Casson

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). 

Casson, N., 1959. In Mill. C.C. (ed.), Rheology of Disperse Systems, Pergamon Press, London. 

Casson-Asbeck plots Casson equation Casson plots CASS test Castable urethanes Castanin... 

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... 

Another model is the Casson equation (13), which is useful in estabHshing the flow characteristics of inks, paints, and other dispersions. An early form of this expression (eq. 1) was modified (14) to give equation 2. 

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. 

Fig. 3. Examples of Casson plots (viscosity) vs (shear rate). The Casson equation is 77 = 77), + Tq 7...

Another method for estimating thixotropy involves the hysteresis of the thixotropic loop. The area of the thixotropic loop is calculated or measured, which works well with printing inks (3). In a variation of this method, the up curve on an undisturbed sample is deterrnined. The sample is then sheared at high shear (>2000 ) for 30—60 s, followed by deterrnination of the down curve (22). The data ate plotted as Casson-Asbeck plots, vs 7 / (14), as... 

Fig. 8. Casson plots of sheared and unsheared paints. The degree of divergence of the lines is used to estimate thixotropy.

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. 

Taking into account all the various stipulations, we shall still assume that yield stress has a certain physical meaning and it can be measured by a stationary method proceeding from the flow curve. However, to measure the points and achieve such a clear pattern as shown in Fig. 1 is not always convenient and it is rather labor-consuming. In practice, it is convenient to use a semi-analytical procedure. It is based on the utilization of an equation for flow curves taking into account the existence of yield stress. The most widespread equation of this kind is the Casson equation. It assumes that the x(y) dependence for filled polymers is expressed in the following way ... 

Fig. 4. Diagram illustrating the method for determining a yield stress by constructing a flow curve in the coordinates of the Casson equation. The content of the filler is more for curve 2 than for curve 1...

Bell-Pedersen D, Cassone VM, Earnest DJ et al (2005) Circadian rhythms from multiple oscillators lessons from diverse organisms. Nat Rev Genet 6(7) 544-556... 

Ball and Casson [1268] have studied the decomposition of laurionite, which they represent as... 

Given that the flow properties of the puree can be described by the Casson equation ... 

Fundaro A, Cassone MC (1980) Boll Soc Ital Biol Sper 56 2364... 

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. 

Shibata, S Cassone, V. M. Moore, R. Y. (1989). Effects of melatonin on neuronal activity in the rat suprachiasmatic nucleus in vitro. Neurosci. Lett. 97, 140-4. 

A poor flowout is generally related to yield stress behavior. A method of assess ing( l) this behavior of a coating is through Casson plots based on the following equation ... 

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

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