Yield value Casson

The power law model can be extended by including the yield value r — Tq = / 7 , which is called the Herschel-BulMey model, or by adding the Newtonian limiting viscosity,. The latter is done in the Sisko model, 77 +. These two models, along with the Newtonian, Bingham, and Casson... 

Chocolate does not behave as a tme Hquid owing to the presence of cocoa particles and the viscosity control of chocolate is quite compHcated. This non-Newtonian behavior has been described (28). When the square root of the rate of shear is plotted against the square root of shear stress for chocolate, a straight line is produced. With this Casson relationship method (29) two values are obtained, Casson viscosity and Casson yield value, which describe the flow of chocolate. The chocolate industry was slow in adopting the Casson relationship but this method now prevails over the simpler MacMichael viscometer. Instmments such as the Carri-Med Rheometer and the Brookfield and Haake Viscometers are now replacing the MacMichael. 

Plastic fluids are Newtonian or pseudoplastic liquids that exhibit a yield value (Fig. 3a and b, curves C). At rest they behave like a solid due to their interparticle association. The external force has to overcome these attractive forces between the particles and disrupt the structure. Beyond this point, the material changes its behavior from that of a solid to that of a liquid. The viscosity can then either be a constant (ideal Bingham liquid) or a function of the shear rate. In the latter case, the viscosity can initially decrease and then become a constant (real Bingham liquid) or continuously decrease, as in the case of a pseudoplastic liquid (Casson liquid). Plastic flow is often observed in flocculated suspensions. 

A Casson fluid is Theologically identified by two parameters yield value and plastic viscosity. The plastic viscosity relates to the asymmetry of the flow particles and the yield value is connected with the forces of attraction between particles. The... 

A more convenient extrapolation technique is to approximate the experimental data with a viscosity model. The Power Law, shown in Eq. 6, is the most commonly used two-parameter model. The Bingham model, shown in Eq. 7, postulates a linear relationship between x and y but can lead to overprediction of the yield stress. Extrapolation of the nonlinear Casson model (1954), shown in Eq. 8, is straightforward from a linear plot of x°5 vs y05. Application of the Herschel-Bulkley model (1926), shown in Eq. 9, is more tedious and less certain although systematic procedures for determining the yield value and the other model parameters are available (11) ... 

Tg and . This is shown in Fig. 7 both for the extrapolated (Bingham) and Casson s yield value. In both cases the linear relationship is maintained indicating that such crude models may be applied to the rheology of the complex system of bentonite clay plus pesticide suspension. It should be mentioned, however, that the elastic floe model is a more realistic description of the system, since the assumption of a maximum of doublets in the floe rupture model is not justified with a concentrated suspension with many body interactions. 

Chocolate can be characterized by a yield stress and plastic viscosity, i.e., as the Bingham plot. Another curve was established by Casson and reported by Holdsworth (1971) in which chocolate is characterized by the yield value and plastic viscosity. The Bingham plot is mainly used for process design and its control in the production of plain chocolate. In the case of Casson plots, some molten chocolates, particularly those containing active surface agents, did not give straight-line relationships. To overcome this difficulty, another expression was developed (Elson, 1977) ... 

Product/Supplier Applications Viscosity, Casson Pas 2S°C Yield Value, Pa 25 >C Process Conditions... 

Product Name/ Supplier Type Viscosity cps Thixo- tropic Index Yield Value N/m Casson) Shelf Life -40°C/ Pot Life 25°C Cure Schedule min °C Lap- Shear Strength psi CTE ppm/°C T, °C Volume Resistivity ohm-cm Thermal Conductivity W/mK... 

Addition Casson plastic viscosity Casson yield value... 

Bingham plastics are fluids which remain rigid under the application of shear stresses less than a yield stress, Ty, but flow like a. simple Newtonian fluid once the applied shear exceeds this value. Different constitutive models representing this type of fluids were developed by Herschel and Bulkley (1926), Oldroyd (1947) and Casson (1959). 

The square root of viscosity is plotted against the reciprocal of the square root of shear rate (Fig. 3). The square of the slope is Tq, the yield stress the square of the intercept is, the viscosity at infinite shear rate. No material actually experiences an infinite shear rate, but is a good representation of the condition where all rheological stmcture has been broken down. The Casson yield stress Tq is somewhat different from the yield stress discussed earlier in that there may or may not be an intercept on the shear stress—shear rate curve for the material. If there is an intercept, then the Casson yield stress is quite close to that value. If there is no intercept, but the material is shear thinning, a Casson plot gives a value for Tq that is indicative of the degree of shear thinning. 

Figure 9 Casson plot, slope of line reflects yield stress value. Interior coating formulation including d.HPMC O, SMAT 0,HEUR.

The extrapolated yield stress gives 0.06 Pa and a plastic viscosity of 3.88 mPas. We can use this to estimate the force between the particles, which gives 425kBT/a, in fair agreement with the value determined using pair potential curves. Here the Casson model has been used to partially linearise a pseudoplastic system rather than a system with a true yield stress. 

Experimental rheologic data were fit to the power law, Herschel-Bulkley, and Casson models. The power law model does not predict yield stress. Yield stress for 21% grain slurries predicted by the Herschel-Bulkley model was a negative value, as shown in Table 6. Yield stress values predicted by the Herschel Bulkley model for 23 and 25% solids were 8.31 and 56.3 dyn/cm2, respectively. Predicted yield stress values from the Casson model were 9.47 dyn/cm2 for 21% solids, 28.5 dyn/cm2 for 23% solids, and 44.0 dyn/cm2 for 25% solids. 

Table 3-2 Casson Yield Stress,

The rheology of a polymer solution can be approximated reasonably well by either a power-law or a Casson model over the shear rate range of 20-100 s . If the power law consistency coefficient, m, is lOPa s" and the flow behaviour index, n, is 0.2, what will be the approximate values of the yield stress and the plastic viscosity in the Casson model ... 

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