Soc. 1882, 1188, 217. (19) Cossali, G. E.; Coghe, A.; Marengo, M. Exp. Fluids 1997, 22, 463. (20) Hobbs, P. V.; Kezweeny, A. J. Science 1967, 155, 1112. (21) Hobbs, P. V.; Osheroff, T. Science 1967, 158, 1184. (22) Macklin, W. C.; Hobbs, P. V. Science 1969, 166, 107. (23) Sabadini, E.; Alkschbirs, M. I. J. Phys. Chem. B 2004, 108, 1183. (24) Inge, C.; Johansson, A. V.; Lindgren, E. R. Phys. Fluids 1979, 22, 824. (25) Little, R. C.; Wiegard, M. J Appl. Polym. Sci. 1970, 14, 409.
Figure 2. Schematic representation of a drop impact against a shallow liquid surface: (a) just before the impact, (b) the crown and cavity formed after the drop impact, and (c) the Rayleigh jet impelled by the collapse of the crown and closing of the cavity. images were captured using a Sony CCD DXC-9000 camera, in which a shutter speed of 1 × 10-4 s was used, set at 30 frames s-1. The captured images were recorded on a tape recorder (Panasonic S-VHS Ag-1980), interfaced with a computer, containing a frame grabber board (Media Cybernetic). Morphological parameters of the impact structures were obtained using the Pro-Plus 3.0 software for image treatment. Averages of the morphologic parameters were obtained from 30 “frozen images” of each splash, and the error bars in the experimental data correspond to one standard deviation. Electronic Spectra. UV-vis spectra of CR aqueous solution with and without PEO were obtained in the range from 200 to 600 nm using a UV/vis spectrometer (HP8453). Fluorescence spectra in the range from 500 to 700 nm were obtained using a luminescence spectrophotometer LS55, Perkin-Elmer, with excitation wavelength ) 500 nm. Viscosity, Surface Tension, and Density Measurements. The shear viscosity of the solutions was measured using an Ostwald viscometer-50. Surface tension measurements were taken using a tensiometer (Sigma 701 System Unit) and the Wilhelmy plate method. The density of the solutions was measured using a density meter (Anton Paar, DMA 58). All of the experiments were conducted at 25 °C.
Results and Discussion Splash Morphology. A three-stage schematic representation of the structures produced after a drop impact against a shallow surface is shown Figure 2. The drop impact energy (Ed) can be determined from eq 2:
Ed ) mgh + mgRd + 4πRd2σ
(2)
where m and Rd are the mass and the radius of the drop, respectively, σ is the surface tension, and h is the height in which the drop is released. In the experimental conditions used in this work, Ed ) 4.5 × 10-4 J. The drop impact produces a cavity and a crownlike structure, and an estimate of the energies of these structures is described in ref 23. Figure 3 shows a comparison among typical crowns (filmed from side and inclined views) obtained for pure water (a), aqueous PEO 4 × 106 g mol-1 solution (40 ppm) (b), and aqueous PEO 4 × 106 g mol-1 (40 ppm) plus 8 ppm of CR (c). It can be seen that secondary jets produced at the top of the crown are smoother and less fragmented for both PEO aqueous solutions in comparison with those formed in water. However, in the presence of CR, these morphologic characteristics are less pronounced. Secondary droplets are produced when the jets at the top of the crown reach the maximum amplitude. At this point, the capillary centripetal force overcomes the inertial force, creating capillary waves which travel back to the center of the jet, creating droplets along the jet (Figure 3a).26 In (26) Mourougou-Candoni, N.; Prunet-Foch, B.; Legay, F.; VignesAadler, M.; Wong, K. J. Colloid Interface Sci. 1997, 192, 129.
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Figure 3. Representative “frozen” pictures (side and inclined views) of crowns formed in the impact of a drop against a liquid target surface for: (a) pure water, (b) 40 ppm of aqueous PEO, and (c) 40 ppm of aqueous PEO solution with 8 ppm of CR. PEO MW ) 4 × 106 g mol-1.
the case of the PEO solutions, the stretching of the polymeric chains produces secondary droplets linked by a thick liquid filament (Figure 3b). The interaction of CR with PEO molecules reduces the chain elongation, increasing the fragmentation of the jets (Figure 3c). The collapse of the crown and the cavity was observed to start approximately 20 ms after the drop impact23 and force a liquid column, known as Rayleigh jet, against the gravitational force. The maximum height of the jet is strongly dependent on the presence of PEO and is affected by the presence of CR (Figure 4). The splash, and mainly the Rayleigh jet, is dependent on the surface tension, shear viscosity, and the elongational properties of the solution. As observed in Table 1, the values of surface tension and shear viscosity of the aqueous PEO solutions are just slightly affected by the
presence of Congo red. This means that the Rayleigh jet is dominated by the elongational viscosity of the solutions. The present interpretation of Rayleigh jet elasticity is fundamentally based only on bulk solution effects. However, the dilatational effects of the surface, due to the PEO molecules adsorbed at the solution-air surface, should also be considered. Typically, the presence of PEO (in the concentration range used) reduced the surface tension by approximately 10 mN m-1 relative to pure water, and this value is practically independent of CR concentration (Table 1). The splash structures are produced so fast that it is possible to assume that there is no change in PEO concentration at the solution-air surface. It is expected that there will be no changes in the PEO excess surface concentration due to the increase in the solution-air surface area during the splash. The short
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Figure 4. Comparison of some representative pictures of the Rayleigh jet for: (a) pure water, (b) 40 ppm of aqueous PEO solution, (c) 40 ppm of aqueous PEO solution containing 8 ppm of CR. PEO MW ) 4 × 106 g mol-1. Table 1. Surface Tension and Shear Viscosity for 40 ppm of Aqueous Solutions of PEO of Different Molecular Weights with and without CR PEO MW/ 105 g mol-1
CR concentration/ ppm
surface tension/ mN m-1
shear viscosity/ cP
1
0 8 0 8 0 8 0 8 0 1 4 8 12 16 20 40 60 80 100
62.70 64.00 62.56 66.33 62.79 66.02 62.76 66.12 62.58 66.13 66.15 64.65 60.70 64.15 65.10 65.32 65.75 66.71 67.03
0.916 0.891 0.908 0.908 0.914 0.910 0.936 0.921 0.914 0.895 0.909 0.922 0.914 0.919 0.922 0.916 0.925 0.955 0.947
6 9 20 40
lifetime of the splash (some milliseconds) is not enough for the PEO molecules to diffuse from the bulk to the solution-air surface. Therefore, we have assumed that the dynamic surface tension is not important. Although the understanding of splash is complex, it has been demonstrated that the height of the Rayleigh jet depends, up to certain limits, on the drop impact energy stored in the process. A linear relationship between the height of the Rayleigh jet of the solvent (Hjs) and the polymeric solution (Hjp) allows an estimation of the percentage of DR, according to eq 3:17
(
)
Hjs %DR ) 1 100 Hjp
(3)
Molecular Considerations. Studies of drop impact of diluted solution of flexible polymers against dry surfaces provide significant insight into the fluid dynamics and the stretching-contraction motion of the polymer chain.27-29 In the present case, we have estimated elongation rates (obtained from the diameter of the cavity during its formation) higher than 3500 s-1.23 This rate is higher than the onset rate in which PEO chains start to stretch.27 During the crown and cavity collapses, similar rates are developed.23 The PEO chains stretch again within an approximately uniaxial flow regime produced during the Rayleigh jet formation. The high local hydrodynamic viscosity experienced by water molecules around the stretched PEO chains reduces not only the probability of eddies being created but also dissipates the energies of eddies, resulting in high levels of DR. The mixing degree of droplet and target liquids has already been determined from experiments using inked droplets. The average area was measured from images of the ink mark taken immediately after the movement of the liquid has stopped. The extent of mixing of the drop and target liquid during the turbulent drop impact for pure water was observed to be almost twice that for an aqueous PEO solution. The global deformation of the primary drop and target liquids is visually higher in the case of PEO solutions. This means that, for water, a significant fraction of the impact energy is dissipated during the mixing of both liquids, resulting in a lower amplitude of the Rayleigh jet.16 The interaction between PEO and CR involves the formation of hydrogen bonds between EO units and NH2 groups of the dye, and the position of the -SO3- groups (27) Bergeron, V.; Bonn, D.; Jean-Yves, M.; Vovelle, L. Nature 2000, 405, 772. (28) Cooper-White, J. J.; Crooks, R. C.; Boger, D. V. Colloids Surf., A 2002, 210, 105. (29) Richard, D.; Clanet, C.; Que´re´, D. Nature 2002, 471, 811.
Effects of Congo Red on the Drag Reduction of PEO
Figure 5. Comparison between the fluorescence spectra of CR in pure aqueous solution (bottom) and in aqueous solution in the presence of 40 ppm of PEO (top). CR concentration ) 8 ppm in both cases. Inset: Dependence of the maximum intensity of CR fluorescence in water and in 40 ppm of PEO on the CR concentration. The curves are drawn as a guide to the eye.
Figure 6. Dependence of the maximum height of the Rayleigh jet and of the ratio of CR fluorescence intensity in aqueous PEO solution (FIPEO+CR) to pure aqueous solution (FICR) on the CR concentration (FI measured at 614 nm). The dashed curves are drawn as a guide to the eye.
was already shown to have an important role in the intensity of this interaction.30 In very diluted solution of polymer and dye, it is more probable that the two NH2 groups of a CR molecule interact with two EO units in different parts of the PEO molecule. Therefore, the CR molecules act as physical cross-linking agents, reducing the elasticity of the PEO chain under flow. The rupture of such interactions has been demonstrated under energetic flow.24 Fluorescence measurements were carried out using the luminescent properties of CR to investigate the interaction between PEO and CR molecules. As shown in Figure 5, the intensity of the CR band at ca. 614 nm is clearly higher in PEO solution than in pure aqueous solution (in both cases, the CR concentration was kept at 8 ppm). The inset in this figure shows the fluorescence intensity measured at 614 nm for CR in 40 ppm of PEO solution as compared to CR in water as a function of CR concentration. Figure 6 shows the concentration effect of CR in the maximum amplitude of the Rayleigh jet, in which the concentration of PEO (4 × 106 g mol-1) was kept constant at 40 ppm. In the range of CR concentration between 0 and 12 ppm, there is a sharp decrease in the height of the jet, and consequently in the capacity of PEO to act as a drag reducing agent. Beyond this point, a plateau is observed. For comparison, the results of CR fluorescence were plotted in the same figure. The ratio between the (30) Berman, N. S.; Berger, R. B.; Leis, J. R. J. Rheol. 1980, 24, 571.
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Figure 7. Dependence of the maximum height of the Rayleigh jet in aqueous solutions containing 40 ppm of PEO and CR on the CR concentration. The dashed curve is drawn as a guide to the eye.
fluorescence intensities for CR with (FIPEO+CR) and without PEO (FICR) as a function of CR concentration is correlated with the results of the Rayleigh jet height. The minimum in the height of Rayleigh jets corresponds to a maximum in the intensity of CR fluorescence ratio. This means that when CR molecules complexes with some EO units, not only the elasticity of PEO but also the translational and rotational freedom-degrees of CR molecules decrease. Therefore, the nonradiative decay is reduced, favoring the luminescent process. An increase in the intensity of CR fluorescence was also observed when CR is in the presence of a peptide solution, and this is attributed to the formation of a self-assembled complex between CR and the helical peptide.31 The capacity of PEO to act as a drag reducing agent decreases from approximately 70% to 50% when ∼10 ppm of CR is present. In this concentration, the ratio of CR molecule/PEO units is low; however, it is enough to change significantly the elasticity of PEO. A decrease in the relaxation time of PEO chains was observed by Berman et al. when CR is present in aqueous PEO solution. This means that the polymer chains become stiffer and more compact. However, when the stress is high enough, a coilstretching transition occurs.32 We have carried out an experiment with higher concentrations of CR to investigate the intermolecular interaction between complexed PEO molecules coupled by CR (Figure 7). A minimum in the height of the Rayleigh jet is achieved when CR concentration is in the range of 10-20 ppm. Beyond this range, the height of the jet increases slightly. This result is in agreement with the DR results observed by Berman et al. for experiments developed in a pipe flow rheometer.30 The increase in the size of the complex PEO-CR-PEO due to the intermolecular complexation overcomes the decrease in the PEO chain flexibility observed for CR concentrations below 1220 ppm, resulting in a slight increase in the Rayleigh jet. The CR effect on the elasticity of PEO with different MW was also investigated (Figure 8). For this study, the concentrations of PEO and CR were fixed at 40 and 8 ppm, respectively. For comparison, the height of the jet with and without CR is presented. The height of the jet for the PEO-CR system is almost the same for PEO with different molecular weights. The height of the Rayleigh jet cannot be sensitive enough to differentiate the complexation of PEO with different molecular weights. The shear viscosity of the studied solutions (inset in Figure 8) (31) Cooper, T. M.; Stone, M. O. Langmuir 1998, 14, 6662. (32) Lee, J. K.; Berman, N. S. J. Rheol. 1996, 40, 1025.
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Conclusions
Figure 8. Height of the Rayleigh jet for 40 ppm of aqueous PEO solution (O) and 40 ppm of aqueous PEO solution containing 8 ppm of CR (9) as a function of PEO MW. Inset: Dependence of the shear viscosity of the solutions as a function of PEO MW. The dashed curves are drawn as a guide to the eye.
is lower for the PEO-CR solution in comparison to the pure aqueous solution of PEO, and the effect is more intense for PEO with high MW. Therefore, it is possible that the elasticity of the PEO-CR is almost the same, in this PEO MW range.
The elasticity of PEO chains is reduced by the intramolecular complexation between the EO units and both extremities of CR. In this case, CR acts as a cross-linking agent. The effects of the complexation can be clearly observed by the changes in the morphology of the structures developed during the short lifetime of the splash. The typical smooth and long secondary jets produced at the top of the crown for PEO aqueous solution become more fragmented when CR is added to the polymer solution. The Rayleigh jet is sensitive to the CR complexation, revealing the decrease of PEO capacity to act as a drag reducing agent, and the effect is more pronounced with high MW PEO. The complexation between PEO units and CR is also observed in CR fluorescence experiments, revealing a good agreement with the results of the drop impact experiments. Acknowledgment. We would like to thank CNPq and FAPESP for financial support. M.I.A. and V.C.B. held graduate fellowships from Fundac¸ a˜o de Amparo a` Pesquisa do Estado de Sa˜o Paulo, FAPESP, and Coordenac¸ a˜o de Aperfeic¸ oamento de Pessoal de Nı´vel Superior, CAPES, respectively. LA0489007
