Fluid plastic viscosity

In a fluid under stress, the ratio of the shear stress, r. to the rate of strain, y, is called the shear viscosity, rj, and is analogous to the modulus of a solid. In an ideal (Newtonian) fluid the viscosity is a material constant. However, for plastics the viscosity varies depending on the stress, strain rate, temperature etc. A typical relationship between shear stress and shear rate for a plastic is shown in Fig. 5.1. 

A fluid with a finite yield. stress is sheared between two concentric cylinders, 50 mm long. The inner cylinder is 30 mm diameter and the gap is 20 mm. The outer cylinder is held stationary while a torque is applied to the inner. The moment required just to produce motion was 0.01 N m. Calculate the force needed to ensure all the fluid is flowing under shear if the plastic viscosity is 0.1 Ns/ni2. 

In nondispersed systems no special agents are added to deflocculate the solids in the fluid. The main advantages of these systems are the higher viscosities and the higher yield point-to-plastics viscosity ratio. These alterated flow properties provide a better cleaning of the bore hole, allow a lower annular circulating rate, and minimize wash out of the bore hole. 

A Casson fluid is Theologically identified by two parameters yield value and plastic viscosity. The plastic viscosity relates to the asymmetry of the flow particles and the yield value is connected with the forces of attraction between particles. The... 

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. 

A Bingham-plastic fluid (yield stress 14.35 N/m2 and plastic viscosity 0.150 Ns/m2) is flowing through a pipe of diameter 40 mm and length 200 m. Starting with the rheological equation, show that the relation between pressure gradient —AP/l and volumetric flowrate Q is ... 

Viscosity and Plasticity—Viscosity and plasticity are closely related. Viscosity may be defined as the force required to move a unit-area of plane surface with unit-speed relative to another parallel plane surface, from which it is separated by a layer of the liquid of unit-thickness. Other definitions have been applied to viscosity, an equivalent one being the ratio of shearing stress to rate of shear. When a mud or slurry is moved in a pipe in more or less plastic condition the viscosity is not the same for all rates of shear, as in the case of ordinary fluids. A material may be called plastic if the apparent viscosity varies with the rate of shear. The physical behavior of muds and slurries is markedly affected by viscosity. However, consistency of muds and slurries is not necessarily the same as viscosity but is dependent upon a number of factors, many of which are not yet clearly understood. The viscosity of a plastic material cannot be measured in the manner used for liquids. The usual instrument consists of a cup in which the plastic material is placed and rotated at constant speed, causing the deflection of a torsional pendulum whose bob is immersed in the liquid. The Stormer viscosimeter, for example, consists of a fixed outer cylinder and an inner cylinder which is revolved by means of a weight or weights. 

The complexity of formation of mesophase must not be underestimated. With the exception of a few model compounds, it is the industrial pitch which is the source of mesophase. Such materials contain thousands of reactive molecules and there is an interdependence in the carbonization system which currently is known to us but not analyzed in depth. This is an area for further research. Formation of mesophase is further complicated because it involves chemistry within a fluid/plastic system of increasing viscosity. And in the delayed coker, volatile release and liquid turbulence are yet additional factors in influencing final structure in mesophase. 

The introduction of defects into a smectic sample destroys its fluidity. This contrasts markedly with nematics, for which the presence of defects hardly alters the fluid s viscosity. Of course, this is because in a smectic the direction locally perpendicular to the layers is solid-like, and when defects are present, all directions acquire some solid-like character. Horn and Kleman (1978) measured shearing stresses in defect-containing smectic samples of 8CB and found that the shear stress was given by the equation of a Bingham plastic ... 

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],... 

Yield stress and plastic viscosity. The most important rheological characteristic determining the foam behavior ( solid-shaped or fluid-shaped ) is the yield stress To. This variable was calculated in [379] for a two-dimensional foam model ... 

The Fann rheometer has been calibrated to give direct readings of plastic viscosity (PV) and yield point (YP) as given by the simple Bingham plastic fluid model relating shear stress (r) to shear rate (7) ... 

In addition to the plastic viscosity and yield point, the gel strength of the drilling fluid is measured after it has been at rest for a given period of time. The usual procedure (64) is to shear the sample and then allow the sample to be unsheared for 10 s or 10 min. After the prescribed... 

Figure 7. Determination of yield point and plastic viscosity of drilling fluid using the Bingham plastic fluid model.

Figure 10. Pressure dependence of parameters from various models of the rheology of invert emulsion oil-based drilling fluids at various temperatures. Casson high shear viscosity Bingham plastic viscosity consistency, power law exponent, and yield stress from Herschel-Bulkley model. (Reproduced with permission from reference 69. Copyright 1986 Society of Petroleum Engineers.)...

The polyacrylate polymers and a derivative of a vinyl acetate maleic anhydride copolymer cause V30 to decrease monotonically with increasing polymer concentration, similar to the CMC polymers (Figure 46). The polymers PVA and poly(vinyl pyridinium) (PVP) hydrochloride markedly increased V30 at low concentration at concentrations above 1 g of polymer per gram of added bentonite PVA functions as a static fluid loss additive. The maximum in the API fluid loss at low PVA concentrations approximately coincides with the maximum in the yield stress and plastic viscosity found by Heath and Tadros (75). The increased static fluid loss is consistent with Heath and Tadros s conclusion that bentonite is flocculated by low concentrations of PVA. The concentration of PVA required to decrease V30 below that of the neat bentonite suspension is significantly larger than the concentration of CMC, where effective static fluid loss control can be achieved at polymer bentonite weight ratios of about 0.1 g/g. More effective fluid loss control has been achieved with other synthetic polymers such as poly(vinyl sulphonate)-poly(vinyl amide) copolymer (40) and other sulphonated polymers (39). 

Chemical potential Viscosity or viscosity coefficient Internal viscosity of fluid drop Bingham plastic viscosity Kinematic viscosity... 

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... 

H is the initial height of slope Ty is the yield stress for Bingham plastic fluid rip is the plastic viscosity Y is the unit weight... 

The pseudoplastic fluids can be consider as the Bingham fluid with the yield stress value and plastic viscosity equal to tg a and it is the reason of their name (see Fig. 5.4). 

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. 

Two observations can be made here. The 25% reduction in the available pressure gradient has lowered the flow rate by 31%. Secondly, in this case the flow rate is only one tenth of that of a Newtonian fluid of the same viscosity as the plastic viscosity of the molten chocolate ... 

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. 

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