Fiber spinning of very dilute solutions of polyacrylamide in water

Journal of Non-Newtonian Fluid Mechanics, 30 (1988) 267-283 Elsevier Science Publishers B.V., Amsterdam - Printed in The Netherlands

267

FIBER SPINNING OF VERY DILUTE SOLUTIONS OF POLYACRYLAMIDE IN WATER

R.C. CHAN and R.K. GUPTA, Department of Chemical Engineering, State University of New York at Buffalo, Buffalo, New York 14260, (U.S.A.) and T. SRIDHAR Department

of Chemical Engineering, Monash University, CIayton, Victoria 3168 (Australia)

(Received November 23,1987)

Summary The extensional viscometer developed earlier by the authors was refined and used to extend very dilute (50 ppm) solutions of polyacrylamide in distilled water. A slender liquid filament was stretched by the use of a suction device, and this resulted in the spinning of the fiber. By varying the volumetric flow rate and the filament length, stretch rates in the 100-1000 s-l range were easily obtained. The corresponding tensile stresses were very large, and these gave apparent extensional viscosities of the order of 200 P (20 Pa s). In contrast to this, the material functions in shear were difficult to measure, except for the shear viscosity which showed pronounced shear thinning. It was found that all the measurements, in shear as well as extension, could be explained based on the four constant Johnson-Segalman constitutive equation.

1. Introduction Extremely dilute solutions of high molecular weight polymers such as polyethyleneoxide and polyacrylamide in water at concentrations as low as a few ppm show a hydrodynamic behavior that is quite different from that of the solvent. In particular, high molecular weight additives are responsible for the extraordinarily high resistance that polymer solutions offer to an extensional deformation. This resistance is exploited for the purpose of turbulent drag reduction [l], and it has also been shown to be related to the increase in the load-bearing capacity of polymeric lubricants [2]. Small amounts of high 0377-0257/88/$03.50

0 1988 Elsevier Science Publishers B.V.

268 molecular weight polymer are also added to aviation fuel to reduce the tendency of kerosene to break up into small droplets in the event of a crash [3]. In addition, dilute solutions of water-soluble polymers are used extensively in enhanced oil recovery operations as mobility control agents [4]. An experimental study of the extensional flow properties of dilute aqueous polymer solutions is clearly relevant to some of the applications cited above. It is also relevant for the purpose of testing rheological models of polymeric behavior. It has been postulated, for example, that, as a result of flow, flexible macromolecules undergo a transition from an equilibrium coiled position to a fully extended rod-like configuration [5]; this happens most easily during elongational flow. While this transition has been inferred from flow birefringence measurements in a four roll mill [6] and also from pressure-drop flow-rate measurements in porous media [7], there has been no validation based on pointwise stress measurements in a deforming fluid. An important point concerning rheological constitutive equations is that most of these have been formulated with the assumption of infinite dilution [8]. Thus, polymer-polymer interactions are neglected, and data need to be obtained in the unentangled regime. Under these conditions, even for stretching flows, fluid forces are relatively small and difficult to measure if water is used as the solvent. Moore and Pearson [9] and Baid and Metzner [lo] reported fiber spinning data on polyacrylamide solutions but used mixtures of glycerine and water as the solvent. Furthermore, with their apparatus, these authors could get data at low stretch rates only. To make measurements at stretch rates much in excess of 10 s-l, one has to use techniques like the triple jet [ll] or flow through converging channels [12]. Such techniques, however, provide single point measurements, only. The present research was undertaken in order to obtain fundamental extensional flow data on very dilute aqueous polymer solutions at high stretch rates. To this end, a polymer filament was stretched with the help of a suction device [13], and stress measurements were made using the extensional viscometer developed recently by Sridhar and Gupta [14]. The fluid used was a 50 ppm solution of polyacrylamide (Separan AP 273) in distilled water. The main intent of the work was to examine the utility of different rheological constitutive equations in extensional flow. It therefore represents a continuation of our earlier work on Newtonian liquids [14], highly elastic constant-viscosity liquids [15,16] and weakly elastic constant-viscosity liquids

1171. 2. Apparatus and procedure A schematic diagram this has been described

of the extensional viscometer is shown in Fig. 1, and previously [14,16]. The flow rate in the system was

269 I

II I

k-F

II II+- G

A B

Fluid Reservoir Pump

E F

Filament

C D

Viscometer Baffle

G

Lower Capillary

H

Manometer

Fig. 1. Schematic

diagram

of the extensional

Upper Capillary

viscometer.

controlled with the help of a four channel cartridge pump (Ismatec Model 7610-20) obtained from the Cole-Parmer Company. According to the manufacturer, the speed control was + 1% of the setting for the entire flow rate range from 0.02 to 154 cc/mm. The liquid flowed from the feed tank into the viscometer and out through the upper capillary which has an inner diameter of 0.119 cm. The capillary dimensions were determined by trial and error. If the diameter was too small, the liquid tended to drip. If the diameter was too large, it was difficult to stretch the liquid stream. To guard against mechanical degradation, the polymer solution was not recycled. Constant temperature was maintained by circulating water through a jacket built around the viscometer. Under steady state conditions the air pressure in the viscometer was atmospheric. The liquid filament emerging from the upper capillary was stretched by utilizing a vacuum to suck the liquid into a capillary of still smaller diameter. The vacuum line was equipped with a needle valve, a pressure gauge, a drying tube and an overflow trap to ensure trouble-free operation. Special care was taken to center the two capillaries below each other and also to keep the filament vertical at all times. The length of the filament could be varied with ease, and a photograph of the stretching set-up is shown in Fig. 2. The extension resulted in a tensile stress at the exit of the upper capillary. As a result of this stress, the air pressure in the viscometer was found to decrease when a new steady state was re-established (within a minute or so) at the original value of the volumetric flow rate. This lowering in pressure was measured using a bent-tube water manometer having one

270

Fig. 2. Photograph

showing

the fluid stretching

device.

arm inclined at 20 o to the horizontal. It can be shown [14] that the decrease in pressure exactly equals the average tensile stress at the exit of the upper capillary. It should be noted that the viscometer air pressure changes because the level of liquid in the viscometer falls; however, the change in liquid level is imperceptible. This is because the change in pressure is given by 1AP 1 = P,,,Ah/(

h + Ah),

0)

where we have used the ideal gas law and where h is the distance measured from the top of the viscometer to the liquid surface. Thus, a 0.1% change in h gives rise to a change in pressure which is equivalent to a 1 cm column of water.

271

Fig. 3. Sketch of the fiber diameter profile before stretching (broken line) and after stretching (solid line).

An implicit assumption in our earlier work [14] was that the fluid flow patterns in the viscometer did not change as stretching commenced. To confirm this view, flow visualization experiments were carried out using tracer particles. It was found that, even in the absence of filament stretching, the flow patterns were somewhat unsteady, and there appeared to be continual mixing of liquid in the viscometer. It was then decided to install in the viscometer, just below the liquid surface, a thin plastic disk having small holes drilled through it. This helped to stabilize the streamlines, and it was found that the flow patterns also did not change on commencement of filament stretching. Note that a tapered entry was used for the flow of the polymer solution from the viscometer into the upper capillary. The diameter of the deforming filament was measured by taking photographs using a camera equipped with a macro-zoom lens and also by casting a shadow of the liquid thread on a wall with the help of a lens and light source arrangement. In the present case, such a procedure gave a magnification of about eighteen. A sketch of the diameter profile before and after fluid stretching is shown in Fig. 3. An interesting feature of this figure is that the filament does not completely fill the mouth of the lower capillary, and a sheath of air is drawn in along with the liquid. The velocity profiles were computed from the measured diameter profiles using a mass balance and assuming a uniform velocity across each cross section. The stretch rates were obtained subsequently by numerical differentiation. Additional details are available in the dissertation [18].

272 3. Solution preparation and characterization The polymer used in this work was Separan AP 273, an anionic polyacrylamide manufactured by the Dow Chemical Company. The polymer had a weight average molecular weight of 6 X 106, and it was used at a concentration of 50 ppm by weight in distilled water. A stock solution of 0.25% by weight was first prepared in a 250 cc conical flask according to the manufacturer’s guidelines [19]. This was diluted to the desired concentration one day before use and allowed to reach equilibrium overnight by slow stirring with a magnetic stirrer. The shear viscosity was measured on a cone-and-plate Rheometrics model 705 mechanical spectrometer fitted with a fluid transducer; shear rates ranged between 2 and 200 s-l and pronounced shear-thinning was observed. The results are shown in Fig. 4. These were double-checked using a Contraves Model LS-30 low-shear viscometer. The two sets of results agreed with each other in the range of overlap of the shear rates. However, the Contraves viscosity did not seem to reach a plateau even at shear rates as low as 0.016 s-‘; this behavior appears to have been observed by other

100

o

is

0 tI

I

10-z

100

103

102

101 Shear

Rate.

frequency

(S-1)

Fig. 4. Shear viscosity (0, o) versus shear rate and dynamic viscosity (W, 0) versus circular frequency for a 50 ppm separan AP 273 solution in distilled water. Data from the Contraves viscometer are represented using circles.

273 240

200

n

A

U

V

160

I,

0

I

I

I

0.002

0.004

0.006

I 0.008

0.01

Concentration g/d1

Fig. 5. Intrinsic viscosity determination by extrapolation of the reduced specific viscosity (Cl) and the inherent viscosity (0) to zero concentration.

researchers as well [20]. Also shown in Fig. 4 are data for the dynamic viscosity as a function of the frequency obtained using both the Mechanical Spectrometer and the Contraves viscometer. At this concentration, the first normal stress difference in shear was too low to be determined with any accuracy with the cone-and-plate instrument; this was also found to be the case by Argumendo et al. [21]. In order to determine the presence or absence of chain entanglements, the intrinsic viscosity, [q], of the Separan polymer was measured using a commercial glass capillary viscometer. The intrinsic viscosity was obtained by extrapolating the reduced specific viscosity to zero concentration. This is shown in Fig. 5 where [q] is found to equal 180 dl/g. The lower limit of the critical polymer concentration C * at which chains begin to overlap is then given as [20] C*

hl = 1,

(2)

so that C* = 56 ppm. While eqn. (2) may not hold exactly due to the ionic nature of the polymer, the results to indicate that a 50 ppm solution can be expected to be reasonably free of polymer chain entanglements.

274 4. Fiber spinning results and data analysis A total of sixteen different runs were carried out at room temperature (23-24OC). The volumetric flow rate was varied over a narrow range from 0.24 to 0.31 cc/s. At each flow rate, the filament length was changed from 1.1 to 2.1 cm, and several different draw ratios were imposed for each filament length. Details concerning four of these runs are listed in Table 1. The corresponding diameter, velocity and stretch rate profiles are shown in Figs. 6-8. Note that the diameter profiles are very dramatically influenced by the addition of only a minute amount of polymer to the pure solvent. For the Newtonian solvent alone, at the same draw ratio, the diameter changes only imperceptibly along most of the filament length. Then, when the fluid is very close to the lower capillary, the diameter attenuates very rapidly. As a consequence, in the absence of polymer, the velocity profile is virtually a horizontal straight line for about 90% of the spin line length; thereafter, the velocity increases rapidly to the final value. Thus, most of the stretching occurs in a very small region adjacent to the entrance of the lower capillary. By contrast, the 50 ppm polymer solution stretches all along the fiber length with stretch rates ranging from 100 s-l to more than 1000 s-l. These stretch rates are very significantly higher than those obtained in other laboratory fiber spinning experiments involving polymer solutions. As mentioned previously, the fluid stress at the exit of the upper capillary (X = 0) was measured as a decrease in the viscometer air pressure. The viscoelastic force F(1) at any other axial position, x1, along the fiber was computed by means of an integral momentum balance: / cs

pV(V.dA)

= CF.

On neglecting air drag, the above equation, when applied to the dotted control volume in Fig. 9, yields F(1) = P(0) - F( ST) - F(G)

J V*dA-

+

(4)

4

TABLE 1 Details of selected fiber spinning runs Run No.

A9

All

Al2

Al5

Flow rate (cc/s) Filament Length (cm) A P (cm of water) Measured diameter at x = 0 (cm) Ambient temperature (OC)

0.287 1.1 2.963 0.1278 23

0.31 1.4 2.184 0.1315 24

0.272 1.4 2.54 0.137 23

0.29 2.1 0.752 0.126 24

275 0.14

0.12

-z :

-*

0.08

5 a.8 t ;

AA % A

k 2 Ir

A A

0.04

BO

A

A

Cl

0

0.4

0.8

2.0

1.6

1.2

2.2

Axial Distance, x (cm)

Fig. 6. Diameter profiles for the four fiber spinning runs listed in Table 1. The symbols represent different run numbers: 0 Run A9, o Run All, 0 Run Al2 and A Run A15.

60(

5OC

z -S 0 x .:: : 2 r( .z I:

.

30(

A

4

40(

A

00

.

o*8

200

A

100

0

Fig. 7. Velocity

0.4

profiles

corresponding

0.8

1.2

1.6 2.0 Axial distance (cm)

to the data shown in Fig. 6.

2.2

276 104,

101’ 0.0

I

I

0.4

0.8

I

I

I

1.2

1.6

2.0

Axial

Distance

(cm)

Fig. 8. Stretch rate profiles corresponding to the data shown in Figs. 6 and 7.

where F(0) is the viscoelastic force at x = 0; F( ST) is the surface tension force which equals 2my( R, cos8,- R, cos 0,,); and F(G) is the gravitational force, which equals pgr/zr*(x) dx. It was found that the liquid tended to spread radially on emerging from the upper capillary, so that the fiber diameter at x = 0 exceeded the inner diameter of the upper capillary. To minimize this phenomenon, the wall thickness was reduced by machining the capillary, but the problem still

Fig. 9. Control volume used for the integral linear momentum balance.

277

0.0

0.4

0.8

1.2

1.6

2.0

Axial Distance (cm)

Fig. 10. Stress difference in extension plotted as a function of axial distance spinning runs of Figs. 6-8. The solid lines are model predictions.

for the fiber

remained. Due to this, F(0) was calculated as the measured change in the viscometer air pressure multiplied by the actual filament cross sectional area, while the integral jA0V2 dA was computed based on the actual capillary diameter and a parabolic velocity profile at the exit of the capillary. jA,V2 dA, was, of course, simply V2A,, due to the assumption of a flat velocity profile across any fiber cross-section. Since the polymer concentration was so low, the coefficient of surface tension, y, was assumed to be 70 dyne/cm, (0.07 N/m), the same as that for pure water at 20°C. Since all the forces on the right hand side of eqn. (4) could be calculated from experimentally measured quantities, the force F(l), at any axial position x1, could be computed with ease. The ratio of this force to the cross-sectional area at xi then gave the viscoelastic total stress uil (xi). With a radial force balance, the stress difference uil - u22 within the fluid is given as [lo] (Jll-022=q,+~/R,

(5)

where R is the filament radius. The left hand side of eqn. (5) is plotted as a function of the axial distance in Fig. 10. It is seen that the stress difference shows no tendency to level off. This was true of all the sixteen runs. Before concluding this section, we mention that flow-induced polymer degradation appeared to be occurring after only a single pass of the polymer

278 solution through the viscometer. It was noted that when solution was recycled through the viscometer, the diameter profile was closer to that of pure water than that of the fresh solution. Simultaneously, and more importantly, no pressure drop developed in the viscometer when a solution was stretched the second time around. This points to mechanical degradation of the higher molecular weight fraction of the polymer. The solution viscosity, as measured at moderate shear rates on the Rheometrics Mechanical Spectrometer, did not decrease by more than lo-20%. All this appears to be consistent with the published work of other researchers [22-241. 5. Constitutive

modeling

In our previous work [16] on constant viscosity elastic liquids, we had used the Oldroyd model B to represent the constitutive behavior of the polymer solution. This model predicts a constant viscosity and is obviously unsuitable for aqueous polyacrylamide solutions due to the shear rate dependence of the shear viscosity. A popular model which can account for shear thinning is the one proposed by Phan-Thien and Tanner [25,26]. For a single relaxation time, X, this has the form K7+X[(l-4):

+f:]=2+),

where K=exp

$ [

tr(T) I

and where 7 and 0 are the contravariant and covariant convected derivatives respectively. The parameter 5 is responsible for the shear-thinning nature of the fluid while a non-zero value of the parameter 6 ensures that the steady uniaxial extensional viscosity remains finite for all values of the stretch rate. Also, when c = 0, one obtains the Johnson-Segalman equation [27]. n0 is, of course, the zero shear viscosity. Note that r in eqn. (6) is the contribution of the polymer alone to the extra stress. To this must be added the contribution of the Newtonian solvent, and this results in the introduction of a fifth parameter, the retardation time, to the fluid constitutive equation. This contribution becomes important in a steady laminar shearing flow, especially at high shear rates, and it guarantees that the solution viscosity does not fall below that of the solvent. For the fiber spinning experiments described here, however, the solvent contribution can be neglected in extensional flow. This is because the maximum value of the stretch rate is about lo3 s-l which implies a solvent contribution to the stress of 30 dyne/cm2 (3 Pa). Since the measured

279 values of the stresses are, at the very least, two orders of magnitude greater than this, such a neglect is justified. The numerical values of three of the four parameters appearing in eqn. (6) are obtained from shear data. While q0 is simply the solution zero shear viscosity minus the solvent viscosity, 5 is found from a dynamic viscosity-shear viscosity shift according to 1251.

and the value of A is then fixed by fitting the viscosity-shear the expression:

rate data to

where qS is the solvent viscosity. Finally e is obtained by use of extensional data. If the model is valid, the same set of parameter values will be adequate for explaining all the transient extensional flow data. For fiber spinning, in the absence of a fluid retardation time, the differential equations for the extra-stresses, rii and r22, in the axial and radial directions respectively are [28]

with K=exp

$(rn (

+2T22)

. i

(12)

To solve eqns. (lo-12), ~~~(0) was taken to be zero. This seems to be a reasonable procedure based on previous work [10,16]. Furthermore, since (711 - r22) always equals (uii - uz2), ~~~(0) equals (a,,(O) - ~~~(0)) which is obtained by experiment. One therefore begins integrating the equations describing the stress, starting from the instant that the fluid emerges from the spinneret. The influence of the prior deformation history is taken into account by using the experimentally measured value of the stress as the initial condition. In this regard, note that pre-shear does not significantly influence the extensional stress for aqueous polyacrylamide solutions [29-311. We have assumed that uniaxial extensional flow begins at x = 0. There is obviously some error involved in making this assumption since there will always be a small region of transition in which the shear flow in the capillary

280 changes to extensional flow in the fiber. Since there was no die swell in the present experiments, it was difficult to determine the position at which uniaxial extension flow began. We therefore chose to neglect the presence of the shearing kinematics in the fiber near x = 0. Since the ratio of the fiber length to the diameter of the upper capillary ranged between 10 and 20, the error involved was unlikely to be large, As noted previously, the zero shear viscosity of the polymer solution, and consequently 3j0, was difficult to measure precisely. This, however, did not prove to be a handicap since the terms involving q0 in eqns. (10-11) were negligible in comparison with the other terms. In other words, the predicted values of err and 722 were independent of the value of n,,. By fitting the shear viscosity data shown in Fig. 4 to eqn. (9), it was determined that q, = 0.104 poise, q, = 0.01 poise and AZ,32 - 5) = 0.0055 s2. The solid line in Fig. 4 represents eqn. (9) with this choice of parameter values. The agreement is fair. The use of eqn. (8) did not yield a single value of 5; any one of a range of 5 values gave equally acceptable results. The corresponding value of X was obtained as 0.0055/(<(2 - 6)) . Consequently, eqns. (10-12) were solved for different 5, X pairs for each value of c. By numerically solving eqns. (10-12) using the Runge-Kutta method and utilizing the kinematic data

103 0.0

I

I

0.4

0.8

I 1.2 Axial

1.6

Distance

(cm)

Fig. 11. Effect on the stress difference of varying the Phan-Thien and Tanner model parameter c for Run A12.

281 presented in Figs. 7 and 8, the best parameter values were found to be 5 = 0.3, X = 0.104 s and 6 = 0. The predicted stresses are shown as the solid lines in Fig. 10. Clearly, the fit is very good. This was found to be the case for all sixteen runs. Letting E be zero means that one is using the Johnson-SegaIman equation, and in practical terms means that aqueous polyacrylamide solutions strain harden. In many cases the apparent extensional viscosity increased monotonically with distance away from the spinneret; in other cases it tended to reach a constant value in the neighborhood of 200 poise.The effect of varying e by a very small amount while keeping 5 and X fixed is shown in Fig. 11; the use of any non-zero value of 6 appears to be unacceptable. Phan-Thien et al. [32] have themselves used c = 0 and 5 = 0.4 to represent the rheological behavior of an aqueous polyacrylamide solution. Their solution, however, was very concentrated. Before concluding this section, we wish to emphasize that the fiber spinning experiments reported here are transient ones in which the total strain is not very large. It is difficult to predict whether the Johnson-Segalman equation will portray the large strain extensional flow behavior of aqueous Separan solutions with equal accuracy. The question is particularly relevant, since the use of the Johnson-Segalman equation does not lead to a limiting value of the steady state extensional viscosity. Indeed, if we were willing to neglect shear-thinning, we could have used the upper convected Maxwell model itself (i.e., 5 = 0) for explaining the extensional data presented here; the agreement between theory and experiment would have been as good as that shown in Fig. 10. In other words, additional large-strain extensional data are needed before one can hope to resolve the question of the validity of any constitutive equation for dilute polymer solutions. 6. Concluding Remarks The Sridhar-Gupta extensional viscometer has been used to obtain high stretch rate fiber spinning data for a 50 ppm polyacrylamide solution in water. This is the first time that uniaxial extensional data have been obtained for such dilute aqueous polymer solutions. Very large stresses were found to occur and apparent extensional viscosities as large as 250 P (25 Pa s) were measured. This again demonstrates that Trouton ratios for polymer solutions are significantly larger than those for polymer melts. Preliminary modeling efforts suggest that the Johnson-Segalman equation may be adequate for describing both the shear and transient extensional properties of dilute solutions of polyacrylamide in water.

282 Acknowledgements Professor M.E. Ryan participated in the early stages of this research. Mr. W.J. Smith of the Dow Chemical Company provided the Separan polymer and many technical details. Rakesh Gupta would like to acknowledge a grant from the New York State/United University Professions Professional Development and Quality of Working Life Committee for travel to the International Conference on Extensional Flow in Chamonix, France, to present this work.The continuing collaboration between the authors is supported by the NSF-DST US-Australia cooperative science program. References 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28

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