Chemical and Rheological Characterization of Drag-Reducing

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Chemical and Rheological Characterization of Drag-Reducing Cationic Surfactant Systems Yunying Qi and Jacques L. Zakin* Department of Chemical Engineering, The Ohio State University, Columbus, Ohio 43210

Surfactant drag-reducing additives are very promising for saving pumping energy in recirculation systems such as district heating and cooling systems because of their “self-repairability” after mechanical degradation compared to polymer drag-reducing additives, which degrade irreversibly. The effectiveness of cationic surfactant drag-reducing additives, as indicated by their effective drag-reduction temperatures and Reynolds number ranges, depends on the chemical structures and concentrations of the surfactants and counterions. In this paper, the effects of the surfactant (alkyl chain length, saturated/unsaturated chain, odd/even numbers of carbons, and surfactant headgroup) and counterion (size, polarity, etc.) chemical structures on surfactant drag reduction, as well as three physical properties postulated to be associated with surfactant drag reduction, are addressed. Shear-induced structure (SIS), viscoelasticity (in the forms of nonzero first normal stress difference, quick recoil, and stress overshoot), and high extensional/ shear viscosity ratios are three rheological characteristics found in many drag-reducing surfactant solutions. It has frequently been postulated that they are vital to surfactant drag reduction. Rheological experimental data on some drag-reducing surfactant solutions indicate, however, that SIS and viscoelasticity are not vital for surfactant drag reduction whereas the criterion of high extensional/shear viscosity ratio might be valid. Introduction The active reduction of drag in turbulent flow of a liquid can be achieved in a number of ways. Most effective is the addition of small amounts of highmolecular-weight polymers or surfactants.1 Starting in the 1950s, research and development studies on turbulent drag-reducing additives focused on high-molecularweight polymers that are now widely utilized in pipeline transport of hydrocarbon liquids such as crude oil. However, high-molecular-weight polymer drag-reducing additives degrade irreversibly when subjected to shear, such as in passing through a pump, and therefore they are only suitable for “once-through” systems. In the past 15 years, drag-reduction research emphasis has shifted to surfactant drag-reducing additives because of the “repairable” self-assembly nature of these systems after mechanical degradation, which permits them to be used in recirculation systems such as district heating and cooling systems. Certain surfactants, such as cetyltrimethylammonium bromide and cetyltrimethylammonium chloride, with the addition of appropriate counterions such as sodium salicylate, form network microstructures at very low concentrations (a few hundred parts per million to 4000 ppm) and are very effective in reducing friction factors in turbulent flow. The mechanism of drag reduction is not clear, even though many investigations have been carried out in the past 15 years. Nonetheless, a great deal of data are available on additive effectiveness in reducing drag and on the characteristics of surfactant drag-reducing solutions such as mean flow and turbulence, rheology, and microstructure. These data can be used to explore possible relationships between these properties and surfactant drag reduction, * Corresponding author. Phone: (614) 688-4113. Fax: (614) 292-3769. E-mail: [email protected].

which could be helpful in the selection of additives for practical applications. Four groups of drag-reduction surfactant solutions of interest are classified by the charge properties of the surfactant hydrophilic headgroup, namely, cationic (positively charged), anionic (negatively charged), zwitterionic (both positively and negatively charged, with zero net charge), and nonionic (uncharged), as well as mixtures of some of these systems such as mixed cationic/anionic surfactants, zwitterionic/anionic surfactants, etc. Cationic drag-reducing surfactant solutions have been the most extensively studied because of their broad drag-reduction temperatures (unlike nonionic surfactants, which have narrow temperature ranges) and insensitivity to the presence of calcium or magnesium ions in water, which cause the precipitation of some anionic surfactants. They are also much less expensive than zwitterionic surfactants. Many dragreducing cationic surfactants are quaternary ammonium salts with one long alkyl chain with typical chemical structures of the form CnH2n+1N+(CH3)3Cl (n ) 12-18). In this paper, we focus on cationic surfactant drag reduction. The effectiveness of cationic surfactant drag-reducing additives, as indicated by the effective drag-reduction temperature range and Reynolds number range, depends on the chemical structures and concentrations of the counterion and surfactant. Rose and Foster2 noticed that, when the concentration of counterion increases, the critical wall shear stress for loss of surfactant drag reduction at a certain temperature increases and the temperature range of effective drag reduction expands. The effect of the counterion and surfactant chemical structures on surfactant drag reduction is more complicated, however, because of the diversity of counterions and surfactants available. However, the effects of chemical structure are very important both for a theo-

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retical understanding of drag reduction and for practical applications to tailor surfactant-counterion drag-reduction systems for different conditions. The effects of a counterion’s polarity, size, and chemical structure and of a surfactant’s chemical structure, including both the alkyl chain configuration (alkyl chain length, saturation/ unsaturation, double bond configuration (cis vs. trans), and odd/even number of carbons) and headgroup of the surfactant on drag reduction, are discussed in this paper. Despite the low concentrations required for effective drag reduction, most drag-reducing surfactant solutions exhibit strong non-Newtonian fluid properties. Many authors have related the occurrence of surfactant drag reduction to the rheological properties of the solutions such as SIS, viscoelasticity (nonzero first normal stress difference, quick recoil, and stress overshoot) and high extensional viscosity/shear viscosity ratios. Possible drag-reduction mechanisms related to the rheological properties of surfactant solutions, such as damping of small turbulent eddies by the elastic properties of the solutions1,3-7 or high extensional viscosity providing resistance to vortex stretching and turbulent eddy growth,1,8 have been proposed. These drag-reduction mechanisms are difficult to verify experimentally, but rheological properties obtained from small-scale laboratory tests could be useful in predicting the dragreduction ability of surfactant solutions if any of the criteria are valid. In the second part of this paper, three rheological properties of surfactant solutions, namely, SIS, viscoelasticity, and high extensional/shear viscosity ratios, are examined to determine whether they are valid criteria for surfactant drag reduction. Effects of Counterion Chemical Structures and Cationic Surfactant Chemical Structure (a) Counterion Chemical Structure Effects. It is generally postulated that long threadlike micelles are needed for surfactant drag reduction. For drag-reducing cationic surfactant solutions, there is a minimum micelle length below which rodlike micelles are unable to induce drag reduction.9 Because of electrostatic interactions between the surfactant headgroups which limit the growth of micelles in the dilute region, cationic surfactants alone cannot form strong threadlike micelles necessary for drag reduction at low concentrations.1 Through the addition of counterions to the solution, electrostatic repulsion forces between cationic surfactant molecules in a micelle can be reduced, thus promoting micelle growth. Because of the greatly screened headgroup repulsion forces between surfactant molecules and the increased dimensional packing parameter of micelles, the length and flexibility of the micelles increase considerably. With strongly binding counterions, the resulting surfactant solution resembles a polymer solution with viscoelasticity and strong extensional resistance.10-13 The chemical structure of the counterion is a critical factor in determining counterion effectiveness. To form elongated, cylindrical, threadlike micelle structures, strongly binding negative counterions that can diffuse the positive charges of the cationic surfactant are needed. By using different aromatic anions as counterions for cationic surfactant micelles in aqueous solution, it is possible to tune the micelle microstructure and dynamics through a range of morphologies and interactive behaviors.14 However, even with the dozens of

studies of counterion effects, the varieties of surfactant headgroups and chains and the varied experimental conditions of the studies make it difficult to develop a coherent picture of counterion effects on micelles. The counterion binding states depend on the chemical structure, charge, size, polarity, etc., of the counterion species. Generally, organic counterions with aromatic rings have stronger effects than inorganic counterions.15-18 Light scattering and determination of the critical micelle concentration (CMC) or of the aggregation number of the surfactant molecules in micelles are techniques commonly used to study the effects of inorganic counterion. The rank of inorganic anionic counterions binding to cationic surfactant micelles increases according to the Hofmeister series, i.e., SO42< HPO42- < F- < Cl- < Br- < NO3- < I- < ClO4- < SCN-.19 Aromatic organic anionic counterions such as salicylates, tosylates, certain mono- and dichlorbenzoates, mono- and dimethylbenzoates, and hydroxynaphthoates are among the most effective in promoting micellar growth in cationic surfactant solutions.1,9,14,15,20 Micellar dynamics, as reflected in the rheological behavior and drag-reduction ability of the solutions, is also sensitive to the nature of the counterions. The effectiveness of counterions depends on the factors discussed below. Hydrophobicity of the Counterions. The hydrophobicity of the counterions plays an important role in determining the micelle structure. The more hydrophobic the counterion, the more effective it is in promoting micellar growth.21-23 According to Hassan et al.,22 the increase in the counterion hydrophobicity increases ion pairing of the surfactant and counterions, which effectively reduces the charge density on the aggregates and promotes micellar growth. This was demonstrated experimentally with the observation of lower surface charge densities of micelles in the presence of hydrophobic counterions compared with micelles formed by surfactants with inorganic counterions.24 Thus, aromatic counterions, as noted above, are much more effective than inorganic salts. Influence of the Counterions on the Packing Parameters of Micelles. Geometric factors of the surfactant molecules determine the most favored structures of micelles.25 The geometric factors of the surfactant molecules are usually described in terms of a surfactant molecular packing parameter p ) v/a0lc, where v is the hydrophobic chain volume, a0 is the effective surface area occupied by the hydrophilic headgroup at the micelle surface, and lc is the critical length of the surfactant molecule hydrophobic chain, which is defined as the maximum extent of the chain.25 The addition of counterions into the surfactant solution suppresses the electrostatic repulsion forces between surfactant molecular headgroups and therefore reduces the distance between surfactant molecule headgroups and the effective surface area of the headgroup at the micelle interface. The packing parameter of surfactant molecules depends on the nature of the counterion and, more specifically, on its ability to bind to the surfactant molecules and on its geometric size.19 In addition to decreasing the headgroup area per surfactant molecule, some bulky aromatic counterions, such as salicylate and 3,5-dichlorobenzoate, can not only change the mean distance between polar headgroups of cationic surfac-

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Figure 2. Orientations of 2-chlorobenzoate, 3-chlorobenzoate, and 4-chlorobenzoate counterions in micelles.38 Figure 1. Comparison of anionic counterions salicylate- and Clon packing parameter of a cationic surfactant micelle.

tant molecules but also increase the average volume per surfactant by penetrating part of their bulky benzene ring beyond the micelle headgroup areas (Figure 1). Counterions such as bromide can also penetrate into the micelle headgroups, but they are not as effective as penetrating aromatic counterions in changing the surfactant molecular volume because of their relatively small size. Israelachvili25 relates the surfactant molecule packing parameter to the micelle structure of surfactant solutions with p < 1/3 for spherical micelles, 1/3 < p < 1/2 for cylindrical micelles, and 1/2 < p < 1 for flexible bilayers or vesicles. Nonpenetrating counterions such as chloride, as shown in Figure 1, adsorb only at the interface of the micelle and the water phase and affect only the surface area per surfactant molecule. As a result, bulky aromatic counterions that can penetrate into the micelle headgroup areas drive micellar growth at much lower concentrations than less penetrating counterions such as Br- and surface-adsorbing counterions such as Cl-.14,26-30 Penetration Ability of the Counterions. Magid et al.14 pointed out that the nature of counterion adsorption by penetration beyond the surfactant headgroups holds the key to micellar growth. As shown in Figure 1, counterions that can penetrate into the hydrophobic interior of the micelles such as salicylate are much more efficient at promoting micelle growth than nonbinding counterions such as chloride.31-33 Counterion hydration and the strength of the dispersion interactions (van der Waals forces) between the surfactant headgroups and the counterions are important factors determining the penetration ability of the counterions into the micelle.32 Compared with bromide counterions, chloride ions are more highly hydrated and thus are less effective in penetrating and shielding the charge of the surfactant aggregate. As a result, there is a lower degree of counterion binding in micellar solutions when chloride is the counterion with small spherical micelles formed over a wide range of surfactant concentrations and salt concentrations.32,34,35 Penetrating counterions are similar to cosurfactants in some respects. For weakly hydrated strongly penetrating counterions such as 3,5-dichlorobenzoate and salicylate, micellar solutions form giant threadlike micelles and are already semidilute at low volume fractions.34 For aromatic counterions, the positions of the substituent groups influence the penetration ability of the counterions and, therefore, the size, shape, and flexibility of the micelles, as well as the properties of their solutions.36-39 Lu et al.39 conducted drag-reduction and rheological tests of the cetyltrimethylammonium chloride-chlorobenzoate system. At the counterion/surfactant concentration ratio of ξ ) 2.5, rheological and dragreduction measurements and cryogenic transmission

electron microscope (cryo-TEM) images showed high viscoelasticity, high extensional viscosity and good drag reduction over a wide temperature range for the 4-chlorobenzoate system with a strong threadlike network.39 The 2-chlorobenzoate system showed no viscoelasticity and no drag reduction, and its microstructure consisted of spherical micelles with diameters of around 5 nm. The 3-chlorobenzoate system was viscoelastic, had high extensional viscosity, and was drag-reducing, but only in the temperature range of 30-50 °C. Cryo-TEM images of the 3-chlorobenzoate system are of special interest.39 Different cryo-TEM images of this system showed both a threadlike network and large vesicles at T ≈ 20 °C. The microstructure is metastable at this temperature, as precipitates were observed after shear in rheological measurements. Presumably, similar precipitation behavior occurred in the high-shear regions in the turbulent drag-reduction measurements at 20 °C, and no drag reduction was observed, whereas a more stable, presumably threadlike microstructure gave good drag reduction at 30 °C From nuclear magnetic resonance (NMR) measurements of the cetyltrimethylammonium chloride-chlorobenzoate system, Smith et al.38 drew the picture of counterion binding shown in Figure 2. As can be seen from Figure 2, the carboxyl group and the two adjacent (2 and 6) positions on the chlorobenzoates resided in the water phase, and the remaining (3, 4, and 5) positions on 2-chloro-, 3-chloro-, or 4-chlorobenzoate resided in the hydrocarbon core of the micelles. Because the chlorine atom is strongly hydrophobic, 4-chlorobenzoate with the chlorine deeply embedded in the hydrocarbon core is bound most strongly, 3-chlorobenzoate is not as strongly bound, and 2-chlorobenzoate is very weakly bound as its chlorine is in the water phase. However, Bachofer and Turbitt17 suggested that the fact that counterions such as 2-chlorobenzoate do not promote viscoelasticity of the surfactant solution might indicate that such counterions do not penetrate into the surfactant headgroups of the micelles. Instead, they might be tilted with their loci tangential to the micellar interface. For those counterions that can promote threadlike micelle growth with viscoelastic properties such as 3- and 4-chlorobenzoate, Bachofer and Turbitt17 described the same picture of counterion-surfactant interactions as Smith et al.,38 with the counterions intercalating into the micellar interface as shown in Figure 2. In fact, the hydrophobicity of a counterion, its penetration ability, and its effect on the micellar packing parameter are closely related to each other. The more hydrophobic the counterion (or the more nonpolar the substituent group on the counterion), the more penetrating the counterion can be, and therefore, the larger the effect of the counterion on the micellar packing parameter. For drag-reducing surfactant solutions with threadlike micelles, the cap energy, Ec, which is related to the


surfactant packing near the cylinder end caps, depends strongly on counterion-specific effects.28 Upon the addition of strongly binding counterions into a surfactant solution, the cap energy, Ec, of the micelles increases, which favors micelle growth with increasing flexibility. It is possible to tune the micellar size or flexibility by varying the counterion. To obtain strong structures of threadlike micelles and effective drag reduction, both the surfactant and the counterion in the micelle must be maintained at some low energy level, with the hydrophobic and hydrophilic portions of the counterions separated as far as possible and residing in their preferred environments.9,38 Examples of very effective counterions are given in the Counterion Chemical Structure Effects section. Chou9 also pointed out that the counterions that can disperse their negative charges by their resonance structure or by the formation of inter- or intramolecular hydrogen bonds are effective in inducing drag reduction. He inferred that hydrogen bonding between -COO- and -OH groups on counterions located on different rodlike micelles helps to strengthen the micelle network structure formed in some drag-reducing surfactant solutions. For drag-reducing surfactant solutions, counterions that can penetrate deeply into micelles and/or form strong intramolecular hydrogen bonds such as salicylate give higher drag-reduction temperature limits.9 (b) Effects of Cationic Surfactant Chemical Structure. The various micelle structures formed in aqueous solution by surfactant molecules are not covalently bonded but are stabilized by much weaker hydrophobic interactions. Chemical and geometrical factors of the surfactant molecules play an important role in determining the most favored structures of micelles. In this section, the effects of hydrophilic headgroups and hydrophobic tails on the packing of cationic surfactants are considered. Generally, the less crowded the hydrophobic tails in fitting the micelles, the larger the micelles will grow. A more crowded hydrophobic region usually results in a higher packing freeenergy penalty when hydrophobic surfactant molecular tails are removed from the water phase to the micellar phase and, therefore, a less stable micelle. The configuration of both the surfactant molecule headgroup and the hydrophobic chain (chain length, saturated/unsaturated, odd or even number of carbon atoms) influences the surfactant molecular packing parameter and therefore, the microstructure, drag-reduction ability, and rheological properties of the surfactant solution. Alkyl Chain Length. As the length of the cationic surfactant hydrophobic alkyl chains increases, to avoid enhanced unfavorable hydrocarbon-water contacts, more and more surfactant molecules tend to stay inside the micelles, which therefore favors micelle growth. For ionic surfactants, Sugihara and Hisatomi21 also noticed that the degree of counterion binding outside the micelle core becomes stronger when the alkyl chain length increases (see also references therein). The changes in cationic surfactant solution microstructure with increasing alkyl chain length of the surfactant molecules influence the rheological properties and drag-reduction ability of the surfactant solutions as observed by several researchers.40-42 Increased upper drag-reduction temperature limits and critical shear stresses were observed in dragreducing surfactant solutions with longer alkyl chains by Rose and Foster,2 Chou,9 Lin et al.,40 Ohlendorf et

al.,41 and Qi et al.42 Ohlendorf et al.41 found that the upper temperature limit of surfactant drag reduction increases by about 8.5 °C with each -CH2- group added. The upper temperature limit of surfactant drag reduction is controlled by the transition of the micelle structure from rodlike to spherical. As the temperature rises, the Brownian motions of the surfactant hydrocarbon chains become stronger. Because the van der Waals forces that hold hydrocarbon chains together inside the micelle core increase with increasing chain length, micelles formed by long-chain surfactant molecules are more stable than those with short chains at high temperatures.9 An increase in the alkyl chain length also reduces the low-temperature solubility, which raises the lower drag-reduction temperature limit.2,9 In short, as the surfactant chain length increases, the effective drag-reduction temperature range of the surfactant solution shifts upward. This property is very useful in tailoring surfactant solutions with different drag-reduction temperature ranges. By adding minor amounts of C12, Chou,9 Lu,43 and Lin et al.44 found that the drag-reduction low-temperature limit of a C22 surfactant was reduced significantly. They ascribed this reduction to the bending and twisting of the long C22 alkyl chains to fill the cavities in the mixed micelle core. As a result, the mixed surfactant solution, with less ordered micelle cores, had a lower drag-reduction temperature limit.9,44 Odd/Even Effect. Effects of odd or even numbers of carbons in the hydrocarbon chains of surfactant molecules originate from possible different packing arrangements of the tails inside the micelle core. This effect was found in the melting points of alcohols, with alcohols with odd numbers of carbons having lower melting points than the corresponding even-numbered alcohols. Lin et al.40 and Qi et al.42 studied the odd/even effects of hydrocarbon chains of cationic surfactant molecules on the rheological properties and drag-reduction effectiveness of alkyltrimethylammonium chloride surfactants with counterions 3-chlorobenzoate and sodium salicylate. Odd/even effects were observed in the Krafft points, critical turbidity temperatures, and lower drag-reduction temperature limits of these solutions but not in the upper drag-reduction temperature limits. Other than these two reports, there are no reports on the effects of odd/even numbers of carbons in the hydrocarbon chains on the drag-reduction and rheological properties of cationic surfactant solutions. Saturation/Unsaturation and Cis/Trans Effects. As mentioned previously, the longer the alkyl chain length of cationic surfactants, the higher the upper dragreduction temperature. However, it was found that solutions with alkyl chain lengths of more than 16 carbons are insoluble at low temperatures, which limits the lower drag-reduction temperature limit of the solutions.2 To overcome this limitation, Rose and Foster2 suggested incorporating a double bond in the alkyl chain or replacing two or three methyl groups with hydroxyethyl groups in the quaternary ammonium surfactant headgroup. Solutions with such species are more soluble at low temperatures but still maintain the high critical temperatures and Reynolds numbers of their saturated alkyltrimethylammonium counterparts. The most important consequence of unsaturation is to lower the lowest temperature at which fluid states can exist.45

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Figure 3. Schematic view of cis and trans forms of surfactant hydrocarbon chains.

Introducing a double bond into the hydrocarbon chain of the surfactant molecule affects the conformational structure of four atoms (two carbons and two hydrogens) in the chain, as the double bond constrains them to lie within a single plane (Figure 3). There are two forms of one-double-bond unsaturation (Figure 3). The cis double bond has both hydrogen atoms on the same side of the double bond. The trans double bond has the hydrogens on opposite sides of the double bond. Israelachvili25 pointed out that the introduction of unsaturation reduces the critical chain length (i.e., the maximum possible extent of the hydrocarbon chain of the surfactant molecules) and therefore increases the packing parameter of the surfactant molecules, which then favors micelle growth. As can be seen in Figure 3, the kink in the hydrocarbon chain of the cis double bond increases the volume occupied by the hydrocarbon tail which results in a large end cap energy, Ec, and favors micelle growth according to Raghavan and Kaler and references therein.31 The trans double bond, however, has a linear shape that is not greatly different from the shape of a saturated chain and but it still lowers the lowest temperature for the fluid state (Krafft point). The steric differences of cis/trans isomer hydrocarbon chains influence the micelle microstructures, the rheological behavior, and the drag-reduction ability of the corresponding drag-reducing surfactant solutions. Qi et al.46 found that, for the same temperature and counterion (sodium salicylate)/surfactant concentration ratios of ξ ) 1.0 and ξ ) 1.5, the critical shear stresses of surfactant solutions with cis configurations are much higher than those of the solutions with trans configurations. Surfactant Headgroup. The chemical nature and configuration of the surfactant headgroup also play an important role in the surfactant microstructure and therefore in the rheological properties and drag-reduction effectiveness of their surfactant solutions. The effects of the surfactant headgroup on micelle formation are mainly due to the hydrophilicity and geometric size of the surfactant headgroup. As mentioned earlier, quaternary ammonia salts with one long alkyl chain are generally the most effective cationic drag-reducing surfactants, and quaternary ammonium salts with trimethylammonium groups are the most extensively studied cationic drag-reducing surfactants. When some or all of the methyl groups in quaternary ammonia are replaced with hydroxyethyl groups, both the hydrophilicity and the geometric size of the surfactant headgroup increase. Increasing the surfactant hydrophilicity by substituting hydroxyethyl groups for methyl groups decreases the Krafft point of cationic surfactant solutions and extends the lowtemperature limit for drag reduction.2 (It is worth noting that the Hoechst Company’s early efforts to develop

commercial drag-reducing additives such as Habon utilized a cetyltrimethyl cationic surfactant. Because of the insolubility of this surfactant at low temperatures, one hydroxyethyl group was included in their later improved product, Habon G.) The increase in size of the surfactant headgroup, i.e., area occupied at the micellar surface, however, retards the growth of micelles, as can be seen from the definition of the surfactant molecular packing parameter. Horiuchi et al.47,48 studied the effect of the surfactant headgroup on rheological properties and drag reduction with 1000-ppm cationic surfactant solutions with NaSal as the counterion and ξ ) 1.5. With the same alkyl chain (18 carbons with one double bond) but different surfactant headgroups (3 methyl groups, 2 methyl plus 1 hydroxyethyl groups, and 3 hydroxyethyl groups), they found that, as the number of hydroxyethyl groups increases from 0 to 1 to 3, the critical shear stress for loss of drag reduction decreases at the same temperature, and the effective drag-reduction temperature range expands. The first normal stress difference (N1) data for four surfactants with 0-3 hydroxyethyl groups showed that the viscoelasticity of the surfactant solutions reached a maximum with 2 methyl and 1 hydroxyethyl groups in the shear rate range of 20-2000 s-1 at 25 °C. With further replacement of methyl groups by hydroxyethyl groups, the viscoelasticity of the surfactant solution decreased. Rheological Properties Related to Surfactant Drag Reduction (a) Shear-Induced Structure (SIS). Dilute dragreducing surfactant solutions are very sensitive to shearing because of the self-assembling nature of micelles. Shear can induce structural transformations in the solution similar to temperature, surfactant chemical structure/concentration, and counterion chemical structure/concentration. As a result, macroscopic properties of the solution also depend on the shear rate of the system.49 However, similar to temperature, the physical changes caused by shear are reversible because of the self-assembling structure of micelles.50 The unusual rheological behaviors of drag-reducing surfactant solutions under shear have been widely investigated because of their theoretical and practical scientific interest. In the shear rate range of 1-1000 s-1, three different kinds of shear viscosity vs shear rate plots have been observed for drag-reducing surfactant solutions at room temperature (Figures 4-6). The shear viscositiy measurements of the surfactant solutions were carried out with a Rheometrics RFSII Couette rheometer with a cup diameter of 34 mm and a bob diameter of 32 mm. Case 1. The most general shear viscosity vs shear rate plot has four regions (Newtonian, shear thinning, shear thickening, and shear thinning). The plot for Arquad 16-50 (cetyltrimethylammonium chloride)/NaSal (5 mM/5 mM) in Figure 4 shows three of these regions. The Newtonian region at very low shear rates is not shown in Figure 4 as viscosities at shear rates below 1 s-1 could not be measured. The effective dragreduction temperature range of this solution is 560 °C. In this case, we postulate that the solution would exhibit Newtonian-like behavior at very low shear rates (not shown in Figure 4) as micelles rotate freely in the solution. At slightly higher shear rates, micelles start


Figure 4. Shear viscosity of drag-reducing surfactant solution Arquad 16-50/NaSal (5 mM/5 mM) at room temperature (T ≈ 22 °C).

Figure 5. Shear viscosity of drag-reducing surfactant solution Arquad 16-50/3,4-methylbenzoate (5 mM/5 mM) at room temperature (T ≈ 22 °C).

to orient in the shearing direction, and shear thinning is observed, as shown in Figure 4.51,52 Then, at a critical shear rate, 16 s-1 in Figure 4, the shear viscosity of the solution shows a steep increase, and the elastic properties of the fluid come into play. The formation of a socalled SIS with micelles that are orders of magnitudes larger than individual rodlike micelles has been suggested as being responsible for the sudden increase in shear viscosity and elasticity.53-58 At this point, the solution is like a viscoelastic gel.59 At a higher shear rate (40 s-1 in Figure 4), the SIS is no longer stable, and the viscosity decreases with shear rate. At the highshear-rate end of the viscosity peak, it is believed that micelles are fully aligned with the flow direction, as confirmed by flow birefringence52 and small-angle neutron scattering (SANS)60-63 experiments. The critical shear rate for the formation of an SIS depends on the surfactant concentration/chemical structure, counterion concentration/chemical structure, temperature, and also the gap of the Couette viscometer if it is Couette flow.64-66 Case 2. Figure 5 shows the shear viscosity of the drag-reducing surfactant solution Arquad 16-50/3,4methylbenzoate at shear rates from 1 to 1000 s-1. The effective drag-reduction temperature range of Arquad 16-50/3,4-methylbenzoate (5 mM/5 mM) is 5-40 °C. There are three regions (Newtonian, shear thickening, and shear thinning) in the shear viscosity vs shear rate plot of this solution. As compared with case 1, the first shear-thinning region of the plot is omitted (or is too

Figure 6. Shear viscosity of drag-reducing surfactant solution oleyltrimethylammonium chloride (cis/trans molar ratio ) 4/6) (5 mM) + NaSal (12.5 mM) at room temperature (T ≈ 22 °C).

narrow to be observed). The other three regions are similar to those in case 1. Case 3. The shear viscosity of the drag-reducing surfactant solution cis-oleyl[(Z)-9-octadecenyl]/transelaidyl[(E)-9-octadecenyl]trimethyl quaternary ammonium chloride in the molar ratio of 4:6 (5 mM) with the counterion sodium salicylate (NaSal) (12.5 mM) in the shear rate range of 1-1000 s-1 is shown in Figure 6. There are only two regions (Newtonian and shear thinning) in the shear viscosity vs shear rate plot of this surfactant solution. In this case, it is possible that an SIS, together with a second shear-thinning region, might appear at shear rates above 1000 s-1. The effective drag-reduction temperature range of the oleyltrimethylammonium chloride (cis/trans molar ratio ) 4/6) (5 mM) + NaSal (12.5 mM) surfactant solution is 4-80 °C. Thus, a variety of responses to shear have been observed, with some solutions exhibiting only shear thinning while others exhibit phenomena such as SISs or shear-induced phase transitions (in shear bands).67,68 Of these phenomena, SISs are the most puzzling.68,69 In addition to rheological studies,57,66-73 the effect of shear has also been studied by birefringence,50,57,59 dynamic light scattering,74 SANS,75,76 and imaging techniques including cryo-TEM 65 and freeze-fracture electron microscopy.77 It was found that the increase in shear viscosity is always accompanied by a buildup of the birefringence, normal stresses, and anisotropic scattering images obtained in SANS experiments. Relaxation of shear stresses and flow birefringence after cessation of shearing were also noticed.50,59 Despite numerous studies on the subject, only indirect evidence for the existence of an SIS has been obtained, and no common understanding has been reached about the origin and nature of the microstructures involved or how they might contribute to shear thickening or drag reduction. Some authors74,78 claim that it is unclear whether a universal SIS exists for all surfactant systems. However, it is clear that, in either ionic surfactant solutions or nonionic surfactant solutions,57 an SIS is only stable under shear conditions that induce viscoelastic properties in the solution and the structure disappears again at high shear rate.41,79 A number of authors have suggested theories to explain SIS formation, for example, Hookian spring,68,69 pseudo-nematic phase separation,49,53,65-68,74,75,77 collision-fusion,12,50,53,58,69,78,79 and pearl-string.49 Here, we will examine only its relation to drag reduction.

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It has been proposed that SISs might be responsible for the drag-reduction phenomenon in turbulent flow.54,69,70,72,78 However, as shown in Figure 6, in some drag-reducing micellar solutions, no obvious sign of an SIS is observed. There are three possible explanations for this. One is that an SIS is not a key feature required for a surfactant solution to be drag-reducing. Second, the micellar microstructures of some surfactant solutions in the quiescent state might already be capable of generating drag reduction, whereas others might require SIS formation to generate drag reduction. The third reason is that the shear rate ranges of the measurements (1-1000 s-1) might not have been broad enough to observe SISs.52,57 In the above three explanations, the first and second indicate that SISs might not be required for drag reduction, whereas the third implies that there could be correlations between drag reduction and SISs if experimental data over a wide enough shear rate range could be obtained. For drag-reducing surfactant solutions, a high value of ξ might eliminate SIS formation or shift it out of the shear rate range (1-1000 s-1) tested. For example, no SIS was observed in the oleyltrimethyl quaternary ammonium chloride (cis/trans molar ratio ) 4/6) (5 mM) + NaSal (ξ ) 2.5) solution shown in Figure 6, whereas the cis/trans (4/6) (5 mM) + NaSal (ξ ) 1.0) solution exhibits an obvious SIS. It was also found that, when ξ of the Arquad 16-50/NaSal system is increased to 2.0, the pronounced SIS shown in Figure 4 essentially disappears. According to Raghavan,80 for surfactant solutions with rodlike or wormlike micelles, SISs exist only in a certain range of micelle length. When the micelles are too short, the micelles are not long enough to interact with each other, and therefore, no SIS can be observed. As ξ increases, the micelles grow and start to entangle with each other heavily. With this initial state, shear will tend to loosen the entanglements, and therefore, no SIS will be observed at high ξ. With this explanation, we can conclude that SIS is not vital for surfactant drag reduction but that threadlike or rodlike micelles are vital for a surfactant solution to be dragreducing. From the shear viscosity plots of a series of drag-reducing surfactant solutions, Myska and Stern52 also concluded that SIS is not an indispensable condition for a surfactant solution to be drag-reducing. (b) Viscoelasticity. Most drag-reducing surfactant solutions exhibit viscoelastic properties in the form of nonzero first normal stress differences (N1), quick recoil, and stress overshoot. Many researchers2,41,81,82 who have studied drag-reducing surfactant systems have stated that the viscoelastic properties of the surfactant solutions are responsible for the drag-reduction behavior. It has also been suggested that elastic properties of the solutions help to damp small turbulent eddies and to store and recover otherwise dissipated turbulent energy. However, drag-reducing surfactant solutions with low viscoelasticity and solutions with strong viscoelasticity but no drag reduction have recently been found. Lu43,83 described a dilute drag-reducing surfactant solution, Arquad S-50 (soyatrimethylammonium chloride)/NaSal (sodium salicylate) (5 mM/12.5 mM), with a drag-reduction ability up to 70% drag reduction from 20 to 80 °C, as shown in Figure 7. The percent drag reduction is based on a comparison with water flow at the same mean velocity and temperature. These turbulent drag-reduction experiments were conducted in a

Figure 7. Drag reduction of the Arquad S-50/NaSal (5 mM/12.5 mM) system.43

Figure 8. First normal stress difference of Arquad S-50/NaSal (5 mM/12.5 mM) system.43

recirculation system with a 1.22-mm-long, 6-mm-i.d. stainless steel tube test section. Surprisingly, first normal stress differences of the solution, which were measured in a Rheometric Scientific Inc. RMS-800 rheometer with a cone-and-plate fixture (50-mm diameter and 0.04-rad cone angle), were found to be close to zero up to a shear rate of about 400 s-1 and to become negative at shear rates above 400 s-1(Figure 8). In addition, no recoil was observed after a swirling motion had been imparted to the solution, and no stress overshoot was found in a step rate shearing experiment on the solution. However, this solution exhibits high apparent extensional/shear viscosity ratios, indicating that there is also no correlation between the viscoelasticity and the extensional/shear viscosity ratio. Another drag-reducing solution with water-like properties was found by Lin et al.84 using the same experimental equipment. The effective drag-reduction temperature range of an Arquad 16-50 (cetyltrimethylammonium chloride)/3,4-chlorobenzoate (5 mM/10 mM) solution is 20-80 °C. This solution also showed no N1, no recoil after swirl, and no stress overshoot. Conversely, Myska et al.85 found a system that has large first normal stress differences at 20 °C but no drag reduction at the same temperature. The solution they studied is Arquad 18-50 (octadecyltrimethylammonium chloride)/sodium salicylate (NaSal) (1.6 mM/4.0 mM), and they measured the first normal stress differences in a Haake Rheometer Rotovisco RV 20 and CV20 N with a cone-and-plate fixture (0.035 rad angle). They also observed that, for this solution, the values of the first normal stress difference decreased with temperature, whereas the drag-reduction effectiveness, observed


at higher temperatures, increased with temperature. This again indicates that viscoelasticity does not correlate directly with drag reduction. However, our experimental data with different drag-reducing surfactant solutions indicate that there appears to be a relationship between SIS and N1. For example, for the surfactant solutions Arquad S-50/NaSal (5 mM/12.5 mM), cis/trans (4/6) (5 mM) + NaSal (ξ ) 2.5) and Arquad 16-50/3,4chlorobenzoate (5 mM/10 mM), no N1 and no SIS were observed, whereas for all of the viscoelastic surfactant solutions we have studied, N1 is always accompanied by SIS. The above three examples show that there is no necessary dependency of drag reduction on viscoelasticity. Therefore, it does not appear that viscoelastic behavior is vital for a surfactant solution to be dragreducing, nor does it appear necessary that it show an SIS. Our data and those of Nowak86 also show that solutions showing SISs have positive N1 values. Gyr and Bewersdorf5,87 noted that the drag-reduction effect is based on the orientation of the threadlike or rodlike micelles. When micelles align along the flow direction, the solution might not exhibit pronounced viscoelastic properties. (c) High Extensional/Shear Viscosity Ratio. Only limited studies have been performed on the extensional viscosities of drag-reducing surfactant solutions because of difficulties in measuring extensional viscosities of lowshear-viscosity liquid solutions. Until now, the Rheometrics Scientific RFX instrument with two opposed flat-face nozzles is the only available instrument for measuring the apparent extensional viscosities of lowshear-viscosity liquid solutions. During experiments, the two nozzles are immersed in the test solution, which is held in a 250-mL jacketed beaker. The beaker is connected to a bath system, allowing temperature control to within (0.5 °C of the desired temperature. By using two syringe pumps connected to the two nozzles, solutions are sucked into the nozzles to generate an extensional flow between the two nozzles. By using three pairs of nozzles (diameters of 0.5, 1, and 2 mm) with the separation gap between the two nozzles set equal to the nozzle diameter, extensional rates from 20 to 10 000 s-1 can be covered. Detailed description and analysis of the instrument can be found in Macosko.88 The reported results are the averages of three repeated experiments. However, the extensional viscosity measured in the opposed nozzles instruments is not the “true” extensional viscosity of the solution. It includes contributions from dynamic pressure, shear on the nozzles, and liquid inertia. Therefore, the RFX apparatus can be used as an indexer rather than as a quantitative instrument for measuring apparent extensional viscosities.88 Although Gyr and Bewersdorff87 stated that extensional viscosity is of minor importance to surfactant drag reduction, relatively high apparent extensional viscosity to shear viscosity ratios (100 or more) are commonly seen in drag-reducing surfactant solutions. In RFX experiments, when surfactant solutions pass through the opposed nozzles, rodlike or threadlike micelles are extended and align along the flow direction, which might cause an increase in the extensional viscosity. It has been proposed that high extensional viscosity of a drag-reducing surfactant solution results in additional resistance to vortex stretching and turbulent eddy growth, leading to drag reduction.1

Figure 9. Extensional viscosity/shear viscosity ratio of (a) Arquad 16-50 (5 mM)/3,4-chlorobenzoate (10 mM) and (b) Arquad 16-50 (5 mM)/3,4-methylbenzoate (5 mM) solutions at T ) 25 °C.84

However, using the RFX instrument to measure the apparent extensional viscosities of solutions, Lin84 recently found two drag-reducing solutions with low extensional viscosity/shear viscosity ratios in the extensional (shear) rate range tested. The two solutions are Arquad 16-50/3,4-methylbenzoate (5 mM/5 mM) and Arquad 16-50/3,4-chlorobenzoate (5 mM/10 mM). As mentioned earlier, the Arquad 16-50/3,4-chlorobenzoate (5 mM/10 mM) solution is a nonviscoelastic dragreducing solution. In addition, as shown in Figure 9, the extensional viscosity/shear viscosity ratio of the solution at T ) 25 °C is also unusually low (around 10) for this drag-reducing solution over the range of apparent extensional and shear rates tested (20-1000 s-1). The uniaxial extensional viscosity/shear viscosity ratio is 3 for Newtonian fluids (Trouton ratio). Experimental values obtained with water in the same opposingnozzles instrument are around 10. Thus, the extensional viscosity/shear viscosity ratios of the Arquad 16-50/3,4chlorobenzoate (5 mM/10 mM) solution are close to the experimental values for water. The surfactant solution Arquad 16-50/3,4-methylbenzoate (5 mM/5 mM) is a good drag reducer in the temperature range of 5-40 °C. Its extensional viscosity/ shear viscosity ratios at T ) 25 °C, shown in Figure 9, are between 1 and 10, however, even lower than those of water measured with the same instrument. Thus, it can be concluded that low extensional viscosity/shear viscosity ratios in the shear/extensional rate range tested (20-1000 s-1) do not necessarily lead to a lack of drag reduction in surfactant solutions. However, as can be seen in Figure 9, apparent extensional viscosity/shear viscosity ratios appear to rise at high extensional rates (above 1000 s-1). Thus, high extensional viscosity/shear viscosity ratios at high extensional rates might be a valid criterion for drag-reducing surfactant solutions, but no definite conclusion can be made. Summary Varying of counterion and surfactant chemical structures and concentrations can be useful for tailor-making cationic drag-reducing surfactant solutions for different application conditions. (1) Counterion Structure Effects. The effectiveness of a counterion in inducing cationic surfactant drag

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reduction depends on the counterion size and its hydrophobicity and penetration ability into the surfactant headgroup, i.e., counterion hydration force and strength of dispersion interactions between surfactant headgroups. The hydrophobic and hydrophilic portions of the surfactants and counterions should be separated as much as possible. Counterions that can form strong inter- or intramolecular hydrogen bonds are more effective in inducing a reduction in drag. The details of the chemical structure of the counterions are critical to ensuring that they are strongly binding. For the chlorobenzoates, 4-chlorobenzoate is strongly viscoelastic with excellent drag-reduction properties and a threadlike micelle microstructure, whereas 2-chloroboenzoate is not viscoelastic, is not drag-reducing, and has small spherical micelles. 3-Chlorobenzoate is intermediate in its properties. (2) Cationic Surfactant Structure Effects. The effective drag-reduction temperature range and critical shear stress of cationic drag-reducing surfactant solutions depend on the alkyl chain length, odd/even numbers of carbons in the surfactant alkyl chain, saturation/ unsaturation of the surfactant alkyl chain, and the surfactant headgroup. As the alkyl chain length increases, the upper effective drag-reduction temperature shifts upward. For surfactant solutions with odd/even numbers of carbons, odd/even effects are observed on the Krafft points, critical turbidity temperatures, and lower drag-reduction temperature limits. By including one double bond in the surfactant alkyl chain, the effective drag-reduction temperature range expands to lower temperature, and the upper dragreduction temperature limit is still maintained at the same level as the corresponding saturated surfactant solution. For unsaturated surfactant solutions with one double bond in the alkyl chain, at ξ ) 1.0 and 1.5, the critical shear stresses of surfactant solutions with cis configurations are much higher than those with trans configurations. Replacing some or all of the methyl groups with hydroxyethyl groups in quaternary ammonium cationic surfactant headgroups decreases the critical shear stress at the same temperature while expanding the effective drag-reduction temperature range. The viscoelastic properties of surfactant solutions reach a maximum when the surfactant headgroup contains one hydroxyethyl group and two methyl groups. (3) Relation of SIS to Drag Reduction. Although most drag-reducing surfactant solutions show SISs, shear viscosity data for drag-reducing solutions [oleyltrimethylammonium chloride (cis/trans molar ratio ) 4/6) (5 mM)/ NaSal (12.5 mM), Arquad S-50/NaSal (5 mM/12.5 mM). and Arquad 16-50/3,4-chlorobenzoate (5 mM/10 mM)] with no SIS within the tested shear rate range 1-1000 s-1 indicate that SIS is not necessary for a surfactant solution to be drag-reducing. However, rodlike or threadlike micelle structures play a very important role in surfactant solution drag reduction. Further, SIS appears to be accompanied by N1, and nonviscoelastic systems do not show SIS. (4) Relation of Viscoelasticity to Drag Reduction. Nonviscoelastic drag-reducing solutions such as Arquad S-50/NaSal (5 mM/12.5 mM) and Arquad 1650/3,4-chlorobenzoate (5 mM/10 mM) indicate that viscoelastic behavior, although common, is not vital for surfactant solutions to be drag-reducing. The opposite trends of drag reduction and viscoelasticity with tem-

perature observed in Arquad 18-50/NaSal (1.6 mM/4.0 mM) solutions support this conclusion. (5) Relation of Extensional Viscosity to Drag Reduction. Two drag-reducing solutions, Arquad 165/3,4-chlorobenzoate (5 mM/10 mM) and Arquad 16-50/ 3,4-methylbenzoate (5 mM/5 mM), with low extensional/ shear viscosity ratios in the tested range were observed. However, their extensional/shear viscosity ratios might increase at extensional/shear rates above 1000 s-1. Therefore, high extensional viscosity/shear viscosity ratios might be a requirement for surfactant solutions to be drag-reducing, but experiments at very high extensional/shear rates are needed to confirm this hypothesis, so no definite conclusion can be made. Literature Cited (1) Zakin, J. L.; Lu, B.; Bewersdorff, H. W. Surfactant Drag Reduction. Rev. Chem. Eng. 1998,14, 253-320. (2) Rose, G. D.; Foster, K. L. Drag Reduction and Rheological Properties of Cationic Viscoelastic Surfactant Formulations. J. Non-Newtonian Fluid Mech. 1989, 31, 59-85. (3) Manfield, P. D.; Lawrence, C. J.; Hewitt, G. F. Drag Reduction with Additives in Multiphase Flow: A Literature Survey. Multiphase Sci. Technol. 1999, 11, 197-221. (4) Fontaine, A. A.; Deutsch, S.; Brungart, T. A.; Petrie, H. L.; Fenstermachker, M. Drag Reduction By Coupled Systems: Microbubble Injection with Homogeneous Polymer and Surfactant Solutions. Exp. Fluids 1999, 26, 397-403. (5) Bewersdorff, H. W.; Gyr, A. Drag Reduction by Polymers and Surfactants. In Physical Processes and Chemical Reactions in Liquid Flows; Balkema: Rotterdam: The Netherlands, 1998; pp 209-221. (6) Usui, H.; Itoh, T.; Saeki, T. On Pipe Diameter Effects in Surfactant Drag-Reducing Pipe Flows. Rheol. Acta 1998, 37, 122128. (7) Kostic, M. On Turbulent Drag and Heat Transfer Reduction Phenomena and Laminar Heat Transfer Enhancement in Noncircular Duct Flow of Certain Non-Newtonian Fluids. Int. J. Heat Mass Transfer 1994, 37 (1), 133-147. (8) Shenoy, A. V. A Review on Drag Reduction with Special Reference to Micellar Systems. Colloid Polym. Sci. 1984, 262, 319337. (9) Chou, L. C. Drag Reducing Cationic Surfactant Solutions for District Heating and Cooling Systems. Ph.D. Dissertation, The Ohio State University, Columbus, OH, 1991. (10) Pal, R. Rheology of Drag-Reducing Surfactant Solutions. ASME 1998, 246, 115-130. (11) Lu, B.; Zheng, Y.; Davis, H. T.; Scriven, L. E.; Talmon, Y.; Zakin, J. L. Effect of Variations in Counterion to Surfactant Ratio on Rheology and Microstructures of Drag Reducing Cationic Surfactant Systems. Rheol. Acta 1998, 37 (6), 528-548. (12) Cates, M. E. Isotropic Phases of Self-Assembled Amphiphilic Aggregates. Philos. Trans. R. Soc. London A 1993, 344, 339-356. (13) Hoffmann, H.; Platz, G.; Rehage, H.; Schorr, W. The Influence of the Salt Concentration on the Aggregation Behavior of Viscoelastic Detergents. Adv. Colloid Interface Sci. 1982, 17, 275-298. (14) Magid, L. J.; Han, Z., Warr, G. G.; Cassidy, M. A.; Butler, P. D.; Hamilton, W. A. Effect of Counterion Competition on Micellar Growth Horizons for Cetyltrimethylammonium Micellar Surfaces: Electrostatic and Specific Binding. J. Phys. Chem. B 1997, 101, 7919-7927. (15) Hartmann, V.; Cressely, R. Linear and Nonlinear Rheology of a Wormlike Micellar System in the Presence of Sodium Tosylate. Rheol. Acta 1998, 37, 115-121. (16) Imae, T.; Kakitani, M.; Kato, M.; Furusaka, M. Effect of Organic Additives or Counterions on the Supramolecular Assembly Structures Constructed by Amphiphilies. A Small-Angle Neutron Scattering Investigation. J. Phys. Chem. 1996, 100, 20051-20055. (17) Bachofer, S. J.; Turbitt, R. M. The Orientational Binding of Substituted Benzoate Anions at the Cetyltrimethyl Ammonium Bromide Interface. J. Colloid Interface Sci. 1989, 135, 325-334.

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Received for review December 30, 2001 Revised manuscript received April 18, 2002 Accepted April 26, 2002 IE0110484

Chemical and Rheological Characterization of Drag-Reducing

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