Shear rate cessation

Fig. 2.7. Drop off of doubled extinction angle 2"/ during stress-relaxation after cessation of steady shear flow according to Wales (59). Measurements on the melt of a high-density polyethylene (Marlex 6002) at a measurement temperature of 147° C. Shear rate of the steady shear flow q = 0.06 sec-1...

Another peculiar property of LCPs is shown in Fig. 15.47, where the transient behaviour of the shear stress after start up of steady shear flow is shown for Vectra A900 at 290 °C at two shear rates. We will come back to this behaviour in Chap. 16 for lyotropic systems where this behaviour is quite common and in contradistinction to the transient behaviour of conventional polymers, as presented in Fig. 15.9. This damped oscillatory behaviour is also found for simple rheological models as the Jeffreys model (Te Nijenhuis 2005) and according to Burghardt and Fuller, it is explicable by the classic Leslie-Ericksen theory for the flow of liquid crystals, which tumble, rather than align, in shear flow. Moreover, it is extra complicated due to the interaction between the tumbling of the molecules and the evolving defect density (polynomial structure) of the LCP, which become finer, at start up, or coarser, after cessation of flow. 

For a viscosity ratio M of order unity or less, r is the relaxation time of the droplet shape and of the resulting viscoelastic stress in the dispersion. Thus, for rjs I cP, F 10 dyn/cm, a (xm, we obtain t 10 sec, and the stress in the emulsion relaxes almost instantly after cessation of flow. However, when the fluid medium is more viscous and the droplets are bigger, say, rjg 100 P, a 10 jxm, with the same F, we obtain T 0.01 sec. Although this latter value of r corresponds to rather fast relaxation, it can produce appreciable normal stress differences at high shear rates thus (Choi and Schowalter 1975)... 

Figure 11.16 Stripe and band patterns produced by shearing PBG solutions between glass plates under crossed polaroids in a microscope. The field of view is 890 m, and the flow direction is horizontal. The two stripe patterns form at steady state the more irregular of the two (upper left) is produced by roll cells at a low shear rate (around 0.07 sec ), while the regular stripe pattern (lower left) occurs at high shear rate, 25 sec. The perpendicular band patterns are transients that occur either during start-up of shearing (upper right), or after cessation of shearing (lower right). The detailed conditions under which these patterns are formed are discussed by Larson (1994).

A single-relaxation-time response is also observed for this fluid in other flow histories, including start-up and cessation of steady shearing, if the shear rate y is low enough. At higher shear rates, the viscoelastic response is more complex. Figure 12-11 shows the time-dependence of the shear viscosity r] after start-up of steady shearing for a solution... 

Two liquid crystalline polybenzylglutamate solutions, adjusted to the same Newtonian viscosity, have been investigated Theologically. The steady state shear properties and the transient behaviour are measured. For the same kind of polymer, the dynamic moduli upon cessation of flow can either increase or decrease with time. This change in dynamic moduli shows a similar dependency on shear rate as the final portion of the stress relaxation but no absolute correlation exists between them. By comparing the transient stress during a stepwise increase in shear rate with that during flow reversal the flow—induced anisotropy of the material is studied. 

The relaxation behavior, or the transient behavior of cellulosic liquid crystalline solutions upon the cessation of steady flow, is unique for LCPs. There are two kinds of relaxation. The bulk stresses relax quickly while the structures relax over a much longer time. Mewis and Moldenaers suggested that two levels of structures exist.Stress relaxation reflects fast relaxation at the molecule level and is independent of the previous shear rate. Structure relaxation reflects the gradual change of the textures. This slow process is unique in... 

Figure 3.73. A transient rheological test showing (a) the start up of an imposed strain rate and the subsequent measurement of the stress build-up, and (b) the cessation of an imposed shear rate and the subsequent stress decay.

In stress relaxation after cessation of steady shear flow, the elastic dumbbells give no dependence of the relaxation process on the steady-state shear rate, but the rigid dumbbells do. In addition the elastic dumbbells show the shear and normal stresses relaxing with exactly the same... 

Figure 31.4 Stress relaxation curves after cessation of steady shear flow for the PET/PEN-clay systems (shear rate is 10 s ). Source Reproduced with permission from Calderas F, Sanchez-Solis A, Maciel A, Manero O. Macromol Symp 2009 283 354 [83], Copyright 2009 Wiley-VCH Verlag GmbH Co. KGaA.

Ig) were measured simultaneously as functions of time, after cessation of steady flow at various shear rates (y = 2 x 10 1.1 X 1q2 s ) at 25°C. Here, and Ig are fractional trans-... 

As an example, results obtained for the sample L2 after cessation of steady flow at various rates are shown in Fig. 4. The ordinate of this figure is the relative retardation F/Tq, where Fq and F are retardations during steady flow and after cessation of the flow, respectively. As is evident from the figure, the higher the applied shear rate, the earlier the retardation decreases. 

Flow curves for L2, M2 and H2 are shown logarithmically mically in Fig. 13. The shear-rate or shear-stress region where the plots are represented by straight lines having a slope of 1 is the so called Newtonian region (Region II). The Regions of the steady flow behavior may be sensitive to the structural re-formation process after the cessation of the steady flow as mentioned above. 

The shearing time prior to cessation must be longer than a certain time which depends on the shear rate. However the band formation does not occur at a particular value of total shear, since a weak dependence on (dy/dt) remains [56], i.e. 

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