Steady-state shear flow field

Note that y appearing in Eq. (2.12) is constant for uniform shear flow and not constant for nonuniform shear flow. In Chapter 5 we present experimental methods for the determination of the rheological properties of polymeric liquids in the uniform shear flow field using a cone-and-plate rheometer and in the nonuniform shear flow field using a capillary or slit rheometer. 

---

Such data has similarities with earlier studies on lyotropic aqueous solutions of HPC (15,16). The equivalent orientational behaviour in steady state shear flow for a 55% w/v aqueous HPC solution is shown in Figure 12. These data also show three regimes although the level of preferred orientation at low shear rates is clearly greater for the aqueous solution, and the distinction between regimes 2 3 are blurred. Lyotropic HPC and thermotropic PPC have considerably different concentrations of liquid crystal forming molecule (55% and 100%), yet their responses to the flow field are similar. It is emphasized that we can make direct comparisons between these two materials since the derivative PPC and the lyotropic solutions were prepared from the polymer Klucel E which was used to prepare the aqueous solutions. 

In regime III, the flow field is very strong and shear-induced molecular orientation becomes important. According to birefringence measurements for anisotropic HPC/H2O solutions and HPC/ m-cresol solutions, the molecular orientation is a monotoni-cally increasing function of the steady state shear rate. 

LDPE, and with polypropylene, PP, was studied In steady state shear, dynamic shear and uniaxial extenslonal fields. Interrelations between diverse rheological functions are discussed In terms of the linear viscoelastic behavior and Its modification by phase separation Into complex morphology. One of the more Important observations Is the difference In elongational flow behavior of LLDPE/PP blends from that of the other blends the strain hardening (Important for e.g. fllm blowing and wire coating) occurs In the latter ones but not In the former. 

So far steady flow conditions have been considered but in practice emulsification is very often carried out under turbulent conditions. Fortunately, the same physical concepts apply but this time in the context of a rapidly changing flow field. Under such conditions the Weber number cannot be defined using a steady-state shear rate and is reformulated as ... 

Atomization. A gas or Hquid may be dispersed into another Hquid by the action of shearing or turbulent impact forces that are present in the flow field. The steady-state drop si2e represents a balance between the fluid forces tending to dismpt the drop and the forces of interfacial tension tending to oppose distortion and breakup. When the flow field is laminar the abiHty to disperse is strongly affected by the ratio of viscosities of the two phases. Dispersion, in the sense of droplet formation, does not occur when the viscosity of the dispersed phase significantly exceeds that of the dispersing medium (13). 

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).

Fixed cylinder. Let us consider a fixed circular cylinder in an arbitrary steady-state linear shear flow of viscous incompressible fluid in the plane normal to the cylinder axis. The velocity field of such a flow remote from the cylinder in the Cartesian coordinates X, X% can be represented in the general case as follows ... 

Predictive model for the morphology variation during simple shear flow under steady state uniform shear field was developed. The model considers the balance between the rate of breakup and the rate of drop coalescence. The theory makes it possible to compute the drop aspect ratio, p a parameter that was directly measured for PS/PMMA =1 9 blends. 

---