Bingham-type plastic flow yield stress

Vehicles that exhibit the unusual property of Bingham-type plastic rheological flow are characterized by the need to overcome a finite yield stress before flow is initiated. Permanent suspension of most pharmaceutical systems requires yield-stress values of at least 2-5 Pa (20-50 dyn/cm ). Bingham plastic flow is rarely produced by pharmaceutical gums and hydrophilic colloids. National Formulary (NF) carbomers exhibit a sufficiently high yield value at low solution concentration and low viscosity to produce permanent suspensions. The carbomers, however, require a pH value between 6 and 8 for maximum suspension performance. The polymer is essentially incompatible... 

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 shearing characteristics of non-Newtonian fluids are shown in Fig. 3.24 of Volume 1. This type of fluid remains rigid when the shear stress is less than the yield stress Ry and flows like a Newtonian fluid when the shear stress exceeds Ry. Examples of Bingham plastics are many fine suspensions and pastes including sewage sludge and toothpaste. The velocity profile in laminar flow is shown in Fig. 3c. 

Illustrated in Fig. 9.1.1, relative to a Newtonian fluid, are the behaviors of the shear stress versus shear rate in a Couette flow for three principal types of non-Newtonian fluids that can be characterized by the form of the apparent viscosity function in Eq. (9.1.3). A number of empirical functions have been widely employed to characterize the apparent viscosities for these classes of fluids. One termed a Bingham plastic behaves like a solid until a yield stress Tq is exceeded subsequent to which it behaves like a Newtonian fluid with a plastic viscosity lip. The apparent viscosity for this fluid may be written... 

The flow behavior of a vtscoplaslir fluid is identified by the. appearance of a yield Stress, i.e., the fluid flows in a viscous manner only after a threshold ha.s been exceeded. Below this threshold, or yield stress, the behavior of the fluid is similar to an elastic solid and should obey Eq. [4) when subjected to a strain or stress sweep. The simplest type of viscoplastic fluid is the so-called Bingham plastic, and its behavior can be expressed by means of the following mathematical model ... 

Certain slurries require a minimum level of stress before they can flow. An example is fresh concrete that does not flow unless the angle of the chute exceeds a certain minimum. Such a mixture is said to posses a yield stress magnitude that must be exceeded before that flow can commence. A number of flows such as Bingham plastics, pseudoplastics, yield pseudoplastics, and dilatant are classified as time independent non Newtonian flu ids. The relationship of wall shear stress versus shear rate is of the type shown in Figure 3 9 (a), and the relationship between the apparent viscosity and the shear rate is shown in Figtne 3-9 (b). The apparent viscosity is defined as... 

Pseudoplastic and dilatant fluids begin to flow as soon as a stress is applied. For plastic fluids, a yield value (Xy) has to be exceeded before flow occurs (Figure 4-2). Two types of yield stress liquids are Bingham plastic and viscoplastic fluids... 

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