Shear rate threshold

New viscosity coefficients pj and A, are related to Leslie coefficients. In particular, po = 0 4 (viscosity of an isotropic liquid). Viscosimetry of SmA liquid crystals is difficult. For instance, in geometry (a), the upper and lower plates should be parallel with a great accuracy (few nanometers) otherwise defects appear. However, for several compounds the correspondent viscosities have been measured. In geometry (b) there was found a shear rate threshold above the threshold the isotropic behaviour (04) was observed. At lower rates, defects control a flow. 

Pseudoplastic fluids have no yield stress threshold and in these fluids the ratio of shear stress to the rate of shear generally falls continuously and rapidly with increase in the shear rate. Very low and very high shear regions are the exceptions, where the flow curve is almost horizontal (Figure 1.1). 

The concentration at which a steep rise in this curve begins has been termed as the critical or threshold concentration (2,3). Figure 6 shows such typical curves for PTF and BTF in n-hexane. Despite the fact that different shear rates are involved in capillary viscometry, it can be qualitatively said that at a given concentration, PTF viscosified n-hexane better than BTF. It is clear from Figure 6 that the critical concentration for these two compounds is above 0.7%, while analogous tri-n-alkyltin fluorides showed a critical concentration of less than 0.4% (3). This may be due to the presence of bulky Me3Si-groups nearer to the Sn-F bond, which causes some steric hindrance to auto-association. 

Fig. 11. The relationship between shear stress (t) and shear rate ( y) for a polymer disperse system showing creeping flow, with very high viscosity, at stresses smaller than the threshold yield stress [1]...

Fluids that show viscosity variations with shear rates are called non-Newtonian fluids. Depending on how the shear stress varies with the shear rate, they are categorized into pseudoplastic, dilatant, and Bingham plastic fluids (Figure 2.2). The viscosity of pseudoplastic fluids decreases with increasing shear rate, whereas dilatant fluids show an increase in viscosity with shear rate. Bingham plastic fluids do not flow until a threshold stress called the yield stress is applied, after which the shear stress increases linearly with the shear rate. In general, the shear stress r can be represented by Equation 2.6 ... 

In the previous sections we have shown that the inclusion of the director of the underlying nematic order in the description of a smectic A like system leads to some important new features. In general, the behavior of the director under external fields differs from the behavior of the layer normal. In this chapter we have only discussed the effect of a velocity gradient, but the effects presented here seem to be of a more general nature and can also be applied to other fields. The key results of our theoretical treatment are a tilt of the director, which is proportional to the shear rate, and an undulation instability which sets in above a threshold value of the tilt angle (or equivalently the shear rate). 

Clearly flow aligning behavior of the director is present and do increases linearly with the tilt angle, do. Above a threshold in the Spain rate, y 0.011, undulations in vorticity direction set in. In Fig. 14 the results of simulations for y 0.015 are shown. In Fig. 15 we have plotted the undulation amplitude obtained as a function of the shear rate. The dashed line indicates a square root behavior corresponding to a forward bifurcation near the onset of undulations. This is, indeed, what is expected, when a weakly nonlinear analysis based on the underlying macroscopic equations is performed [54], In Fig. 16 we have plotted an example for the dynamic behavior obtained from molecular dynamics simulations. It shows the time evolution after a step-type start for two shear rates below the onset of undulations. The two solid lines correspond to a fit to the data using the solutions of the averaged linearized form of (27). The shear approaches its stationary value for small tilt angle (implied by the use of the linearized equation) with a characteristic time scale t = fi/Bi. 

In some colloidal dispersions, the shear rate (flow) remains at zero until a threshold shear stress is reached, termed the yield stress (rY), and then Newtonian or pseudoplastic flow begins. A common cause of such behaviour is the existence of an interparticle or intermolecular network which initially acts like a solid and offers resistance to any positional changes of the volume elements. In this case flow only occurs when the applied stress exceeds the strength of the network and what was a solid becomes instead a fluid. 

The threshold is even more visible on this representation, as when the strong slip starts, the shear rate experienced by the polymer is no longer proportional to Vt. In fact, at the onset of strong slip, the shear stress remains locked, while the velocity at the wall strongly increases. 

Figure 6. Slip length b deduced from the data of Fig. 4 and 5 as a function of the slip velocity Vg. The threshold for the onset of strong slip appears as a kink in the b (Vg) curve, at the critical velocity V. Above V, b increases with Vg. following a power law with an exponent 0.8 0.04. At very high shear rates, b deviates from the power law and the Vg dependence tends to saturate, indicating that a new regime of linear strong slip is approached.

We do not know a lot however about the second point, because the deformability of a highly polydisperse brush is not easy to model. We have begun to understand how a monodisperse brush responds to a shear stress [25], and qualitatively we expect these dense structures to be far more rigid than the weakly dense surface layers investigated in 3.2. It is thus plausible that the threshold for the onset of strong slip appears at higher shear rates for dense surface layers than for weakly dense ones, as observed experimentally. Up to now we do not have predictions for the molecular weight dependence of these thresholds. 

Yield Stress For some fluids, the shear rate (flow) remains at zero until a threshold shear stress, termed the yield stress, is reached. Beyond the yield stress flow begins. 

A convenient way to summarize the flow properties of fluids is by plotting flow curves of shear stress versus shear rate (r versus 7). These curves can be categorized into several rheological classifications. Foams are frequently pseudoplastic that is, as shear rate increases, viscosity decreases. This is also termed shear-thinning. Persistent foams (polyeder-schaum) usually exhibit a yield stress (rY), that is, the shear rate (flow) remains zero until a threshold shear stress is reached, then pseudoplastic or Newtonian flow begins. An example would be a foam for which the stress due to gravity is insufficient to cause the foam to flow, but the application of additional mechanical shear does cause flow (Figure 17). 

Fluids in which no deformation occurs until a certain threshold shear stress is applied, in which upon the shear stress x becomes a linear function of shear rate y. The characteristics of the function are the slope (viscosity) and the shear stress intercept (yield value) Xy. The rheological expression for this type of material, known as a Bingham solid, is... 

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