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Effect of the Flow Field on the Rheological Behavior of Aqueous Cetyltrimethylammonium p-Toluenesulfonate Solutions A. J. Mu¨ller,*,† M. F. Torres,† and A. E. Sa´ez*,‡ Grupo de Polı´meros USB, Departamento de Ciencias de los Materiales, Universidad Simo´ n Bolı´var, Apartado 89000, Caracas 1080-A, Venezuela, and Department of Chemical and Environmental Engineering, University of Arizona, Tucson, Arizona 85721 Received January 6, 2004. In Final Form: February 25, 2004 It is well-known that solutions of cetyltrimethylammonium p-toluenesulfonate in water exhibit a pronounced shear-thickening phenomenon in a specific concentration range (0.1-0.8%) when they are subjected to simple-shear flows, as a consequence of flow-induced self-assembly of wormlike micelles. This work shows that a strong elongational flow field (opposed-jets flow), applied to the same solutions, does not lead to extension thickening because the extensional flow prevents or destroys micellar association. In flow through a porous medium, a substantial increase in apparent viscosity is observed beyond a critical apparent shear rate, which surpasses increases observed in simple-shear flows. This is explained as the result of a synergistic effect of shear and relatively weak elongation on the solution microstructure.
Introduction Wormlike micelles have attracted much attention in recent years in view of their intriguing rheological and thermodynamic properties and for potential applications in drag reduction and enhanced oil recovery and as templates for material synthesis.1-5 A typical example of a surfactant capable of forming wormlike micelles in aqueous solution is cetyltrimethylammonium p-toluenesulfonate (CTAT). Dilute cationic surfactant solutions such as CTAT in water typically exhibit a shear-thickening behavior that has been studied by a number of techniques, including shear rheometry, small-angle neutron scattering (SANS), light scattering microscopy, flow birefringence, and cryo-transmission electron microscopy.6-18 The shear-thickening behavior * Authors for correspondence. † Universidad Simo ´ n Bolı´var. ‡ University of Arizona. (1) Schubert, B. A.; Kaler, E. W.; Wagner, N. J. Langmuir 2003, 19, 4079-4089. (2) Bautista, F.; Soltero, F. A.; Macı´as, E. R.; Puig, J. E.; Manero, O. J. Phys. Chem. B 2002, 106, 13018-13026. (3) Zakin, J. L.; Bewersdorff, H. W. Rev. Chem. Eng. 1998, 14, 253320. (4) Maitland, G. C. Curr. Opin. Colloid Interface Sci. 2000, 5, 301311. (5) Kim, W. J.; Yang, S. M. Chem. Mater. 2000, 12, 3227-3235. (6) Truong, M. T.; Walker, L. M. Langmuir 2002, 18, 2024-2031. (7) Gravsholt, S. Proc. Int. Congr. Rheol. 1980, 8, 629. (8) Rehage, H.; Hoffmann, H. Rheol. Acta 1982, 21, 561. (9) Hu, Y.; Wang, S.; Jamieson, A. J. Rheol. 1993, 37, 531. (10) Hoffmann, H.; Hofmann, S.; Rauscher, A.; Kalus, J. Prog. Colloid Polym. Sci. 1991, 84, 24. (11) Jindal, V. K.; Kalus, J.; Pilsl, H.; Hoffmann, H.; Lindner, P. J. Phys. Chem. 1990, 94, 3129. (12) Schmitt, V.; Schosseler, F.; Lequeux, F. Europhys. Lett. 1995, 30, 31. (13) Berret, J.-F.; Gamez-Corrales, R.; Oberdisse, J.; Walker, L. M.; Lindner, P. Europhys. Lett. 1998, 41, 677-682. (14) Lu, B.; Li, X.; Scriven, L.; Davis, H.; Talmon, Y.; Zakin, J. Langmuir 1998, 14, 8. (15) Boltenhagen, P.; Hu, Y.; Matthys, E. F.; Pine, D. J. Europhys. Lett. 1997, 38, 389. (16) Rehage, H.; Wunderlich, I.; Hoffmann, H. Prog. Colloid Polym. Sci. 1986, 72, 51. (17) Oda, R.; Panizza, P.; Schmutz, M.; Lequeux, F. Langmuir 1997, 13, 6407. (18) Keller, S.; Boltenhagen, P.; Pine, D.; Zasadzinski, J. Phys. Rev. Lett. 1998, 80, 2725.
has been explained in terms of either shear-induced structures (SIS) or shear-induced phase transitions.13,16,19,20 Microgels and other types of aggregates, such as interlinked micellar rings, have been proposed as SIS in this type of system.21 In particular, a certain number of works in the literature13,22-25 have investigated the shear flow behavior of CTAT in the dilute to semidilute concentration range, where the shear-thickening phenomenon is observed. Berret et al.25 provided evidence for the existence of a strongly aligned, birefringent phase in the shearthickening regime. Studies of wormlike micellar solutions in elongational flows are not as common as those for shear flows. We are not aware of works dealing with the elongational flow of CTAT solutions, but other cationic surfactants that form wormlike micelles have been studied. Prud’homme and Warr26 investigated the behavior of solutions of tetradecyltrimethylammonium salicylate in high ionic strength environments using an opposed-jets, Rheometrics RFX extensional rheometer. The solutions exhibited shear thinning and extension thickening. The authors concluded that the wormlike micelles behaved as flexible polymers. However, they hypothesized that micelle scission occurred after a critical strain rate in elongational flow, a fact that was later confirmed by light-scattering measurements.27 The RFX rheometer was used also by Walker et al.28 to perform experiments with solutions of cetylpyridinium chloride/sodium salicylate (NaSal)/sodium chloride. By comparing their measurements of apparent elongational viscosity with measured linear viscoelastic properties, they (19) Hu, Y. T.; Boltenhagen, P.; Pine, D. J. J. Rheol. 1998, 42, 1185. (20) Barentin, C.; Liu, A. J. Europhys. Lett. 2001, 55, 432-438. (21) Oelschlaeger, C.; Waton, G.; Buhler, E.; Candau, S. G.; Cates, M. E. Langmuir 2002, 18, 3076-3085. (22) Gamez-Corrales, R.; Berret, J.-F.; Walker, L. M.; Oberdisse, J. Langmuir 1999, 15, 6755-6763. (23) Truong, M. T.; Walker, L. M. Langmuir 2000, 16, 7991-7998. (24) Berret, J.-F.; Gamez-Corrales, R.; Se´re´ro, Y.; Molino, F.; Lindner, P. Europhys. Lett. 2001, 54, 605-611. (25) Berret, J.-F.; Lerouge, S.; Decruppe, J.-P. Langmuir 2002, 18, 7279-7286. (26) Prud’homme, R. K.; Warr, G. G. Langmuir 1994, 10, 34193426. (27) Chen, C.-M.; Warr, G. G. Langmuir 1997, 13, 1374-1376. (28) Walker, L. M.; Moldenaers, P.; Berret, J.-F. Langmuir 1996, 12, 6309-6314.
10.1021/la0499517 CCC: $27.50 © 2004 American Chemical Society Published on Web 04/17/2004
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concluded that the flow did not induce apparent changes in the structure of the micelles. Recently, Rothstein29 performed elongational flow experiments in a filament stretching rheometer with concentrated solutions of cetyltrimethylammonium bromide in NaSal. They observed strain hardening of the material, which would be consistent with extension thickening, and found evidence of micelle scission. In this work, we report experimental results on the influence of the flow field on the rheological response and the viscosity enhancement capabilities of aqueous solutions of CTAT in the dilute and semidilute range. The results on porous media flow in particular could have important implications for practical applications because this type of flow is present in tertiary oil recovery and soil remediation operations. Experimental Section Materials. 99% pure CTAT was purchased from Sigma and used without any further purification. Water that has been distilled and deionized was employed as the solvent. The solutions were prepared at 25 °C and maintained at that temperature at all times and throughout the experiments to keep them above the Krafft point of CTAT (22.5 °C).23 The solutions were prepared at the desired concentration and left to stand at 25 °C during 20 h before any measurements were performed. Shear Rheometry. For the simple-shear experiments, a Rheometrics ARES shear rheometer with a double-wall Couette fixture was used to measure shear viscosity as a function of shear rate under controlled strain rate conditions. Opposed Jets. The opposed-jets system consisted of two aligned glass capillaries with a separation δ ) 1.21 mm and an internal diameter D ) 0.6 mm. The experimental setup is described in detail elsewhere.30 The pressure drop of the liquid flowing through the jets is measured as a function of the apparent strain rate in the extensional flow field, calculated by
4Q ˘ ) πD2δ
(1)
where Q is the total volumetric flow rate going through the jets. All the experiments consist of a controlled increasing strain rate starting from rest (i.e., a controlled strain rate measurement); measurements of the pressure drop were reported when steady state was reached at each strain rate value. Control stress experiments, where the ∆P was linearly increased and the strain rate was measured, yielded in this case exactly the same results. Flow through Porous Media. Porous media flow experiments are conducted in the same equipment used previously.31,32 The porous medium employed is a Plexiglas cylinder, with a 31.6-mm internal diameter and 29.9-cm length, filled with a disordered packing of monodisperse glass spheres 1.13 mm in diameter. The experimentally determined porosity was 0.38. The pressure drop between the entrance and exit sections of the medium was set, and the resulting flow rate was measured. Results are reported in terms of the resistance coefficient, Λ, defined by
Λ)
d2φ3(∆P/L) µν(1 - φ)2
(2)
Note that Λ can be interpreted as a dimensionless apparent viscosity.32 In this equation, ∆P is the pressure drop over a length L of porous medium, φ is the medium porosity, d is the particle (29) Rothstein, J. P. J. Rheol. 2003, 47, 1227-1247. (30) Smitter, L. M.; Torres, M. E.; Mu¨ller, A. J.; Sa´ez, A. E. J. Colloid Interface Sci. 2001, 244, 164-172. (31) DaRocha, C. M.; Patruyo, L. G.; Ramı´rez, N. E.; Mu¨ller, A. J.; Sa´ez, A. E. Polym. Bull. 1999, 42, 109-116. (32) Mu¨ller, A. J.; Sa´ez, A. E. In Flexible Polymer Chains in Elongational Flow: Theories and Experiments; Nguyen, T. Q., Kausch, H.-H., Eds.; Springer-Verlag: Heidelberg, 1999; Chapter 11, pp 335393.
Figure 1. Shear viscosity as a function of shear rate for solutions of the indicated CTAT concentration in water at 25 °C. The CTAT concentration ranges from dilute to semidilute conditions; see text. diameter, µ is the viscosity of the solvent (water), and v is the superficial velocity. The rheological behavior of the solution is analyzed by measuring the resistance coefficient as a function of an apparent shear rate, defined as
γ˘ ap )
ν φl
(3)
where ν/φ is the interstitial fluid velocity and l is a characteristic length representative of the pore-scale velocity gradients. In a previous work,33 we have determined that, for this porous medium, l ≈ 0.05d is a good approximation to find local shear rates for the flow of polymer solutions. Because this relation is empirical, we will use it in this work simply as an approximation.
Results and Discussion The rheological behavior of aqueous CTAT solutions has been extensively studied in the literature in simpleshear flows.13,22-24 Figure 1 shows the rheological behavior measured in this work. The solutions have a very low viscosity at low shear rates with a nearly Newtonian behavior, followed by a shear-thickening region at intermediate shear rates, in which flow-induced self-assembly of wormlike micelles takes place, and finally the behavior turns shear thinning at high shear rates, where the induced microstructure is destroyed. Above a specific CTAT concentration (>0.8%, see Figure 2) the solutions exhibit a relatively high zero-shear viscosity and a classic shear-thinning behavior in the entire range of shear rates examined. The dependence of the rheological behavior on CTAT concentration is illustrated in a wide concentration range in Figure 2 where the zero-shear viscosity has been plotted as a function of the CTAT concentration. The insets provide examples of the typical viscosity-shear rate plots in the three different regions. Gamez-Corrales et al.22 found by shear rheology and SANS experiments that the shear-thickening transition was displayed by both dilute solutions (CCTAT < 0.5%) and semidilute solutions (0.5% < CCTAT < 0.8%). The so-called overlap concentration that defines the limit between the dilute and the semidilute regime was determined to be 0.5%. All the solutions that displayed shear thickening had a local morphology consisting of cylindrical micelles with a radius of 21 Å, regardless of whether they were in the dilute or semidilute regimes. Our simple-shear results are fully consistent with those of Gamez-Corrales et al.,22 as well as those of Truong and Walker,23 including the (33) Patruyo, L. G.; Mu¨ller, A. J.; Sa´ez, A. E. Polymer 2002, 43, 64816493.
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Figure 2. Zero-shear viscosity as a function of CTAT concentration in a wide concentration range at 25 °C. The insets show typical shear viscosity versus shear rate plots that illustrate a behavior that varies depending on the CTAT concentration range.
Figure 3. Pressure drop across the opposed jets divided by strain rate, a quantity proportional to the elongational viscosity of the solution, as a function of strain rate for the indicated CTAT concentrations in water at 25 °C.
same scaling exponent (7, Figure 2) to relate zero-shear viscosity with the CTAT concentration in the high end of the concentration range. Results on the flow of CTAT solutions through opposed jets are shown in Figure 3, expressed as the ratio between the pressure drop across the jets to the strain rate as a function of the strain rate. The ratio ∆P/˘ should be proportional to the elongational viscosity when inertial effects in the flow between the jets are negligible.35 All solutions with concentrations of 0.23% CTAT or lower show results identical to those of water. The increase in the curves at high strain rates for these solutions reflects inertial effects in the flow. These results should be compared with those of simple-shear flow (Figure 1), in which solutions in the same concentration range displayed shear-thickening effects. Figure 3 shows that when the solutions are in the semidilute regime (CCTAT > 0.5%), they do not exhibit a critical extension thickening, but rather they seem to have a slight extension-thinning trend. (34) Tatham, J. P.; Carrington, S.; Odell, J. A.; Gamboa, A. C.; Mu¨ller, A. J.; Sa´ez, A. E. J. Rheol. 1995, 39, 961-986. (35) Odell, J. A.; Carrington, S. In Flexible Polymer Chains in Elongational Flow: Theories and Experiments; Nguyen, T. Q., Kausch, H.-H., Eds.; Springer-Verlag: Heidelberg, 1999; Chapter 7, pp 137184.
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These results resemble the opposed-jets rheology of semirigid polymers in solution.34 This indicates that a strong elongational flow (note the range of strain rates employed) either destroys or prevents the formation of intermicellar associations to an extent that they can affect the apparent elongational viscosity, and the surfactant solution behaves as a Newtonian fluid, as long as the CTAT solutions are in the dilute regime. Extensional flows have an important aligning effect upon macromolecules. Previous works have shown that strong uniaxial extension may cause complete chain stretching of polymer molecules in dilute solutions.35-37 In that case, the repeating units in the polymer chain are chemically bound by covalent bonds that can withstand the elongational flow without breaking (although mechanical degradation can also occur during opposed-jets flow but for relatively long molecules and at relatively high strain rates).35,36 In the case of CTAT micellar aggregates, the wormlike structures can break and reform in solution depending on the characteristic nature and strength of the applied flow field. It should be evident that the secondary forces that govern the structure build up leading to SIS under simple-shear flow do not withstand the strong nature of ideal extensional flow in the range of strain rates employed here. Porous media flows have important elongational components, but at the same time, there is extensive shear due to the local velocity gradients induced by the no-slip condition on the surface of the solid phase. Solutions of flexible polymers, which are typically shear-thinning, can exhibit a strong extension-thickening effect in porous media flow, which is more consistent with their behavior in purely elongational flows (such as in opposed-jets flow, in which they also exhibit a sudden increase in elongational viscosity with strain rate) than in shear flows.32 As shown above, dilute aqueous CTAT solutions exhibit a noticeably different behavior; namely, they can display a strong shear-thickening behavior under simple shear and a Newtonian behavior with an elongational viscosity comparable to that of water in opposed-jets flow. One would predict that a lower viscosity enhancement would be found in porous-media flows, as compared to that encountered in simple shear, in view of the complex nature of the flow field with its combination of shear and extensional components. Contrary to these expectations, the results on porous-media flow of CTAT/water solutions show that a synergistic viscosity enhancement is produced beyond a critical apparent shear rate, as can be seen in Figure 4. This behavior is obtained even for the most dilute solutions explored. Because the porous media experiments are performed by controlling and continuously increasing the pressure drop, the resistance coefficient versus apparent shear rate curves are seen to turn back on themselves once the critical apparent shear rate for viscosity enhancement is reached, and two different Λ values are obtained for the same apparent shear rate. Note that the critical apparent shear rates in Figure 4 are appreciably lower than the shear rates for the onset of shear thickening (Figure 1). After the critical apparent shear rate for viscosity enhancement is reached, further increases in the pressure drop produce a reduction in flow rate. This behavior is a result of a flow instability brought about by a possible plugging of some of the pores due to the formation of transient gel-like structures that consist of a strong entanglement network (36) Keller, A.; Odell, J. A. Colloid Polym. Sci. 1985, 263, 181-201. (37) Chu, S.; Babcock, H. P.; Teixeira, R. E.; Hur, J. S.; Shaqfeh, E. S. G. Macromolecules 2003, 36, 4544-4548.
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solution flowing through the porous medium was 70 times more viscous than water. This is remarkable because in simple shear the apparent shear viscosity was 9.5 times that of water and in opposed-jets flow the apparent elongational viscosity was identical to that of water. These results could be very relevant for practical applications such as enhanced oil recovery or soil remediation processes, in which an increased viscosity is required to enhance the capability of the aqueous medium to displace an organic phase in a porous medium.32 In the concentration range of 0.1-0.23% CTAT, the dependence of both the critical shear rate for shear thickening and the critical apparent shear rate for the viscosity enhancement in porous media flow were found to depend on the CTAT concentration as follows: Figure 4. Porous media flow results for aqueous CTAT solutions expressed in terms of the resistance coefficient (Λ) as a function of apparent shear rate at the indicated CTAT concentrations in water at 25 °C. Table 1. Viscosity Enhancement Expressed as the Ratio of Maximum to Zero-Shear-Rate Viscosity or Resistance Coefficient CCTAT, % (mM)
ηmax/η0
Λmax/Λ0
0.05 (1.1) 0.08 (1.7) 0.10 (2.2) 0.14 (3.0) 0.18 (4.0) 0.23 (5.0)
1.0 1.0 2.4 4.2 7.7 9.5
2.7 4.1 9.3 14.7 37.9 70.0
of micelles. After this plugging effect occurs, the flow rate drops and an extra pressure is required to make the solution flow at the same apparent shear rate. This reduction in flow rate with increase in pressure drop would not be observed if the experiment were carried out by control and increase of the flow rate. The same effect has been encountered in porous media flow of polymersurfactant mixtures.31 It is interesting to note that, as in the shear flow case (Figure 1), all the curves shown in Figure 4 start at low apparent shear rates with an apparent viscosity that is nearly that of water until the critical flow rate at which the viscosity enhancement develops. The criticality of the onset of viscosity enhancement is consistent with the existence of a characteristic relaxation time for the formation of transient micelle networks. A comparison between the values of the maximum shear viscosity and that of the zero-shear viscosity in Figure 1 gives an idea of the viscosity enhancement obtained at the point of maximum structure buildup. These values can be compared with the ratio of the maximum resistance coefficient obtained to Λ0, the resistance coefficient at zero shear rate. Table 1 shows how these viscosity enhancement ratios depend on the CTAT concentration. In porous media flow, the viscosity enhancement is always much greater than in simple-shear flow, and at the maximum CTAT concentration examined the viscosity of the 0.23% CTAT
γ˘ c ∝ c-1.5
(4)
γ˘ ap,c ∝ c-1.5
(5)
In view of this identical dependence, it is reasonable to postulate that the mechanism behind the initial stages of the viscosity increase is similar in porous media and in simple-shear flow. Therefore, we envisage that it is the shear component of the porous media flow that promotes the interactions between the cylindrical micelles in solution. However, it could be argued that the complexity of the flow, once the structures are beginning to form, induces an increased amount of physical interactions between micelles. In this case, the elongational flow component of the porous media flow seems to be strong enough to promote molecular contacts and interactions when it is combined with shear flow but not strong enough to completely break these interactions and prevent them like in the case of the stronger opposed-jets flow. In this case, the elongational component of the flow acts upon the micellar structures in a manner similar to the effect of uniaxial extension on semidilute solutions of flexible polymers. Conclusions The rheological behavior of aqueous solutions of CTAT has been determined in simple-shear, pure extensional flow and porous media flow situations. The results show that simple-shear flows may induce entanglements of wormlike micelles, and as a result, shear thickening is produced. On the contrary, strong elongational flows prevent these interactions, and in the dilute regime the solutions behave as Newtonian fluids with a viscosity similar to that of water. Finally, a pronounced synergistic viscosity enhancement effect was found when CTAT aqueous solutions are made to flow through a porous medium where the complex flow field contains both shear and elongational components. LA0499517
