Start-up of steady shear flow

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. 

Besides the sinusoidal oscillations, transient tests such as stress relaxation, start-up of steady shear flow, and cessation of steady shear flow are also important in the rheological characterization of polymeric liquids. The instrument limitations and features, and their effect on the data obtained in some types of transient tests, are examined in this section. Also, we shall illustrate the use of linear viscoelastic transformation to obtain, for example, stress relaxation data from tests such as start-up of steady shear flow and sinusoidal oscillations. 

FIG. 15.47 Transient behaviour after start up of steady state flow in Vectra A900 at 290 °C at shear rates of 0.1 and 1 s-, based on results of Guskey and Winter (1991). From Cogswell and Wissbrun, 1996. Courtesy Chapmann Hall. 

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... 

In fast shearing flows, with shear rates greater than I/Tj, the DEMG theory shows overshoots in both shear stress <7 and first normal stress dilference Nj as functions of time after start-up of steady shearing [21 ], in agreement with experiments (as will be presented in Section 11.5.1.1). These overshoots in both <7 and are an improvement over DE theory, which shows only the... 

Lodge and Meissner have recently examined in detail the stresses during start-up of steady elongational and shear flows (374). The Lodge equation [Eq.(6.15)], with its flow-independent memory function, described the build-up of stress rather well (even for rapid deformations) until a critical strain was reached. Beyond the critical strain (which differed somewhat in shear and... 

Amount of birefringence An at start of steady shear flow. Directions of pips represent rates of shear pip up, 0.0066 s" with successive 45° rotations clockwise representing 0.0118, 0.0216, 0.038, 0.066, 0.118, and 0.214 s , respectively. Open and solid circles, respectively, indicate data obtained with 2 and 3 mm widths of cylindrical gap. From Osaki et al. (1979). 

In Section 10.8.1 it was noted that molecular orientation results in flow birefringence in a polarizable polymer, and if the melt is transparent, optical techniques can be used to determine the three components of the stress tensor in uniform, shear flows [91-93]. To determine the transient normal stress differences, the phase-modulated polarization technique was developed by Frattini and Fuller [ 126]. Kalogrianitis and van Egmond [ 127] used this technique to determine the shear stress and both the normal stress differences as functions of time in start-up of steady simple shear. Optical techniques are particularly attractive for measurements of normal stress differences, since such methods do not require the use of a mechanical transducer, whose compliance plagues measurements of normal stress differences by mechanical rheometry. 

When comparing extensional flow data with the LVE prediction, care must be taken in the calculation of the linear prediction. If the data used to establish the relaxation spectrum do not include very short-time (high-frequency) data, the initial portion of the curve will not be correct. It may thus be better to use data from start-up of steady simple shear to measure tfit) directly rather than inferring it from complex modulus data. 

Extensional flows yield information about rheological behavior that cannot be inferred from shear flow data. The test most widely used is start-up of steady, uniaxial extension. It is common practice to compare the transient tensile stress with the response predicted by the Boltzmann superposition principle using the linear relaxation spectrum a nonlinear response should approach this curve at short times or low strain rates. A transient response that rises significantly above this curve is said to reflect strain-hardening behavior, while a material whose stress falls... 

The transient viscosity f] = T2i(t)/y0 diverges gradually without ever reaching steady shear flow conditions. This clarifies the type of singularity which the viscosity exhibits at the LST The steady shear viscosity is undefined at LST, since the infinitely long relaxation time of the critical gel would require an infinitely long start-up time. 

Four aspects of unsteady fluid flow will be considered in this chapter quasi-steady flow as in the filling or emptying of vessels, incremental calculations, start-up of shearing flow, and pressure surge in pipelines. 

This recoverable shear strain shows up when the flow of a polymer melt in a capillary rheometer is suddenly stopped. The material that has just left the capillary rheometer will clearly recover to a certain extent, in principle equal to 1/2xi>i.o/(qVo)- Fig. 15.11 the various strains are shown after starting a steady shear flow at time f = 0 and stopping it at time fi. 

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).

The rheological behavior of these materials is still far from being fully understood but relationships between their rheology and the degree of exfoliation of the nanoparticles have been reported [73]. An increase in the steady shear flow viscosity with the clay content has been reported for most systems [62, 74], while in some cases, viscosity decreases with low clay loading [46, 75]. Another important characteristic of exfoliated nanocomposites is the loss of the complex viscosity Newtonian plateau in oscillatory shear flow [76-80]. Transient experiments have also been used to study the rheological response of polymer nanocomposites. The degree of exfoliation is associated with the amplitude of stress overshoots in start-up experiment [81]. Two main modes of relaxation have been observed in the stress relaxation (step shear) test, namely, a fast mode associated with the polymer matrix and a slow mode associated with the polymer-clay network [60]. The presence of a clay-polymer network has also been evidenced by Cole-Cole plots [82]. 

Under transient flow conditions, such as inception and cessation of steady shear, P becomes a function of time with parametric dependence on shear rate. It can be calculated by integrating Equation 3 for various transient conditions y(t). For start-up experiments which impose instantaneously a constant y upon a state of equilibrium. 

Fig. 14 Stress overshoot Obs. initial shear stress before the onset of the long-time sigmoidal relaxation and steady-state shear stress tJj, gathered from start-up of flow experiments on the semidilute sample of CPCl/NaSal (12wt.%)in O.SMNaCl brine. The purely Newtonian behavior (Tjof) has been added for comparison. Reprinted from Berret [138]...

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