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Advances in Mechanical Engineering

Volume 2011 (2011), Article ID 345328, 5 pages

http://dx.doi.org/10.1155/2011/345328

## On Relationships among the Aggregation Number, Rheological Property, and Turbulent Drag-Reducing Effect of Surfactant Solutions

^{1}School of Energy Science and Engineering, Harbin Institute of Technology, Harbin 150001, China^{2}State Key Laboratory of Multiphase Flow in Power Engineering, Xi'an Jiaotong University, Xi'an 710049, China^{3}Beijing Key Laboratory of Urban Oil and Gas Distribution Technology, China University of Petroleum-Beijing, Beijing 102249, China

Received 31 May 2011; Accepted 29 June 2011

Academic Editor: Yasuo Kawaguchi

Copyright © 2011 Ying-Bo Zhou et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

In this study, turbulent drag-reducing effect, rheological characteristics and micelle aggregation number of aqueous solutions of anionic surfactant, sodium dodecyl sulfate (SDS), and cationic surfactant cetyltrimethylammonium chloride (CTAC) aided with sodium salicylate (NaSal). SDS solution was experimentally investigated at various concentrations in CMCs (critical micelle concentration) with and without sodium chloride. 200 ppm (ppm means part per million) CTAC/NaSal (mass ratio 1 : 1) solution was tested within temperature range from 20^{∘}C to 80^{∘}C. We were aiming at gaining insights into relationships among turbulent drag reduction rate, rheological properties and micelle microstructures of drag-reducing surfactant solution. Experiments on aggregation number, turbulent drag reduction and shear-rate dependent shear viscosity were performed for solution of SDS and 200 ppm CTAC/NaSal, respectively. The relationships among these three parameters were analyzed and discussed. The results are of importance from both theoretical and practical viewpoints for micellar transitions of surfactant solution.

#### 1. Introduction

By dissolving a minute amount of additives such us polymers and surfactants in water, the frictional drag of turbulent flow through pipes and channels can be reduced dramatically [1–3]. This phenomenon is called turbulent drag reduction. For drag-reducing surfactant solutions, it is proposed that the transition of large aggregates into rod-like micelles is responsible for the onset of drag reduction behavior of these systems [4, 5]. The drag-reducing effect is determined by many factors, such as the chemical structure of surfactants, counterions, the concentration, and the ratio of counterions to surfactants. The number of surfactant monomers forming a micelle is a structurally relevant parameter that contains indirect information on the micelle geometries. Most surfactant drag-reducing systems form rod-like micelles in the quiescent state and have distinctive rheological properties such as high zero-shear viscosities, shear thinning behavior with increasing shear rate, and shear-induced structure represented by a local increase in both shear viscosity and the first normal stress difference at a certain shear rate range [6, 7].

In order to clarify the factors influencing on the turbulent drag-reducing ability of surfactant additives, we measured the aggregation number, drag reduction rate of turbulent pipe flow, and shear-rate-dependent shear viscosity of aqueous solutions of anionic surfactant sodium dodecyl sulfate (SDS) with/without addition of NaCl and cationic surfactant cetyltrimethylammonium chloride (CTAC) aided with sodium salicylate (NaSal). This study focuses on investigating the inherent relationships among the aggregation number, rheological property, and turbulent drag-reducing effect of surfactant additives.

#### 2. Experimental Setup and Procedures

##### 2.1. Working Fluids

Aqueous solution of anionic surfactant SDS (Chengxin Ltd.) with/without addition of sodium chloride (NaCl, Sigma Chemical Company) and 200 ppm (ppm means part per million) CTAC/NaSal (mass ratio 1 : 1) was tested in the present study. The SDS and CTAC were used after repeated recrystallization from an ethanol-water mixture. No minimum in surface tension versus concentration plot was observed in the purified surfactant. Pyrene 99.0% pure, benzophenone 99.0% pure (Aldrich, USA), and triple-distilled water were used for preparation of solutions in which benzophenone was used as the quencher and pyrene for probing. The temperature of working fluid was controlled to be 40°C for SDS solution measurements and be from 15°C to 60°C for CTAC/NaSal solution measurements.

##### 2.2. Test Facility

###### 2.2.1. Aggregation Number Measurement

Steady-state fluorescent quenching method was utilized for measurement of aggregation number, , of surfactant. The steady-state fluorescent quenching technique belongs to fluorescence probing methods, which uses a fluorescent probe, commonly pyrene in the case of aqueous solution. of surfactant, that is, the number of surfactant monomers forming a micelle, is a structurally relevant parameter that contains indirect information on the micelle geometries [8].

Steady-state fluorescence quenching experiments of anionic surfactant SDS and CTAC/NaSal were performed with a spectrofluorometer (Tianjin Gangdong Company, China), which is usually equipped in most chemistry laboratories. The excitation source was successive xenon light. Take SDS for example, there exist five emission wave crests at wavelengths of 373 nm, 379 nm, 384 nm, 390 nm, and 393 nm [8, 9], among which 393 nm was chosen to be emission wavelength. Fluorescence emission spectra were recorded using an excitation wavelength of 335 nm. The aggregation number, , is determined from the slope obtained from the plot of versus according to some mathematical assumptions, where and are the fluorescence intensities in the absence and presence of a quencher, respectively, and is the quencher concentration [9].

###### 2.2.2. Measurement of Turbulent Drag Reduction

Drag reduction was measured in two closed loop fluid flow facilities. The test sections are acrylic resin tube with inner diameter of 0.025 m and length of 1.4 m and channel with height of 0.01 m, width of 0.125 m, and length of 3.0 m, respectively [10]. The pressure drop was measured with a differential pressure transducer, and flow rate was measured with an electromagnetic flow meter. The system was temperature controlled, which allows for the experiments being carried out at a temperature range of 5°C to 90°C. The turbulent drag reduction rate is defined as , where is the pressure drop of solvent flow and is the pressure drop of solution flow at the same flow rate [4]. Before experiments, the reliability of this loop has been verified: the measured friction factor for water flow agrees very well with commonly accepted correlation for turbulent pipe flow () or channel flow of the Newtonian fluids ().

###### 2.2.3. Shear Viscosity Measurement

The shear-rate-dependent shear viscosity of SDS and CTAC/NaSal solutions was measured with a stress-controlled rheometer AR-G2 (TA Instruments). Parallel plate and cone-and-plate geometries offered by TA Instruments are available for AR-G2. The cone-and-plate measuring system has the best advantage of the shear rate across the entire surface being uniform. In this paper, we choose the cone-and-plate geometry with 60 mm cone diameter, 2° cone angle, 58 *μ*m gap for the rheological measurements. The sample is loaded between the cone-and-plate discs. The upper cone is driven by an oscillatory force on the axis normal to the plate surface.

#### 3. Results and Discussions

##### 3.1. Aggregation Number

Figure 1 shows the variation of aggregation numbers of SDS solution with addition of NaCl, in which aggregation numbers are plotted against concentrations at 40°C. The concentration range within which the solution has a fluctuation in a narrow range is called “stabilized zone” in this study. At each stabilized zone the tested aggregation numbers increase by small degree. Between stabilized zones there exist some concentration ranges where aggregation numbers have a sharp increase. Contrasting to other researcher’s cryo-TEM results [11], in salt-free system, micelle shapes transform from spherical to rodlike, then to hexagonal, till lamellar [4]. Every stabilized zone corresponds to one micelle configuration, that is, concentrations less than 15 CMCs stand for spherical, bigger than 17 CMCs but less than 47 CMCs stand for rodlike and hexagonal, and bigger than 60 CMCs stand for lamellar shapes, respectively. When the concentration goes on increasing, transmittance of the solution decreased too much to determine aggregation numbers.

Figure 2 shows the variation of aggregation numbers of SDS in water without addition of NaCl, in which aggregation numbers are plotted against concentrations at 40°C. Salt-free systems have similar stabilized zones with salt systems. Generally, without counterions, cationic surfactants would not form rod-like micelles which are necessary for drag reduction at low concentration. In most cases organic salts play a role of counterions in cationic surfactant solution, and inorganic salts play a role of counterions in anionic surfactant solution. Therefore, the addition of NaCl has great effects on micelle aggregation ability of surfactant SDS. For instance, in salt-free system rod-like micelles appear at 75 CMCs (94 mM) in SDS solution, while in salt system they turn out to be 17 CMCs (64 mM). Inorganic salts make less powerful effects than organic salts in bonding surfactant monomers. For the same concentration, salt system has larger aggregation number than that of salt-free system, that is to say, micelles in salt system may be stronger and get more powerful shearing ability [4]. As the concentration increases to 360 CMCs, phase separation happens so that aggregation number increases suddenly.

Figure 3 shows the variation of aggregation numbers of 200 ppm CTAC/NaSal solution, in which aggregation numbers are plotted against temperature. When temperature is varied from 15 to 30°C, aggregation number increases slowly in a stabilized zone (lager than 95 but smaller than 100). As temperature goes on rising to 50°C, micellar aggregation number enters into another stage (average size 120) in a narrow temperature range. This maybe presents two different kinds of micellar structures.

##### 3.2. Shear Viscosity

Figure 4 shows the measured zero-shear viscosity for the case of SDS solution without NaCl (the aggregation number replotted together with viscosity for comparison). It can be seen that in every stabilized zone shear viscosity has an increase-then-decrease tendency. When aggregation number rises towards the local maximum values, shear viscosity in those stabilized zones turns to be larger. In the first half of each stabilized zone representing micelle shape formation, the corresponding viscosity increases obviously, which might be caused by more monomers arranging in order. In the last half of shape-changing stage, the corresponding viscosity decreases, which is probably due to more monomers being arranged disorderedly.

Figure 5 shows the measured shear viscosity versus shear rate of 200 ppm CTAC/NaSal solution at different temperatures. We can see that the shear viscosity first increases sharply and then decreases gradually with increasing shear rate at 20°C and 30°C in the present measurement. The increase of viscosity at very low shear rate might be due to the system error of the rheometer during operation, since from zero-shear rate, there should be a plateau range characterizing the zero-shear viscosity. The effect of shear rate becomes small, and the measured shear viscosity is close to that of water when temperature is increased up to 40°C and 50°C. Generally speaking there exists a critical temperature exceeding which rheological properties of 200 ppm CTAC/NaSal solution are the same as those of water.

##### 3.3. Drag Reduction in Surfactant Solution Flows

Measurement of drag reduction characteristics was performed for flows of SDS solution at a concentration from 17 CMCs to 60 CMCs with NaCl and from 75 CMCs to 300 CMCs without NaCl within a temperature range from 10°C to 50°C, and 200 ppm CTAC/NaSal solution at a Reynolds number range from 20000 to 120000 at 20°C in pipe and at a Reynolds number range from around 2600 to 50000 and within a temperature range from 15°C to 55°C in channel.

It is concluded that no obvious drag reduction phenomenon occurs in SDS solution flows. Most researchers argued rod-like micelles were responsible for drag reduction behavior. In this experiment, however, rod-like micelles are found [4], but no turbulent drag reducing effect is observed, which implies that the formation of rod-like micelles only is not enough for the occurrence of turbulent drag reduction.

Obvious drag reduction phenomenon is observed for 200 ppm CTAC/NaSal solution cases. Figure 6 shows the drag reduction measurement results for 200 ppm CTAC/NaSal solution flow at 20°C in pipe. Due to the limitation of this pipe-flow facility, lower Reynolds number was not realized (as shown in Figure 6(a)). All the measured Reynolds numbers have been in the range over the optimum drag-reducing state for 200 ppm CTAC/NaSal solution. However, obvious turbulent drag-reducing effect still exists for all the measured runs, which can be used for comparative analysis with the shear viscosity.

As shown in Figure 6(b), the abscissa is changed to be average shear rate (mean velocity divided by the diameter of pipe) corresponding to each measured Reynolds number. It can be seen that the average shear rates for all the measurements are all in the range at which shear thinning becomes serious as shown in Figure 5. The phenomena of both the decrease of turbulent drag-reducing ability and the serious shear thinning appearing in the shear viscosity within the measured shear rate are closely relevant to each other.

Figure 7 shows the results of drag reduction measurement versus the Reynolds number for 200 ppm CTAC/NaSal solution flows within a temperature range from 15°C to 55°C in a channel flow [10]. It can be seen that, for the two cases at temperatures of 50°C and 55°C, the turbulent drag-reducing effect of 200 ppm CTAC/NaSal solution is significant in a much broader range of the Reynolds number. In the aggregation number measurement, as shown in Figure 3, it has been demonstrated that from 50°C begins to increase and reaches to a local maximum plateau value (120) from around 55°C. The above-mentioned two phenomena appearing in drag reducing ability and aggregation number, again, are closely relevant to each other, that is, a larger aggregation number corresponds to stronger microstructures in the surfactant solution flow that shows significant turbulent drag-reducing effect in a broader Reynolds number, or in other words, a higher shear stress is needed to destroy the microstructures in a surfactant solution with larger aggregation number.

#### 4. Conclusion

Aggregation number, turbulent frictional drag, and shear viscosity characteristics of SDS solution with and without NaCl and of 200 ppm CTAC/NaSal solution at various temperatures were experimentally investigated. The relationships among the shear viscosity, turbulent drag reduction, and aggregation number that can indirectly characterizes the micellar microstructures in surfactant solution have been analyzed. The main conclusions are as follows. (1)There exist stabilized zones according to the changing of aggregation numbers, which corresponds to the micelle shape change process. In every stabilized zone, shear viscosity has an increase-then-decrease tendency. This phenomenon is probably caused by formation and breakdown of the micelle network structures.(2)The pipe flow test of 200 ppm CTAC/NaSal solution at 20°C indicates that the shear-rate-dependent shear viscosity and drag reduction efficiency exhibited a close relevance. Experiments on SDS solution flows imply that the formation of rod-like micelles only is not enough for the occurrence of turbulent drag reduction.(3)The channel flow test of 200 ppm CTAC/NaSal solution at different temperatures shows that the aggregation number and drag-reducing ability of a surfactant solution flow have close relevance, that is, larger aggregation number corresponds to a larger range of effective Reynolds number for drag reduction.

#### Acknowledgments

The authors acknowledge the support from the National Natural Science Foundation of China (no. 51076036, no. 50876114, no. 51076124) and the Fundamental Research Funds for the Central Universities (HIT.BRET1.2010008).

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