Start-up of shear

Fig. 13. Shear stress t12 and first normal stress difference N1 during start-up of shear flow at constant rate, y0 = 0.5 s 1, for PDMS near the gel point [71]. The broken line with a slope of one is predicted by the gel equation for finite strain. The critical strain for network rupture is reached at the point at which the shear stress attains its maximum value...

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. 

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).

Figure 3.74. An example of a typical stress build-up during start up of shearing for a polymer melt.

The transient shear flow experiments described in Figure 2 may provide the most insight into development of orientation and structure in LCP. We first look at stress growth at the start up of shear flow. In this experiment the stress build up at the start up of flow is monitored as a function of time. Some representative data for a 60 mole % PHB/PET copolyester are presented in Figure 16. At this particular temperature we observe two stress peaks. 

Fig. 16. Stress growth (shear stress) at the start up of shear flow for 60 mole % PHB/PET.

For start-up of shear flow at constant rate, the transient viscosity grows in a power law with time. This might be utilized for detecting GP. The total strain must be kept small because, near GP, stress relaxation is infinitely slow and shear modification cannot be avoided even at extremely low rates of deformation. 

In the equilibrium state (t = 0), the number of broken bonds is equal to zero, and hence r (0) -> oo. On the start-up of shear flow, the shear stress is given... 

To reproduce the complex response at a start up of shear flow for a series of the LDPE/LDH nanocomposites (Fig. 20), it is necessary to take into account the shift of the second stress overshoot to smaller deformations with increasing LDH loading. To our knowledge, this shift can be explained by the effect of strain amplification in the polymer matrix foxmd previously in the case of filled elastomers [103]. Upon shearing, the hard filler particles cannot be stretched however, they can reorganize their positions in the polymer matrix, which hence experiences a noticeably higher effective deformation, yeff> than the strain externally applied to the sheared sample, yo [103] ... 

For time dependent models there will still be a large deviation of H versus t at short times. This deviation is primarily due to the transient viscosity the overshoot in shear stress at the start-up of shear flow (recall Figure 4.2.3). Leider and Bird (1974) incorporated an empirical stress overshoot function into their anal-... 

It is the portion of the response curves around the maxima that are of primary interest in the characterization of nonlinear behavior, because this is where chain stretch has its most pronoimced effect. At longer times convective constraint release becomes dominant. Wagner etal. [23] used start-up of shear flow to evaluate the molecular stress function model for nonlinear behavior in which chain stretch and tube diameter are strain dependent. This theory was found to be suitable for describing an HDPE having a broad molecular weight distribution and an LDPE with random long-chain branching. 

The predictions of simplified tube models that include CCR, such as the MLD model [27], and the models of Likhtman etal [28, 37, 38] and of lanniruberto and Marrucci [31-33], discussed in Section 11.3.4, as well as the related theory of Fang ef a/. [29], have been compared to experimental data on start-up of shear flow for entangled monodisperse polymer solutions. 

---