Bingham plastic fluid, properties

However, Shah et al. (IS) proposed an empirical correlation between the rheological properties of a large number of cement slurries as measured with the two types equipments (modified Fann35, and pipe nominal IDs of V2, %, 1, and ll/4 in.). These slurries are assumed to behave as Bingham plastic fluids and... 

Consider the differential control volume shown in Figure 6.3. The velocity profile is assumed to be fully developed in the direction of flow, i.e. V r). Furthermore, all physical properties including m and n for a power-law fluid and plastic viscosity and yield stress for a Bingham plastic fluid, are assumed to be independent of temperature. 

One simple rheological model that is often used to describe the behavior of foams is that of a Bingham plastic. This appHes for flows over length scales sufficiently 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 soHd with the viscous flow of a Hquid. In simple Newtonian fluids, the shear stress T is proportional to the strain rate y, with the constant of proportionaHty being the fluid viscosity. In Bingham plastics, by contrast, the relation between stress and strain rate is r = where is... 

A wide variety of nonnewtonian fluids are encountered industrially. They may exhibit Bingham-plastic, pseudoplastic, or dilatant behavior and may or may not be thixotropic. For design of equipment to handle or process nonnewtonian fluids, the properties must usually be measured experimentally, since no generahzed relationships exist to pi e-dicl the properties or behavior of the fluids. Details of handling nonnewtonian fluids are described completely by Skelland (Non-Newtonian Flow and Heat Transfer, Wiley, New York, 1967). The generalized shear-stress rate-of-strain relationship for nonnewtonian fluids is given as... 

The transition to turbulent flow begins at Re R in the range of 2,000 to 2,500 (Metzuer and Reed, AIChE J., 1, 434 [1955]). For Bingham plastic materials, K and n must be evaluated for the condition in question in order to determine Re R and establish whether the flow is laminar. An alternative method for Bingham plastics is by Hanks (Hanks, AIChE J., 9, 306 [1963] 14, 691 [1968] Hanks and Pratt, Soc. Petrol. Engrs. J., 7, 342 [1967] and Govier and Aziz, pp. 213-215). The transition from laminar to turbulent flow is influenced by viscoelastic properties (Metzuer and Park, J. Fluid Mech., 20, 291 [1964]) with the critical value of Re R increased to beyond 10,000 for some materials. 

Until much more progress is made on these very fundamental approaches, greater accuracy is believed possible in engineering work that is based on the better developed discussion reviewed here. To this end a method has recently been proposed whereby the properties of all four time-independent fluids (Newtonian, pseudoplastic, dilatant, and Bingham plastic) may be quantitatively compared. 

That is to say, the same variables are relevant in both problems with the exception of the rheological properties of the fluid. For Newtonian fluids, the viscosity y. defines these adequately for Bingham plastics, the two parameters t and ij are required. 

Based on the magnitude of n and to, the non-Newtonian behavior can be classified as shear thinning, shear thickening, Bingham plastic, pseudoplastic with yield stress, or dilatant with yield stress (see Fig. 2 and Table I). The Herschel-Bulkley model is able to describe the general flow properties of fluid foods within a certain shear range. The discussion on this classiflcation and examples of food materials has been reviewed by Sherman (1970), DeMan (1976), Barbosa-Canovas and Peleg (1983), and Barbosa-Canovas et al. (1993). 

One further feature must be mentioned about pharmaceutical suspensions, namely, their desirable rheolt ical properties (7). In practice, a Bingham plastic" behavior is most used a minimum shear stress yield stress) is needed for the suspension to begin to flow. For tower stresses—and, of course, when the system is left undisturbed—the viscosity is so high that the particles will likely remain homogeneously dispersed. According to Falkiewicz (7). thixotropy is another flow characteristic that can be useful, since in thixotropic fluids a finite lime is needed to rebuild the structure after, for instance, shaking it for administration. For this reason, most formulations contain thixotropic flow regulators intended to confer optima viscous flow propertie.s to the suspensions. The reader is referred to Chapter 5 of this book for details. 

The mechanism(s) of a particulate fluid electroviscous effect is still not fully resolved and quantified. It is not strictly relevant to this work and is therefore not dealt with in detail. At this stage it can only be said that it is a very multi-parameter and multidisciplinary event and, secondly, it should be understood that there is little change in the viscosity p of the fluid as it is normally defined in its continuum context save for a derived effective or non Newtonian viscosity sense. The term electroviscous, which has often been used to describe the present class of fluids, is misleading in this case. Rather, the held imposes a yield stress type of property on the fluid which is similar to, but not the same as, that which is a feature of the ideal Bingham plastic. This can readily be seen by referring to Figs. 6.63 to 6.66 inclusive. It is alternatively possible to claim that either the plastic viscosity changes with shear rate or the electrode surface yield stress does. 

As early mentioned, the viscosity of PE dispersions is highly dependent on the concentration as it is shown in Fig. 14 for the system C-lidocaine. It was also observed that the elastic modulus of C varies from almost purely newtonian properties in diluted dispersion to the pseudoplastic behavior. At concentrations above 0.25 % C dispersion show a yield stress value with a plastic behavior which can be described by the Bingham fluid model [43, 44]. 

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