Casson viscosity model

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) ... 

The viscosity reduction by water addition is not due to the presence of the surfactant (HAB). For the sand-in-bitumen suspension, the viscosity variation is shown in Figure 31. It can be observed from Figure 31 that the sand-in-bitumen suspensions are slightly shear thinning type. A low shear limit viscosity is observed, although a yield stress may be assumed if Casson s model is used (194). The shear thinning behavior is more severe when the solid volume fraction is increased. 

Rheology experiments also give information in the determination of wax appearance temperatures of crude oils. In this research, WATs of crude oils were determined by viscometry from the point where the experimental curve deviates from the extrapolated Arrhenius curve (Figure 4). It was observed that all crude oils, except highly asphaltenic samples, are Newtonian fluids above their wax appearance temperatures. The flow behaviour of crude oils is considerably modified by the crystallization of paraffins corresponding to the variation of the apparent viscosity with temperature. Below the WAT, flow becomes non-Newtonian and approaches that of the Bingham and Casson plastic model [17,18]. 

Casson model x = rj y + Xy, for ItI > Xy and 7 = 0, otherwise, where x, y, rjc, and Xy denote shear stress, shear rate, Casson viscosity, and yield stress, respectively. 

The rheological curves of thixotropic fluids, such as IP 680 in Figure 21, show that there is a yield stress tq to overcome before shear can take place. This phenomenon is taken into account in Casson s model represented by the equation = (tq) - - [tioldy/dt)] , where the yield stress tq is usually determined by extrapolating to zero shear the curve representing the variation of the shear stress at different shear rates. For the sake of convenience, conductive adhesive pastes are often characterized by a thixotropy index, which is the ratio of the viscosities... 

The other models can be appHed to non-Newtonian materials where time-dependent effects are absent. This situation encompasses many technically important materials from polymer solutions to latices, pigment slurries, and polymer melts. At high shear rates most of these materials tend to a Newtonian viscosity limit. At low shear rates they tend either to a yield point or to a low shear Newtonian limiting viscosity. At intermediate shear rates, the power law or the Casson model is a useful approximation. 

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... 

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. 

For a food whose flow behavior follows the Casson model, a straight line results when the square root of shear rate, (y), is plotted against the square root of shear stress, (cr) , with slope Kc and intercept Kqc (Figure 2-2). The Casson yield stress is calculated as the square of the intercept, ctoc = (Kocf and the Casson plastic viscosity as the square of the slope, r]ca = The data in Figure 2-2 are of Steiner (1958) on a chocolate sample. The International Office of Cocoa and Chocolate has adopted the Casson model as the official method for interpretation of flow data on chocolates. However, it was suggested that the vane yield stress would be a more reliable measure of the yield stress of chocolate and cocoa products (Servais et al., 2004). 

Figure 2-2 Plot of versus for a Food that Follows the Casson Model. The Square of the intercept is the yield stress and that of slope is the casson plastic viscosity.

Table 5-H Casson Model Parameters Yield Stress (croc) nd Plastic Viscosity (rjoo) of Cocoa Mass as a Function of Temperature (Fang et ai., 1996)...

Figure 10 compares the pressure dependence of the rheological parameters of the Casson model (high shear viscosity k 2), the Bingham... 

Figure 10. Pressure dependence of parameters from various models of the rheology of invert emulsion oil-based drilling fluids at various temperatures. Casson high shear viscosity Bingham plastic viscosity consistency, power law exponent, and yield stress from Herschel-Bulkley model. (Reproduced with permission from reference 69. Copyright 1986 Society of Petroleum Engineers.)...

Houwen and Geehan (69) used an Arrhenius-like equation to model the temperature and pressure dependence of the Casson high shear viscosity kx2 and Casson yield stress k02 by... 

Besides the Brookfield viscometers, the Haake rotoviscometer, PKIO MlO/PKl 2 Cone, Casson Model is used to measure viscosity at shear rates of 0.4—30 second . This instrument is used alone or in combination with a Brookfield viscometer for SMT adhesives. The equipment is used not only to measure viscosities, but also to provide flow properties in the form of graphs of shear stress versus shear rate. 

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 ... 

From a physical standpoint, at small velocities, the polymeric chains of the alginate have a random orientation, increasing the viscosity, while under a sufficient shear they align with the flow, and the viscosity is reduced. Different laws exist for the viscosity of alginate solutions the Carreau-Yasuda law is often used to describe the viscosity of semi-dilute alginate solutions. Similarly, at small velocities, red blood cells form stacks that considerably increase the viscosity. These stacks are dispersed at sufficiently high velocity. Usually blood viscosity is modeled by Cassons law, and an asymptotic value of 4.0 10 Pa.s for the viscosity is obtained when the cells are dispersed. 

Perhaps the best picture of a viscoplastic fluid is that of a very viscous, even solidlike, material at low stresses. Over a narrow stress range, which can often be modeled as a single yield stress, its viscosity drops dramatically. This is shown clearly in Figure 2.5.5b, where viscosity drops over five decades as shear stress increases from 1 to 3 Pa. (The drop is even more dramatic in Figure 10.7.2.) Above this yield stress the fluid flows like a relatively low viscosity, even Newtonian, liquid. Because of the different behaviors exhibited by these fluids, the model (Bingham, Casson, etc.) and the range of shear rates used to calculate the parameters must be chosen carefully. In Section 10.7 we will discuss microstructural bases for r. It is also important to note that experimental problems like wall slip are particularly prevelant with viscoplastic materials. Aspects of slip are discussed in Section 5.3. 

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