Threshold shear stress

Dick et al. [29] present additional data on the <100) shock compression of LiF which further establishes a threshold shear stress of between 0.24 GPa and 0.30 GPa for nucleation of dislocations in the shock front. 

Fig. 19. Variation of exposure time associated with cell rupture and the threshold shear stress for various systems [112]...

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. 

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... 

Pseudoplastic with yield stress (plastic) Pseudoplastic or Newtonian flow begins only after a threshold shear stress, the yield stress, is exceeded Toothpaste, lipstick, grease, oil well drilling mud In an oil well drilling mud, the inter-particle network offers resistance to any positional changes. Flow only occurs when these forces are overcome... 

The efficiency of separation (Ep) in dense-medium baths was found to depend on the plastic viscosity of the media, and a high yield stress (to) of the medium is claimed to cause elutriation of the finer particles into the float as they (and near-density particles) are unable to overcome the threshold shear stress required before the movement takes place. When a particle is held in a suspension, the yield stress is responsible for it but when it is moving, its velocity is a function of plastic viscosity. It is understandable then that dispersing agents used to decrease medium viscosity may improve separation efficiency quite significantly. They may also decrease mag-nitite loses. 

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). 

Imposition of no-slip velocity conditions at solid walls is based on the assumption that the shear stress at these surfaces always remains below a critical value to allow a complete welting of the wall by the fluid. This iraplie.s that the fluid is constantly sticking to the wall and is moving with a velocity exactly equal to the wall velocity. It is well known that in polymer flow processes the shear stress at the domain walls frequently surpasses the critical threshold and fluid slippage at the solid surfaces occurs. Wall-slip phenomenon is described by Navier s slip condition, which is a relationship between the tangential component of the momentum flux at the wall and the local slip velocity (Sillrman and Scriven, 1980). In a two-dimensional domain this relationship is expressed as... 

G is a multiplier which is zero at locations where slip condition does not apply and is a sufficiently large number at the nodes where slip may occur. It is important to note that, when the shear stress at a wall exceeds the threshold of slip and the fluid slides over the solid surface, this may reduce the shearing to below the critical value resulting in a renewed stick. Therefore imposition of wall slip introduces a form of non-linearity into the flow model which should be handled via an iterative loop. The slip coefficient (i.e. /I in the Navier s slip condition given as Equation (3.59) is defined as... 

Figure 7.7. Shear stress and mechanical threshold stress for 3.0 GPa and 5.4 GPa shock waves in copper.

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 ... 

Polymer chains anchored on solid surfaces play a key role on the flow behavior of polymer melts. An important practical example is that of constant speed extrusion processes where various flow instabilities (called sharkskin , periodic deformation or melt fracture) have been observed to develop above given shear stress thresholds. The origin of these anomalies has long remained poorly understood [123-138]. It is now well admitted that these anomalies are related to the appearance of flow with slip at the wall. It is reasonable to think that the onset of wall slip is related to the strength of the interactions between the solid surface and the melt, and thus should be sensitive to the presence of polymer chains attached to the surface. 

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. 

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. 

If the skin friction exceeds the critical threshold for resuspension, sedimentary material is I ifted off from the bottom and is transported into the water body. Grainy particles may also be moved by the so-called bed-load transport that occurs already at a lower threshold. Deposition results from the settling of the sediment particles, if the shear stress falls below a certain limit. The critical thresholds, the settling velocities, and the erosion and deposition rates are material constants derived from experiments (Soulsby, 1997). 

An analysis of the contributions to the skin friction shows that the surface waves play the dominant role. The shear stress induced by bottom currents exceeds the low fluff threshold only occasionally, especially during inflow events of saline water through the narrow channels. Therefore, an estimation of the resuspension potential of bottom sediments may be based on waves only, as, for instance, done by Jonsson (2006). However, without bottom currents some events will be missing, and, more important, no conclusions about the transport paths are possible. 

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