Rheology Bingham solid

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... 

The rheological characteristics of AB cements are complex. Mostly, the unset cement paste behaves as a plastic or plastoelastic body, rather than as a Newtonian or viscoelastic substance. In other words, it does not flow unless the applied stress exceeds a certain value known as the yield point. Below the yield point a plastoelastic body behaves as an elastic solid and above the yield point it behaves as a viscoelastic one (Andrade, 1947). This makes a mathematical treatment complicated, and although the theories of viscoelasticity are well developed, as are those of an ideal plastic (Bingham body), plastoelasticity has received much less attention. In many AB cements, yield stress appears to be more important than viscosity in determining the stiffness of a paste. 

The branch of science related to the study of deformation and flow of materials was given the name rheology by Bingham, whom some call the father of modern rheology. The prefix rheo is derived from the Greek rheos, meaning current of flow. The study of rheology includes two vastly different branches of mechanics—fluid and solid. The polymer scientist is usually concerned with viscoelastic materials that act as both solids and liquids. 

One simple rheological model that is often used to describe the behavior of foams is thai of a Bingham plastic. This applies for hows over length scales sufficient ly large that the foam can be reasonably considered as a continuous medium. The Bingham plastic model combines the properties of a yield stress like that of a solid with the viscous flow of a liquid. 

It is easy to understand that these solutions must exhibit viscoelastic properties. Under shear flow the vesicles have to pass each other and, hence, they have to be deformed. On deformation, the distance of the lamellae is changed against the electrostatic forces between them and the lamellae leave their natural curvature. The macroscopic consequence is an elastic restoring force. If a small shear stress below the yield stress ery is applied, the vesicles cannot pass each other at all. The solution is only deformed elastically and behaves like Bingham s solid. This rheological behaviour is shown in Figure 3.35. which clearly reveals the yield stress value, beyond which the sample shows a quite low viscosity. 

The size distribution of particles will control the amount of liquid needed to fluidize a given quantity of coal. In general, a fine size distribution will produce a more viscous slurry than a coarse size distribution at the same wt% solids, and the fine particles will produce a more non-Newtonian rheological curve. This can be seen in the laboratory results shown in Fig. 3, which compares a coarse coal slurry to a fine coal slurry. It is clearly seen that the fine slurry is much more viscous, its pseudoplastic character is very pronounced, and its yield value is high, while the coarse coal slurry is clearly a Bingham plastic. ... 

Fig. 3 Comparison of the rheological curves for a fine coal slurry (80% passing 34 gm, top size lOOgm, 52wt% solids) and for a coarse coal slurry (58wt% solids). Neither slurry used any additives. Because it is extremely difficult to measure the rheology of unstable slurries with conventional rheometers, these results were obtained using a continuous-pressure-vessel rheometer, which was specially designed for this purpose. The fine coal curve is the average of 10 measurements and the coarse coal curve is the average of 5 measurements, and the standard error of the shear rate measurements was approximately 1.0 Pa for these slurries. The fine coal slurry is clearly pseudoplastic with a yield value of approximately 18 Pa, while the coarse coal slurry is Bingham plastic with an estimated yield value of 4 Pa.

Casson models were used to compare their yield stress results to those calculated with the direct methods, the stress growth and impeller methods. Table 2 shows the parameters obtained when the experimental shear stress-shear rate data for the fermentation suspensions were fitted with all models at initial process. The correlation coefficients (/P) between the shear rate and shear stress are from 0.994 to 0.995 for the Herschel-Bulkley model, 0.988 to 0.994 for the Bingham, 0.982 to 0.990 for the Casson model, and 0.948 to 0.972 for the power law model for enzymatic hydrolysis at 10% solids concentration (Table 1). The rheological parameters for Solka Floe suspensions were employed to determine if there was any relationship between the shear rate constant, k, and the power law index flow, n. The relationship between the shear rate constant and the index flow for fermentation broth at concentrations ranging from 10 to 20% is shown on Table 2. The yield stress obtained by the FL 100/6W impeller technique decreased significantly as the fimetion of time and concentration during enzyme reaction and fermentation. 

This is not simply because of the presence of rheology modifiers or other polymers a simple NaPA-stabilized GCC suspension will also show a plastic-like behaviour. Typically, this involves the suspension behaving like a solid at low shear rates and stresses, and only yielding to liquid-like behaviour above a certain yield stress [Pg.150]

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