RESULTADOS DE LA ESPECTROMETRÍA
6.1.2. Metodología y presentación de datos
diameter cannot be observed with the lowest contraction ratio but the lower slip velocity could be attributed to the different Xanthan solution used. This is in line with the Mooney assumption that the slip velocity depends only on the wall stress and thus could be seen as justification of the Mooney assumption. In support of this interpretation, figure 5 . 19 shows an agreement of the slip velocities obtained for
ij
= 1 5 .4( 1 ) ,ij
= 8 and the capillary rheometer data. The NMR data was collected on the same day using the same solution but two different capillaries. In contrast data is in disagreement using the same tube but different reservoirs(ij
= 8,ij
= 4). According to Mooney one would expect similar wall stresses forthe different reservoir contractions and thus comparable slip velocities. It is noted that one solution was used to obtain the larger contraction data and another two solutions, prepared weeks apart, were used for the smaller contractions. In addi tion, another data set collected at the largest reservoir contraction
( ij
= 15.4(2)) does not agree with any previous data. Thus in terms of the Mooney theory the interpretation of our results remains unclear.The accuracy of the determination of the slip velocity must be highlighted. As other authors have suggested, the thickness of the depletion layer is on the order of 300 nm[3 1]. Some doubt as to the magnitude of the slip velocity arises since the imaging resolution used in this work was 30 J..Lm. Thus the pixel of the velocity profile closest to the edge of the wall is determined by the signal obtained from the depletion layer, bulk fluid and the lack of signal from the glass capillary. The data processing technique chooses the highest velocity signal within the pixel. Thus if any bulk fluid signal is present within the pixel, a higher slip velocity will be obtained. Noise from signal-free regions will also add further complication to the velocity profile. Whether these anomalies are the cause for the varying slip
CHAPTER 5. SLIP BEHAVIOR OF XANTHAN G UM SOL UTIONS 88 velocities found in figure 5 . 1 9 is doubtful. Such errors would manifest themselves as random occurences and not systematic.
G P C data suggest that the slip phenomena may depend upon the majority of the polymer being at a high molecular mass since peristaltic pumping of the solu tions resulted in slip being abolished. This high mass dependence is supported by Aldrich and Kelsan Xanthan, which did not exhibit slip, having a larger percent age of their mass in the low molecular mass regime. The Xanthan polymers which did not exhibit slip had a slightly lower power law index of 0.36 but revealed a markedly different dynamic response when compared to the Unam polymer. Both the storage and loss modulus was half of the slipping Xanthan. The phase difference is the same for all Xanthan polymers at around 20°.
Another possible explanation in determining slip, associated with molecular properties, could be flow-induced molecular alignment . This process could be caused by extensional flow and elastic effects at the entrance contraction. As the extensional strain rates are larger in the center of the pipe, one would expect a high degree of molecular order in the bulk of the fluid. Whereas closer to the tube walls a more random molecular orientation might be expected. As a consequence the shear viscosity might be comparatively low near the wall surface leading to a high shear rate-slip regime.
To investigate whether molecular orientation effects are dominant in our mea surements, it is helpful to calculate the magnitude of the Peclet number, Err ' E
is the local extensional strain rate and rr is molecular rotational correlation time for a Xanthan rigid rod. Where extensional strain rates exceed the time for the rod to re-orientate itself, ie. Err � 1 , molecular alignment might be expected to occur. Estimates of E for the largest contraction ratio and larger flow rates are of the order of 10 s- 1 . The molecular rotational correlation time can be estimated with the knowledge of the translational diffusion coefficient, Ds, for a known rod length, L, at infinite dilution[38] . This result leads to:
L2
r "-' --
r
- 18Ds(5. 1 ) The length and diffusion coefficient of the Xanthan solution used here can be calculated by the data of Coviello et al[94] . 3 X 106 da Xanthan in water gives
a correlation time of around 0 . 1 s. Thus the Peclet number would appear to approach, if not exceed, unity for the flow rates where slip is observed. Further, we note as E increases, a process which occurs as the contraction ratio is increased, the degree of slip increases. Furthermore, as previous data suggest slip is sensitive to molecular size, a fact not surprising given that rr "-' [38] .
CHAPTER 5. SLIP BEHAVIOR OF XANTHAN G UM SOL UTIONS 89 ulative. The exact nature of slip is very dependent on the nature of sample prepa ration, even when the sample has been obtained from the same batch. Further experiments were tried investigating the contraction ratio hypothesis by construct ing a 1 .0 mm capillary insert. Not only did the arrangement give a larger con traction ratio but larger
15
ratios were also possible. However, the next solution of Xanthan did not slip and had dynamic rheometric properties similar to that of the Xanthan destroyed by peristaltic pumping.Although the relationship of slip velocity and wall stress is similar
(
Fig. 5 . 1 9)
for the two capillary techniques, a substantial variability in the imaging data is unrelated to contraction ratio. Although these differences cannot be explained satisfactorily, possible causes such as sample preparation, temperature, rheometer calibration and imaging calibration are mentioned. Care was taken to standardise the samples between the collaborative groups, nonetheless it is possible that the preparations were sufficiently different to not warrant a comparison. Estimates of the wall stress for the imaging experiments were calculated using earlier rheometric data and not the data included in figure 5.19. Previous data supports the inclusion of Xanthan as being described as a power law fluid, however it may be possible the absolute viscosity values used were not those of the solutions in figure 5.19. Although the experiments were completed at different temperatures; 25°C for the Mexican group and 22°C for the New Zealand group, there is evidence that temperature effects, if any, are small[95] .The appearance of slip in the cylindrical-Couette images is of some concern for the viscometric data. Cohen and Metzner[96] suggest that slip in dilute solutions is a product of an inhomogeneous stress field . In the usual Couette rheometric devices the sample gap is small, resulting in a small stress gradient. However this is not the case with the Couette imaging rheometer we have designed, perhaps a reason why slip is so apparent in this system.
It has been suggested by Walters[97] that inconsistent results are obtained for a capillary geometry if the contraction ratio is less than 18. In contrast consistent repeatable measurements have been found below this value.
5 . 5 Conclusions
Dilute solutions of Xanthan gum can exhibit slip which appears to be molecular weight dependent. The fractional slip velocity appears dependent upon the con traction ratio at the capillary entrance and is independent of
15
values in excess of 16. The magnitude of the capillary slip velocities are in line with the measure ments inferred from a Mooney analysis of capillary rheometric data. Slip was alsoCHAPTER 5. SLIP BEHAVIOR OF XANTHAN G UM SOL UTIONS 90
observed in a cylindrical-Couette cell. We suggest a possible mechanism for slip may be the effect of molecular alignment caused by the extensional strain at the entrance to the capillary, but note sample preparation and other effects can also