Viscoplastic fluid behaviour

It is interesting to note that a viscoplastic material also displays an apparent viscosity which decreases with increasing shear rate. At very low shear rates, the apparent viscosity is elFectively infinite at the instant immediately before the substance yields and begins to flow. It is thus possible to regard these materials as possessing a particular class of shear-thinning behaviour. 

Strictly speaking, it is virtually impossible to ascertain whether any real material has a true yield stress or not, but nevertheless the concept of a yield stress has proved to be convenient in practice because some materials closely approximate to this type of flow behaviour, e.g. see [Barnes and Walters, 1985 Astarita, 1990 Schurz, 1990 and Evans, 1992]. The answer to the question whether a fluid has a yield stress or not seems to be related to the choice of a time scale of observation. Common examples of viscoplastic 

Over the years, many empirical expressions have been proposed as a result of straightforward cmve fltting exercises. A model based on sound theory is yet to emerge. Three commonly used models for viscoplastic fluids are briefly described here. 

This is the simplest equation describing the flow behaviom of a fluid with a yield stress and, in steady one dimensional shear, it is written as  

the two model parameters, Tq and /rg, are treated as curve fltting constants irrespective of whether or not the fluid possesses a true yield stress. 

---

The flow of viscoplastic fluids through beds of particles has not been studied as extensively as that of power-law fluids. However, since the expressions for the average shear stress and the nominal shear rate at the wall, equations (5.41) and (5.42), are independent of fluid model, they may be used in conjimction with any time-independent behaviour fluid model, as illuslrated here for the streamline flow of Bingham plastic fluids. The mean velocity for a Bingham plastic fluid in a circular tube is given by equation (3.13) ... 

A fluid with a linear flow curve for Ty > ro is called a Bingham plastic fluid and is characterised by a constant plastic viscosity (the slope of the shear stress versus shear rate curve) and a yield stress. On the other hand, a substance possessing a yield stress as well as a non-linear flow curve on linear coordinates (for Xyx > ro ), is called a yield-pseudoplastic material. Figure 1.8 illustrates viscoplastic behaviour as observed in a meat extract and in a polymer solution. 

Industrial fluids exhibiting viscoplastic behaviour are often best modelled using the Herschel-Bulkley model (Govier Aziz, 1972 and Hanks, 1979). The constitutive rheological equation is given by Eqn. (5). 

---