Characterization of micellar structure dynamics for a drag-reducing surfactant solution under shear: normal stress studies and flow geometry effects

Rheol Acta 34:450-460 (1995) © Steinkopff Verlag 1995

Yuntao Hu Eric F. Matthys

Characterization of micellar structure dynamics for a drag-reducing surfactant solution under shear: normal stress studies and flow geometry effects

Received: 20 March 1995 Accepted: 21 July 1995

Y. Hu • E. E Matthys (~) Mechanical Engineering Department University of California Santa Barbara, California 93106-5070, USA

A b s t r a c t Some surfactant solutions have been observed to exhibit a strong drag reduction behavior in turbulent flow. This effect is generally believed to result from the formation of large cylindrical micelles or micellar structures. To characterize and understand better these fluids, we have studied the transient rheological properties of an efficient drag-reducing aqueous solution: tris (2-hydroxyethyl) tallowalkyl ammonium acetate (TTAA) with added sodium salicylate (NaSal) as counterion. For a 5/5 mM equimolar TTAA/NaSal solution, there is no measurable first normal stress difference (N 0 immediately after the inception of shear, but N~ begins to increase after a well-defined induction time - presumably as shear- induced structures (SIS) are formed - and it finally reaches a fluc- tuating plateau region where its average value is two orders of

magnitude larger than that of the shear stress. The SIS buildup times obtained by first normal stress measurements were approximately inversely proportional to the shear rate, which is consistent with a kinetic process during which individual micelles are incorporated through shear into large micellar structures. The SIS buildup after a strong preshear and the relaxation processes after flow cessation were also studied and quantified with first normal stress difference measurements. The SIS buildup times and final state were also found to be highly dependent on flow geometry. With an increase in gap between parallel plates, for example, the SIS buildup times decreased, whereas the plateau viscosity in- creased.

Key w o r d s Mice l l e s - surfactant - rheology - normal stresses - shear-thickening

Introduction

There has been strong interest recently in the possible im- plementation of drag-reducing surfactant solutions as an energy conservation approach for recirculating hydronic systems (Gasljevic and Matthys, 1993), but a good understanding of the properties of these fluids is still elusive. One way to improve this understanding is to investigate their rheological properties. For practical applications, both steady state and transient behavior are important,

and one might note that there may be some connection between the steady state rheological properties and the effectiveness of the drag reduction in developed flow zones, on the one hand, and between the transient rheological behavior and the drag reduction in developing flow zones, on the other hand.

In this article we focus on the transient flow behavior. The time-dependent rheological behavior of these drag- reducing systems is of importance for several reasons. First, in a typical hydronic cooling and heating system, ~- there are numerous fittings, valves and elbows. In these

Y. Hu and E. E Matthys 451 Characterization of micellar structure dynamics for a drag-reducing surfactant solution

components, the shear stress may be significantly higher than that in the straight pipes, which may result in flow redevelopment or even temporary fluid "degradation". We have indeed obtained data showing extensive transient regions downstream of such disturbances (Gasljevic and Matthys, 1994). In order to predict the overall drag reduction level for the whole system, it is therefore necessary to know how fast the flow redevelops or how soon the fluid will be restored to its original condition. Secondly, since drag reduction is normally accompanied by heat transfer reduction as well, it may be desirable to eliminate these effects intentionally in order to restore the performance of heat exchangers. We have been able to do so through various techniques, but here again, one needs to understand the dynamics of flow and fluid changes. Finally, besides these practical considerations, rheological studies of these transient phenomena can also shed light on the fundamental behavior of these micellar solutions.

Ideally, we would therefore like to be able to answer the following questions concerning the transient flow behavior of drag-reducing surfactarLt systems:

- How long does it take for a solution that has experi- enced a very high shear (and thus partly or totally lost its drag-reducing ability) to regain its drag-reducing capability once the shear rate is reduced?

- What is the flow geometry dependence of these times?

Even though in principle one might want to answer these questions through actual drag reduction experiments, in practice the flow field in turbulent flows is very complicated and not easily analyzed. It is therefore relatively complicated to perform well-designed and well-controlled transient drag reduction measurements. On the other hand, the time evolution of the laminar flow behavior of a drag-reducing fluid can be easily followed with a rheometer. If we could find rheological parameters for these fluids that correlate with their drag-reducing capability, we could at least partially answer the questions above by measuring those rheological parameters. Such information may be useful to provide us with some quan- titative guidance as far as which drag reduction experiments might be most appropriate to do. Naturally, this approach is also related to the more :fundamental issue of how one might predict the drag-reduction effectiveness of a fluid based strictly on the knowledge of its material properties, a difficult problem indeed.

The first step is to identify a proper rheological parameter. Previous rheological studies have shed partial light on the correlation between rheological properties and drag reduction of surfactant systems (Shenoy, 1984; Ohlendorf et al., 1986; Rose and Foster, 1989; Bewersdorff et al., 1986, 1989; Mygka and Stern, 1994; Hofmann et al., 1994). It is generally agreed that the ex- istence of rodlike or wormlike micelles is essential for the drag reduction effect. The question then is whether

rodlike or wormlike micelles alone are sufficient for drag reduction, or whether there must also be some flow-induced micellar structures (often called SIS). Several studies have been aimed at a better understanding of the SIS. For example, it has been proposed that the SIS con- sist of nematic domains (Hofmann et al., 1991) or a hexagonal structure (Kalus et al., 1989) based on neutron scattering patterns. Even though the details of the SIS microstructure remain to be fully understood, some information on their macroscopic properties has been obtained and their salient features are thought to involve:

- high elasticity. The SIS are usually accompanied by a significant first normal stress difference (Wunderlich et al., 1987);

- highly birefringent fluid and complete alignment in the flow direction. The SIS show large birefringence and zero or near-zero orientation angle, in contrast to little or no birefringence shown by the fluid at rest presumably featuring micelles at equilibrium (Hof- mann et al., 1991; Wunderlich et al., 1987; Hu et al., 1993 a, b).

- higher viscosity. The solution with SIS usually has higher viscosity than the same solution before SIS are produced. Therefore, such a solution may exhibit rheopexy and shear-thickening, especially for dilute concentrations (Ohlendorf et al., 1986; Hu et al., 1993 a, b; Wunderlich et al., 1987). The magnitude of the viscosity increase is also flow geometry-dependent for a given solution (Wunderlich and Brunn, 1989).

Ohlendorf et al. (1986) proposed two mechanisms for drag reduction with surfactant solutions: (a) a buildup of ordered structures which damp the large scale turbulence in the core region of the pipe and (b) damping of the turbulent eddies in the near-wall boundary layer of the pipe by structures of aligned rods which were induced by elongational flow. Both mechanisms rely on either SIS or other flow-induced structures. It was indeed found that rodlike micelles alone are not sufficient to reduce drag in some cases. Part of the evidence is that at high surfactant concentrations no drag reduction is found above a certain temperature, even though rodlike micelles can be detected by electric birefringence measurements in the solution (Ohlendorf et al., 1986). More evidence favoring the no- tion that a secondary structure is responsible for drag reduction was obtained by Bewersdorff et al. using in-situ small-angle neutron scattering. They found that the loss of drag reduction beyond the critical wall shear stress is accompanied by the loss of alignment of micelles but that the individual rodlike micelles on the other hand are in- tact (Bewersdorff et al., 1986). In view of these and other experimental results, it does seem that flow-induced structures may indeed be responsible for the drag reduction.

We chose therefore to focus our investigations on these SIS in drag-reducing surfactant solutions. The model

452 Rheologica Acta, Vol. 34, No. 5 (1995) © Steinkopff Verlag 1995

system consists of tris (2-hydroxyethyl) tallowalkyl ammonium acetate and sodium salicylate. This system has been widely used in drag reduction studies (Gasljevic and Matthys, 1994). In these series of experiments we used the system at equimolar ratio. Three simple parameters may in principle be used to quantify the formation of SIS: viscosity, flow birefringence, and first normal stress difference. However, as discussed below, it appears that normal stress measurements are much more sensitive to the onset of SIS formation than viscosity measurements. Compared with flow birefringence, normal stress measurements are also more representative of the elasticity of the sample solution, the parameter generally thought to be responsible for the drag reduction phenomenon (Shenoy, 1984). Accordingly, we have used in this study the first normal stress difference as the pr imary rheological parameter for characterization of the time-dependent behavior of the SIS, and for the study of the possible connection between the rheology and the drag-reducing behavior of these surfactant solutions.

Experimental procedure

Materials

The surfactant investigated in this study is tris (2-hydroxyethyl) tallowalkyl ammonium acetate (tallowalkyl- N(C2H4OH)3Ac) from AKZO Chemicals (Ethoquad T/13-50). The master fluid is in liquid form with 50°70 of surfactant, 36% of isopropanol, and 14% of water by weight. The molecular weight of the surfactant is approximately 454 (gram/mole). We used as counterion 2-hydroxyl benzoate (sodium salicylate) from Aceto Inc. The use of this counterion is thought to increase the drag reduction effectiveness of the fluid through improved formation of cylindrical micelles. The solvent was deionized water produced in house with ion exchange columns. All the materials were used as received. The samples were prepared by weighing out the required amount of surfac- tants and salts with 0.0005 gram resolution and adding them to 100 or 200 ml of water. The solutions were mixed

with a magnetic stirrer at a moderate rate for at least 30 min and kept at room temperature for at least 12 h before rheological measurements.

Instrumentat ion

A Rheometrics RMS-800 Mechanical Spectrometer was used for transient and steady shear measurements. The torque range for shear stress measurement is 2 to 2000 g- cm and the normal force range is 2 to 2000 grams for the transducer used. In view of the low viscosity of our samples, a large custom-made coni-cylinder fixture was used for most of the simultaneous viscosity and first normal stress measurements. This fixture consists of two concentric cylinders, the inner one having a conical bot- tom so that the first normal stress difference can be measured. Other geometries were also used to study the effect of flow geometry and size. A Rheometrics DSR controlled stress rheometer with a torque range of 0.01 to 100 g-cm was also used for low shear rate viscosity measurements. This rheometer can be programmed to perform constant shear rate tests, but may need a significant time to reach the desired shear rate, a drawback for ac- curate transient flow experiments. Table 1 summarizes the dimensions of the flow fixtures used in this study.

All the measurements with the RMS-800 were carried out at room temperature (22.8+1°C unless otherwise specified) because the existing temperature chamber is not suited for use with the large custom-made coni- cylinder fixture. Two measures were adopted to minimize the effect of temperature variation, however. First, we usually kept the sample solution in a constant temperature bath of 22.5+0.1 °C for at least 10min before the rheological measurement. Second, when data were collected over a period of time and used for comparison pur- poses, we always made sure that the temperature variation did not exceed _+0.5 °C for all the tests involved. This was achieved by monitoring the room temperature and only conducting the experiments when the temperature was in the desired range. The temperature for the DSR tests was kept at 22.5 +0.2 °C. Both rheometers have been checked with Newtonian fluids to make sure that they were func- tioning well and that all the data presented are reliable.

Table 1 Flow geometries used in this study Rheometer Geometry

RMS-800

DSR

Code Bob, cone, or Cup Gap Cone Bob name plate diameter diameter (mm) angle length

(ram) (ram) (rad) (mm)

big coni-cylinder CC77 50.3 small coni-cylinder CC20 50 cone & plate I CP50 50 cone & plate 2 CP25 25 plate & plate PP 50 50

concentric cylinder CC44 29.5

52.2 0.95 0.04 52 1 0.04

0.04 0.1

0.3 - 1.5

32 1.25

77 20

44

Y. Hu and E.F. Matthys 453 Characterization of micellar structure dynamics for a drag-reducing surfactant solution

Results

Start-up flow

General features

Figure 1 shows the simultaneous time evolution of the first normal stress difference (N 1 = a l l - 0"22) and shear stress in a 5 / 5 m M equimolar tris (2-hydroxyethyl) tallowalkyl ammonium acetate (TTAA) and sodium salicylate (NaSal) solution. The shear rate is kept constant at 100 s -1. (The measured viscosity of the fluid is therefore proportional to the shear stress.) Both N 1 and the shear stress show essentially no change in the first 60 s and then increase for about 130s, finally reaching a plateau region where they fluctuate about an average value. Similar behaviors for either viscosity (Rehage and Hoffmann, 1982; Hu et al., 1993a, b) or N 1 (Rehage et al., 1986) under a constant shear has been reported for other surfactant solutions. Here we also demonstrate that the increase in viscosity by a factor of three is accompanied by a much more dramatic increase in the first normal stress difference, which eventually reaches a level two orders of magnitude higher than the shear stress. These increases in N t and viscosity under shear flow suggest that new micellar structures have been formed. The ex- istence of shear-induced structures (SIS) which are different from the homogeneous equilibrium solution structure has been confirmed by various techniques for many charged surfactant solutions (Hofmann et al., 1982; Kalus et al., 1989; Jindal et al., 1990; Hofmann et al., 1991; Miinch et al., 1991; Hu et al., 1993 a; b) and therefore will not be further discussed here. Instead, we will focus on

the characteristic times of the SIS buildup and decay, which is of practical interest for drag-reducing applications.

Effects o f shear rate

The time scale of the viscosity and N l growth depends on the applied shear rate, as shown in Fig. 2 which shows N~ growth curves for three different shear rates. (The data for the viscosity show similar trends.) Two characteristic times can be used to represent the rate of the SIS buildup. One is the induction time ti, defined as the length of the period during which no increase in viscosity or Nl is detected. This time can be obtained from the intersection of the prestructure N1 value and the early N 1 growth slope as illustrated in Fig. 2 for the 100 s -I run. Another characteristic time is the "plateau" time t s that it takes for the viscosity or N 1 to reach the average value in the plateau region. The plateau time can be quantified by identifying the first intersection of the viscosity or N 1 curve with the average plateau value. In Figs. 3 and 4 we show the induction and plateau times obtained from the N 1 and viscosity curves, respectively. Most of the data points shown represent the average of two to three measurements with the same or different samples (the bars show the spread of measurements). In the shear rate range tested (25 to 800 s-1), the induction times were found to be a function of shear rate to the -0.93 power, for both N1 and viscosity. At lower shear rates the rheometer is not sensitive enough to make reliable measurements, and at higher shear rates, the induction time is too short to be measured without much error. Note that the viscosity in-

¢)

z

3000.0

2500.0

2000.0

1500.0

1000.0

500.0

0.0

- 1 i00 s ~ ~

N 1 /" !,. / \ /

0 100 200 300 400

S h e a r T i m e ( s )

20

:r 15

io

¢D

O

ro

Fig. 1 Time evolution of shear stress and first normal stress difference upon applying a constant shear flow of 100 s -I in a 5/5 mM TTAA/NaSal solution. [Coni-cylinder CC77. T = 22.7+0.2°C1

5000.0

4000.0

3000.0

2000.0

1000.0

0.0

- 1 0 0 0 . 0

0 100 200 300 400


Fig. 2 Time evolution of first normal stress difference upon applying a constant shear flow with three different shear rates. [5/5 mM TTAA/NaSal solution. Coni-cylinder CC77. T = 22.7+0.2°C]


I000.0

1 0 0 . 0

1 0 . 0

1 . 0

• N 1 I n d u c t i o n t i m e

P l a t e a u t i m e

I0 I00 I000 I0000

S h e a r R a t e ( l / s )

Fig. 3 Induction and plateau times for first normal stress difference vs shear rate. The slope for the induction and plateau times are 0.93 and 0.83 respectively. [5/5 mM TTAA/NaSal solution. Coni- cylinder CC77. T = 22.7_+0.2 °C]

I000.0

o~

I00.0

i 0 . 0 iP

• Viscosity induction time v Viscosity plateau time

1 . 0 . . . . . . . . , . . . . . . . . , . . . . . . . .

i0 i00 I000 i0000

S h e a r Ra te ( I / s )

Fig. 4 Induction and plateau times for shear viscosity vs shear rate. The slope for the induction and plateau times are 0.93 and 0.77 respectively. [5/5 mM TTAA/NaSal solution. Coni cylinder CC77. T= 22.7+0.2 °C]

duction time is the same as the NI induction time. How- ever, the viscosity plateau time is often slightly greater than the N 1 plateau time at a given shear rate. This discrepancy may be due to flow cell geometry effects because only the bot tom of the inner cylinder detects the normal stress while both the bot tom and wall of the cylinder measure the viscosity, and we shall see later that the SIS buildup time is indeed sensitive to the geometry of the flow cell.

It should be noted that since N I remains essentially zero during the induction period and increases abruptly subsequently, the induction time can be obtained with little arbitrariness. Even though careful analysis of the viscosity curve usually reveals under magnification the same induction time for the viscosity, N 1 measurements do generally provide a more sensitive method for studying the time evolution of the shear-induced structures. To measure accurately either induction or plateau time, caution must also be taken to ensure that the sample is in an equilibrium state before the start of flow. To minimize the effect of sample loading or of a previous flow, the sample must be left to relax for a sufficiently long time before each test. The minimum waiting time can be estimated by delayed-step experiments (Hu et ah, 1993 a), and this time may strongly depend on the temperature, surfactant concentration, or salt concentration and should be obtained for each sample. For our 5/5 mM TTAA/NaSal solution, this time is about 10 rain. The relationship between the induction time and shear rate, which is very close to an inversely proportional law, suggests that the growth in viscosity and N I under a constant shear rate is of kinetic origin similar to shear-induced coagulation. A similar inversely proportional relationship between the induction time and shear rate for viscosity was observed for two other surfactant solutions (Hu et al., 1993 a, b). Our new results may then provide a further suggestion of the generality of the kinetic mechanism for the shear-thickening of surfactant solutions.

Effects of f low direction

The buildup of SIS is insensitive to the flow direction as illustrated in Fig. 5, showing results of an experiment where the direction of the shear flow was alternated three times as indicated by the change of sign of the shear stress. Comparing with Fig. 1, where the flow direction is unchanged, the induction time in the two cases appears to be the same (about 60 s). For a different surfactant system, Hu et al. (1993b) have reported the same behavior for flow birefringence under an alternating flow. The insensitivity of the SIS buildup to the flow direction is indeed perhaps another indication of a kinetic process.

Critical shear rate

The formation of SIS occurs only when the shear rate is above a certain value. Figure 6 shows the initial and plateau viscosities as a function of shear rate. There is an increase in viscosity if the shear rate exceeds about 10 s-1, implying that a critical shear rate between 5 and l 0 s - 1 is required for the formation of SIS. Note that to determine the critical shear rate, the minimum shear time must be longer than the expected induction time of the SIS at the

Y. H u and E. E Mat thys 455 Characterization of micellar structure dynamics for a drag-reducing surfactant solution

3 0 0 0 . 0

2 5 0 0 . 0

2 0 0 0 . 0

1500.0

1 0 0 0 . 0 Z

5 0 0 . 0

0 .0

S h e a r S t r e s s --" ; " [ ' ~ J - . ~ l ~ t l [ I I

50 100 150

15


5 ¢ - -

5~ 0 m

- 5

- 1 0

- 1 5

200 250

Fig. 5 Time evolution of shear stress and first normal stress difference under an alternating shear flow of 100 s ~ during which the flow direction is reversed every 20 s for three periods and then preserved for 190 s. [5/5 m M T T A A / N a S a l solution. Coni-cylinder CC77. T = 2 2 . 7 _ 0 . 2 ° C ]

50 s -1 is measured to be about 120 s (see Fig. 13). In our tests the viscosity remained nevertheless at a low level for as long as 3600 s at a shear rate of 5 s -~, whereas a significant increase was readily observed at 10s -~. (Note that the tools used were different for the low and high ranges of shear rate which may have affected the absolute value of the viscosity measurements because of the geometry effect discussed below. The sharp shear- thickening phenomenon does, however, take place entirely within the range covered by a single tool.)

Figure 7 shows the plateau first normal stress difference N1 and first normal stress difference coefficient ~'l = N1/~ 2 as a function of the shear rate. No data is available below 25s -~ because the normal force transducer is not sufficiently sensitive at these low shear rates. (Data at shear rates above 200 s -~ are corrected for inertia effects (Macosko, 1994) by N 1 = 2 F z / ( ~ R 2 ) - O . 1 5 p f J 2 R 2, where F z is the measured vertical force, R the inner cylinder diameter, p the fluid density, and fJ the rotational velocity.) The monotonic decrease of the first normal stress coefficient indicates that the solution is already in the nonlinear region at the shear rates covered.

1.00

%- . ) , - i o

0 .10

©

¢ 9

0.01

o-- o ~ Plateau v iscos i ty

~ '~, ......... .i~\~a,o,o

Initial v iscos i ty '"'"Z~. %

. . . . . . . . I . . . . . . . . I . . . . . . . . I . . . . . . . .

i0 I00 I000 I0000

Shear Rate ( i / s )

Fig. 6 Initial and plateau viscosities. The coni-cylinder CC77 was used except for the data at shear rates equal or smaller than 50 s - l , where coni-cylinder CC20 was used. [5/5 m M T T A A / N a S a l solution. T = 22.5_+0.5°C]

shear rate applied. The expected induction time can be calculated from the induction time at a higher shear rate using the inversely proportional relationship we observed between the induction time and the shear rate. For the 5 / 5 m M solution in the CC44 concentric cylinder geometry of the DSR, the expected induction time at 5 s -1 is estimated to be 1200 s since the induction time at

Stress f luctuations

Another notable feature seen in Fig. 1 is the periodic viscosity fluctuations in the plateau region. The fluctuations resemble those generated by elastic instabilities in Couette flow of polymer solutions with viscous solvents (Larson et al., 1990; Shaqfeh et al., 1992) or the stress response in multiphase fluids, such as director tumbling in liquid crystal fluids (Gu et al., 1993). Indeed, the solu-

i 0 0 0 0 . 0 101

a~ 1 0 0 0 . 0

O9

i 0 0 . 0 Z 10 .0

I0 °

i0-i

i0-2

10-a ~ -

1 0 - 4

. . . . . . . . ~ . . . . . . . . ~ . . . . . . . . 10 -5

10 100 1000 10000


Fig. 7 First normal stress difference and coefficient as a function of shear rate. [ 5 / 5 m M T T A A / N a S a l solution. Coni-cylinder CC77 , T = 2 2 . 5 + 0 . 5 ° C ]


tion containing SIS is very elastic, as suggested by the strong normal stress difference which is two orders of magnitude larger than the corresponding shear stress. The possibility of multiphase flow, on the other hand, arises from the suggestion that SIS may be hexagonal liquid crystal structures (Kalus et al., 1989) or nematic domains (Hofmann et al., 1991). This interesting phenomenon observed with these surfactant solutions will be further studied in our future work.

SIS buildup after a strong shear

structures which have survived the 2000 s -1 preshear. These small residual micellar structures may then con- tribute to a faster SIS buildup upon reduction to low shear rate. The re-building process after start of the second flow phase is then expected to depend on the strength of the preshear. Indeed, Fig. 9 shows the initial viscosity and N1 (measured at 100 s -1) immediately after preshear at different shear rates. Both quantities decrease with increasing preshear rate, suggesting again that the higher the preshear rate, the smaller or fewer SIS will exist at the

1500.0 0.10

An issue of practical importance is the re-building of the SIS after it has been partially or completely "destroyed". This process can be simulated by applying an initial high

o 1000.0 shear rate to eliminate or reduce the SIS, followed by a

( D

lower shear rate of interest. Figure 8 shows such an example. The sample is first sheared at 2000 s -~ for 50 s. At

v

this high shear rate, both the viscosity and N 1 are reduced to a very low level, indicating that no large SIS ex- z ~ 5o0.0 ists. The shear is then reduced abruptly to a lower .~ 100s -~. Shown in Fig. 8 is the time evolution of the viscosity and N1 in response to the low shear flow, which reflects the SIS re-building process. Note that N1 is zero 0.0 at the start of the second flow, again suggesting that few or no large micelles or micellar structures exist at this point. In this case of initial high shear, however, no induction period for both viscosity and N~ is observed in contrast to flow startup from equilibrium, and the plateau times are also significantly shorter. The lack of an induction time suggests that there exist some smaller micellar structures at the beginning of the second flow phase,

-1 100 s

osity

0

@ . . . . . . . . . . . . .

* ' ' ' I . . . . I ' ' ' ' I . . . . I . . . . I . . . .

0.08

0.06 r / /

0 r ~

0.04 t~

o 0.02

v

0.00 500 1000 1500 2000 2500 3000

P reshea r Rate ( I / s )

Fig. 9 Initial viscosity and first normal stress difference measured at a shear rate of 100 s -~ immediately after preshear vs the preshear rate. [5/5 mM TTAA/NaSal solution. Coni-cylinder CC77. T= 22.7_+0.2 °C]

3000.0 , 0.20 I00.0

'\ "'~'..4"

0.15

o

0.10

O

0.05

0.00 250

2500.0

2000.0 0

1500.0

,~ 1000.0 Z

500.0

-1 100 s

gl

0 50

/:..' '-., // ',,. Viscosity

100 150 200

Shear Time (s)

0.0

Fig. 8 Time evolution of shear stress and first normal stress difference at a shear rate of 100s -1 immediately after a preshear of 2000 s l has been applied for 50 s. [5/5 mM TTAA/NaSal solution. Coni-cylinder CC77. T= 22.7+0.2°C1

.--. 80.0

60.0

40.0

20.0

0.0

- 1 I00 s

o//"

N t ° ~ v

gisco ~ s i ~ ~

v

. . . . I . . . . I . . . . I . . . . I . . . . I . . . .

500 i000 1500 2000 2500 3000

P r e s h e a r Rate ( l / s )

Fig. 10 SIS re-building time under a shear rate of 100s -1 for viscosity and first normal stress difference after preshear vs the preshear rate. [5/5mM TTAA/NaSal solution. Coni-cylinder CC77. T= 22.7_+0.2°C]

Y. H u and E.F. Ma t thys 457 Charac te r iza t ion o f micel lar s t ructure dynamics for a drag-reducing sur fac tan t solut ion

start of the second phase. As expected, the SIS re-formation process takes more time overall at increasing preshear rate, as shown in Fig. 10 for viscosity and N~.

Relaxation of SIS after cessation of flow

Figure 11 shows the decay of first normal stress difference after the abrupt cessation of a shear rate of 100 s -~ applied for 200 s. The decay of N~ likely corresponds to the disassembly or reorganization of the SIS. A double exponential function N 1 = A e - t / r ' + B e t / h fits the decay curve well as seen in Fig. 11. Curve fitting gave us two relaxation times: T~ = 6 s and r2 = 36 s. Figure 12 shows that the slower decay rate of SIS as quantified by the second relaxation time r2 for NI decreases with increasing applied shear rate. This might be because the shear-induced structures are smaller at higher shear rates, perhaps as the result of a balance between formation and destruc- tion processes. Indeed, both the plateau viscosity and first normal stress coefficient decrease with increasing shear rate as shown in Figs. 6 and 7. The decrease in viscosity in the shear-thickened region has also been observed for many other surfactant solutions (Wunderlich and Brunn, 1989; Rehage et al., 1986; Hu et al., 1993a, b) and appears to be of some generality.

Effects of flow geometry and tool size

The increase of viscosity and first normal stress difference under a constant shear occurred under all the flow

1 0 0 0 0 . 0

1000.0

09 100.0

z 10.0

1.0

• N t m e a s u r e d - - N t f i t t e d

. . . . I . . . . I . . . .

~00 250 300 350

T i m e ( s )

Fig. 11 First n o r m a l stress difference re laxat ion u p o n cessa t ion o f a cons tan t shear o f 100 s -1 appl ied for 200 s. The solid line is a double exponent ia l fit. [5/5 m M T T A A / N a S a l solut ion. Coni- cylinder CC20 . T = 21 .6+0 .4 °C]

100 .0

0

¢5

N

10 .0

1.0 . . . . . . . . I . . . . . . . . I . . . . . . . .

100 1000 1 0 0 0 0


Fig. 12 Second relaxat ion t ime for N 1 after flow cessa t ion as a func t ion o f shear rate. (The N 1 was allowed to reach its p la teau value in all cases before the flow was interrupted.) [5/5 m M T T A A / N a S a l solut ion. Coni-cyl inder CC20. T = 21.6_+0.4°C]

geometries we tried, including coni-cylinder, concentric cylinder, cone and plate, and parallel plates. For example, Fig. 13 shows the time evolution of the viscosity at 50 s -~ measured in the DSR controlled-stress rheometer with a concentric cylinder geometry (the fluctuations in the beginning are because the constant shear rate is achieved by software, which requires a long stabilization time for low viscosity fluids in this device.)

In most cases, the qualitative features of the time evolution of viscosity and N~ measured with these

0.5 -T r 100

5~

O

C3 5~

0 .4

0 .3

0 .2

0.1

S h e a r R a t e

o.o - F ~ - ~ - ~ o 0 100 200 300 400 500 600


80 5 O

6 0

~o

40 ~-~

.7. o ]

20

Fig. 13 T ime evolut ion o f viscosi ty u p o n apply ing a " cons t an t " shear flow of 50 s -~. [5/5 m M T T A A / N a S a l solut ion. D SR with concentr ic cylinder f ixture CC 44. T = 22.5_+ 0.2 °C]


geometries are similar to those measured with others (e.g., Fig. 1), i.e., growth to either regularly- or randomly-fluc- tuating plateaus after an induction time. The characteristic times and the final theological properties, however, may strongly depend on the flow cell geometry or size as discussed below.

Induction and plateau times

Figure 14 shows the time evolution of N 1 measured with two different cone and plate fixtures. Evidently, both the induction and plateau times measured with the fixture with a 25 mm diameter and 0.1 radian cone angle are shorter than those obtained with the fixture with a 50 mm diameter and 0.04 radian cone angle.

The geometry effect was further studied with the parallel plate geometry by varying the gap between plates. Figure 15 shows the induction and plateau times for N~ as a function of gap distance. We see that both induction and plateau times decrease with increasing gap. It should be pointed out that, even though the shear rate in a parallel plate geometry is not constant but increase linear- ly with the distance from the center, the shear rate variation with radial direction is kept the same regardless of the gap (with proper choice of velocity). Therefore, the non-uniformity of the shear rate in a parallel plate geometry should not have a significant effect on the SIS buildup times. Figure 16 shows a similar dependence of the viscosity induction and plateau times on the gap. The effect is rather large, and the strong dependence of the SIS buildup time on flow geometry may well be responsi-

ble for the discrepancies in the SIS buildup times measured with various fixtures in other studies.

Plateau viscosity

Figure 17 shows both the initial and plateau viscosities measured with different geometries and various gaps. Most data are averages of two or more measurements. It is important to note that the initial viscosity is about

100.0

1000.0

2500 .0

- i 1 0 0 s P P 5 0

Q

N i P l a t e a u t i m e

N i I n d u c t i o n t i m e

10.0 . . . . i . . . . i . . . . , . . . .

0.0 0.5 1.0 1.5 2.0

G a p ( m m )

Fig. 15 N 1 induction and plateau times measured at a shear rate of 1 0 0 s ~ vs gap for parallel plate fixtures PP50. [ 5 / 5 m M TTAA/NaSa l solution. T = 22.8 + 1 °C]

2000 .0

- 1 100 s ~"

p 1500.0

1000.0

500 .0

0.0

- 5 0 0 . 0 I . . . . [ . . . . I

50 100 150


200

Fig. 14 Time evolution of first normal stress difference upon applying a constant shear flow of 100 s - j measured with two different cone and plate fixtures (CP50 and CP25). [ 5 / 5 m M TTAA/NaSa l solution. T = 22.7+_0.6 °C]

1000.0

100.0

- 1 1 0 0 s P P 5 0

t e a u t i m e

V i s c I n d u c t i o n t i m e

10.0 . . . . i . . . . i . . . . i . . . .

0.0 0.5 1.0 1.5 2.0

G a p ( m m )

Fig. 16 Viscosity induction and plateau times measured at a shear rate of 100s -1 vs gap for parallel plate fixtures PP50. [5/5 mM TTAA/NaSa l solution. T = 22.8_+ 1 °C]

Y. Hu and E. E Mat thys 459 Charac te r i za t ion of mice l la r s t ructure dynamics for a drag-reducing sur fac tan t so lu t ion

0

~ 9

0.5

0 .4

0 .3

0.2

0.1

0.0

-1 100 s

o In i t ia l . P a r a l l e l p l a t e • P l a t eau , P a r a l l e l p l a t e

In i t i a l . C o - c y l i n d e r • P l a t eau , C o - c y l i n d e r

.......... ii ............ i

• i

a . o ............... ~ " N ,~''-'n~x .............

. . . . I . . . . [ . . . . I . . . .

0.0 0 .5 1.0 1.5 2.0

G a p ( m m )

Fig. 17 Initial and plateau viscosities measured at a shear flow of 100s -~ with various flow cell geometries and sizes. [5/5mM TTAA/NaSal solution. T = 22.8 + 1 °C]

4.5 cP regardless of the flow geometry or gap used. How- ever, for both parallel plate and coni-cylinder, the plateau viscosity increases with increasing gap. The viscosity appears to become constant when the gap of the parallel plate reaches about 1.0 mm. When the gap is larger than 1.5 mm, it becomes very difficult te confine the solution between the plates and no reliable data could be collected. Large variations in measured plateau viscosity can also be seen depending on the size of the cone-and-plate tool. For example, the measured viscosity obtained with the CP 50 tool was 15.5 cP at 100s -1 but 25 cP when measured with a CP25 tool. Wunderlich et al. (1989) have reported a similar effect of the gap on the shear viscosity for a concentric cylinder geometry and have suggested that the effect is not due to slip at the walls.

The dependence of the first normal stress difference on the gap cannot be readily quantified because the vertical thrust force in a parallel plate geometry results from the difference between the first and second normal stress differences.

The decrease in SIS buildup time with increasing gap is not likely due to slip on the wall of the tools. Indeed, velocity slip would decrease the effective shear rate, and this effect might be more significant at smaller gaps, which would suggest a longer buildup time and a smaller plateau viscosity. Figure 17, however, shows that the viscosity during the induction time is the same for all gaps, indicating that we have the same effective shear rate regardless of the flow geometry and gap. The possibility that the wall slip is significant is therefore not very likely. The effect of the geometry seen here might then be a true dimensional issue, with the SIS formation and size being

affected by - or adjusting to the physical dimensions of the liquid layer. This is an interesting phenomenon which may provide - after further study - some additional information on the fundamental nature of the SIS.

The dependence of the SIS buildup time, the plateau viscosity, and possibly the plateau first normal stress difference on the gap brings out an important point: that caution must be exercised as to the size of the flow cell when comparing the values obtained with different flow fixtures and when trying to extrapolate results to other flow geometries such as pipes, for example.

Summary and conclusions

We have undertaken a rheological study of a TTAA/ NaSal surfactant solution that is used for drag reduction studies and which exhibits self-assembling structures. For the surfactant solution studied, we observed simultaneous increases with time of the viscosity and first normal stress difference when subjected to a constant shear rate. The induction time for both the viscosity and first normal stress difference is approximately inversely proportional to the shear rate and is independent of the flow direction. These characteristics of the SIS buildup, when added to similar observations for other surfactant systems suggest that the kinetic nature of the process may be of wide generality.

The dynamics of the SIS rebuilding process after an intense preshear have also been quantified. As expected, the rebuilding time increases with increasing preshear. The relatively long duration (tens of seconds) of this process confirms the potential feasibility of drag reduction suppression by supercritical shear stress if there is a need to maximize locally the heat transfer in industrial applications. On the other hand, this long reformation time is counterproductive as far as the drag reduction itself, and a compromise needs to be reached. The type of studies conducted here will give us the tools to investigate or de- velop fluids that will enable us to reach such a compromise.

Relaxation of the SIS after cessation of shear has also been quantified and shows a double exponential decay process. The relaxation time decreases with increasing shear rate for the higher shear rates covered here.

It was also observed that the SIS formation process depends greatly on the flow cell geometry. For a parallel plate geometry, for example, both the induction and plateau times for N~ and the viscosity decrease with increasing gaps, whereas the plateau viscosity increases. The dependence of the transient flow behavior on the geometry calls for great caution when one compares results obtained with different flow fixtures and when one attempts to extrapolate results to other flow geometries.


Acknowledgments The authors gratefully acknowledge the finan- cial support of the US National Science Foundation through fund- ing of the UCSB MRL (Award No. DMR-9123048) and the col- laboration opportunities extended by Prof. T. Cheetham (UCSB);

the donation of samples by AKZO chemicals; the access to equip- ment provided by Prof. G. Leal (UCSB) and Prof. E Lange (UCSB); and the kind assistance by J. Yanez and other researchers in the rheology laboratory.

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Documents

Characterization of micellar structure dynamics for a drag-reducing surfactant solution under shear: normal stress studies and flow geometry effects