Rheology threshold shear stress

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... 

Let us first consider an inverted W/O emulsion made of 10% of 0.1 M NaCl large droplets dispersed in sorbitan monooleate (Span 80), a liquid surfactant which also acts as the dispersing continuous phase. At this low droplet volume fraction, the rheological properties of the premixed emulsion is essentially determined by the continuous medium. The rheological behavior of the oil phase can be described as follows it exhibits a Newtonian behavior with a viscosity of 1 Pa s up to 1000 s 1 and a pronounced shear thinning behavior above this threshold value. Between 1000 s 1 and 3000 s1, although the stress is approximately unchanged, the viscosity ratio is increased by a factor of 4. 

Khalkhal and Carreau (2011) examined the linear viscoelastic properties as well as the evolution of the stmcture in multiwall carbon nanotube-epoxy suspensions at different concentration under the influence of flow history and temperature. Initially, based on the frequency sweep measurements, the critical concentration in which the storage and loss moduli shows a transition from liquid-like to solid-like behavior at low angular frequencies was found to be about 2 wt%. This transition indicates the formation of a percolated carbon nanotube network. Consequently, 2 wt% was considered as the rheological percolation threshold. The appearance of an apparent yield stress, at about 2 wt% and higher concentration in the steady shear measurements performed from the low shear of 0.01 s to high shear of 100 s confirmed the formation of a percolated network (Fig. 7.9). The authors used the Herschel-Bulkley model to estimate the apparent yield stress. As a result they showed that the apparent yield stress scales with concentration as Xy (Khalkhal and Carreau 2011). 

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