Bingham viscoplastic flow

The analysis of full rheological curve illustrates how the complex mechanical behavior can be subdivided into several regions, and how within each of these regions it can be represented by a simple model that utilizes only one or two constant parameters. For this reason, such phenomena as Schwedov s creep and Bingham s viscoplastic flow, whose molecular mechanisms are so different, can be described by substantially different parameters within otherwise the same model. Such subdivision of complex behavior into a finite number of simpler constituents with particular quantitative characteristics illustrates the universal role of macrorheology. At the same time, detailed description of a mechanism involved in each of these elementary stages requires the use of molecular-kinetic concepts and may be characterized as a microrheological approach. 

Both polymeric and some biological reactors often contain non-Newtonian liquids in which viscosity is a function of shear rate. Basically, three types of non-Newtonian liquids are encountered power-law fluids, which consist of pseudoplastic and dilatant fluids viscoplastic (Bingham plastic) fluids and viscoelastic fluids with time-dependent viscosity. Viscoelastic fluids are encountered in bread dough and fluids containing long-chain polymers such as polyamide and polyacrylonitrite that exhibit coelastic flow behavior. These... 

Substituting (6.2.20) into (6.2.17)—(6.2.19), we find the basic characteristics of film flow of a viscoplastic Shvedov-Bingham fluid along an inclined plane (the results of the corresponding calculations are presented in Table 6.4). 

Figure 6.3. Velocity profile in the flow of a viscoplastic Shvedov-Bingham medium...

A similar problem on a nonisothermal rectilinear flow of a viscoplastic Shvedov-Bingham fluid in a circular tube for the case in which the yield stress and the plastic viscosity are inversely proportional to temperature was studied in [298],... 

Viscoplastic fluids. In the case of a spherical bubble in a translational Stokes flow of a viscoplastic Shvedov-Bingham fluid with a small yield stress, the following two-term asymptotic expansion is valid for the drag coefficient [37] ... 

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 ... 

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. 

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) ... 

The rheology of yield-stress (or viscoplastic) fluids is complex and often time dependent. Considerable insight can be gained, however, by considering the simplest example, the Bingham material. The classical Bingham material is defined for a shear flow with a positive shear rate 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... 

A plastic material is one that shows little or no deformation up to a certain level of stress. Above this yield stress the material flows readily. Plasticity is conunon to widely different materials. Many metals yield at strains less than 1%. Concentrated suspensions of solid particles in Newtonian liquids often show a yield stress followed by nearly Newtonian flow. These materials are called viscoplastic or Bingham plastics after E. C. Bingham, who first described paint in this way in 1916. House paint and food substances like margarine, mayonnaise, and ketchup are good examples of viscoplastic materials. 

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. 

---