Fluid yield stress

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 ... 

In the laboratory, the density of a cement slurry is usually derived from the measured mass or volume of the different ingredients and from their respective densities. When a measurement is performed, it is usually done with pressurized equipment like a pressurized mud balance (Appendix C of reference 6) as cement slurries always contain a small quantity of air bubbles (these are trapped into the slurry and difficult to eliminate because of the fluid yield stress). In the field, measuring slurry density is a key issue as it is much more cumbersome if not impossible (for continuous mix operations) to measure the mass or volume of the different ingredients. Different types of equipments are used like pressurized mud balances, radioactive densitometers, or vibrating tube devices. Once the slurry is mixed at the right density, it is of utmost importance to make sure it is stable. 

Some fluids yield stress. When subjected to stresses below the yield stress they... 

The power law fluid yield stress is zero, and the fluid is deformed as long as the effect of a small force on the fluid. Particle density is greater than that of the fluid. In addition there is a vertical downward force formed by particle gravity and buoyancy force of the particle fluid. Therefore, particles settle. When the particle diameter is small to a certain extent, it will not overcome the yield stress and get a suspension in the fluid. Then sedimentation does not occur, which is known as natural suspended state. When the fluid stops circulating, it can make the solid phase suspension in the annulus to prevent the deposition of the solid phase at the bottom of the borehole. In this case, accidents can be avoided. Conditions for particles sedimentation is shown as follows ... 

Bingham y = 00 T < Tq Tq = fluid yield stress below which no (i) Used mainly for pastes, slurries and... 

The boundary of the cavern can be defined as the surface where the local shear stress equals the fluid yield stress. If it is assumed that the predominant flow in the cavern is tangential [and EDA studies suggest that this is a reasonable approximation (Hirata et al., 1994)] and that the cavern shape, fluid yield stress, and impeller power number are known, the cavern size may be determined. A right circular cylinder of height He and diameter Dc centered on the impeller is a good model for the cavern shape, which allows for the effect of different impellers (Elson et al., 1986). Thus,... 

Solomon et al. (1981a) proposed a physical model to estimate cavern sizes based on a torque balance to predict its diameter, Dc. They assumed that the cavern was spherical, that the predominant motion at the cavern boundary was tangential in nature (applicable to radial flow impellers), and that the stress imparted by the impeller at the cavern boundary was equal to the fluid yield stress. This model was later modified by Elson et al. (1986) assuming the cavern to be a right circular cylinder with height. He, centered on the impeller to give... 

An alternative model was developed to address the problem of estimating fluid yield stress and is based on a fluid velocity approach (Amanullah et al, 1998a). This model considers the total momentum imparted by the impeller as the sum of both tangential and axial components and assumes a torus-shaped cavern. It combines torque and axial force measurements (for axial flow impellers) with the simple power law equation to predict the cavern diameter with the cavern... 

Yield stress fluids create caverns around impellers. The cavern boundary is delineated by the surface where the imposed shear force does not exceed the fluid yield stress. Pulp suspensions exhibit this behavior. The approach developed by Soloman et al. (1981) was used to characterize pulp suspension behavior in a laboratory mixer. A force balance at Ihe cavern boundary (assumed cylindrical) gives its radial extent, r, as ... 

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). 

Pseudoplastic fluids have no yield stress threshold and in these fluids the ratio of shear stress to the rate of shear generally falls continuously and rapidly with increase in the shear rate. Very low and very high shear regions are the exceptions, where the flow curve is almost horizontal (Figure 1.1). 

The apparent viscosity, defined as du/dj) drops with increased rate of strain. Dilatant fluids foUow a constitutive relation similar to that for pseudoplastics except that the viscosities increase with increased rate of strain, ie, n > 1 in equation 22. Dilatancy is observed in highly concentrated suspensions of very small particles such as titanium oxide in a sucrose solution. Bingham fluids display a linear stress—strain curve similar to Newtonian fluids, but have a nonzero intercept termed the yield stress (eq. 23) ... 

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... 

Foams have a wide variety of appHcations that exploit their different physical properties. The low density, or high volume fraction of gas, enable foams to float on top of other fluids and to fiU large volumes with relatively Httle fluid material. These features are of particular importance in their use for fire fighting. The very high internal surface area of foams makes them useful in many separation processes. The unique rheology of foams also results in a wide variety of uses, as a foam can behave as a soHd, while stiH being able to flow once its yield stress is exceeded. 

When an electric field is appHed to an ER fluid, it responds by forming fibrous or chain stmctures parallel to the appHed field. These stmctures greatly increase the viscosity of the fluid, by a factor of 10 in some cases. At low shear stress the material behaves like a soHd. The material has a yield stress, above which it will flow, but with a high viscosity. The force necessary to shear the fluid is proportional to the square of the electric field (116). 

Non-Newtonian fluids include those for which a finite stress 1,. is reqjiired before continuous deformation occurs these are c ailed yield-stress materials. The Bingbam plastic fluid is the simplest yield-stress material its rheogram has a constant slope [L, called the infinite shear viscosity. 

In an ideal fluid, the stresses are isotropic. There is no strength, so there are no shear stresses the normal stress and lateral stresses are equal and are identical to the pressure. On the other hand, a solid with strength can support shear stresses. However, when the applied stress greatly exceeds the yield stress of a solid, its behavior can be approximated by that of a fluid because the fractional deviations from stress isotropy are small. Under these conditions, the solid is considered to be hydrodynamic. In the absence of rate-dependent behavior such as viscous relaxation or heat conduction, the equation of state of an isotropic fluid or hydrodynamic solid can be expressed in terms of specific internal energy as a function of pressure and specific volume E(P, V). A familiar equation of state is that for an ideal gas... 

Figure 8.3. VeJocily flow profile in a tube for a fluid with zero yield stress and assuming no slip at...

Further pressure will cause it to fail and release the process fluid. The yield stress is taken as a design criterion beyond which failure will occur. Table 3.1-1 provides some representative values. 

We wish to calculate the relationship between the fluid pressure and the yield stress. 

For Newtonian fluids the dynamic viscosity is constant (Equation 2-57), for power-law fluids the dynamic viscosity varies with shear rate (Equation 2-58), and for Bingham plastic fluids flow occurs only after some minimum shear stress, called the yield stress, is imposed (Equation 2-59). 

He Hedsfrom Rypd2 Flow of fluid exhibiting yield stress... 

Some materials have the characteristics of both solids and liquids. For instance, tooth paste behaves as a solid in the tube, but when the tube is squeezed the paste flows as a plug. The essentia] characteristic of such a material is that it will not flow until a certain critical shear stress, known as the yield stress is exceeded. Thus, it behaves as a solid at low shear stresses and as a fluid at high shear stress. It is a further example of a shear-thinning fluid, with an infinite apparent viscosity at stress values below the yield value, and a falling finite value as the stress is progressively increased beyond this point. 

Some fluids exhibit a yield stress. When subjected to stresses below the yield stress they do not flow and effectively can be regarded as fluids of infinite viscosities, or alternatively as solids. When the yield stress is exceeded they flow as fluids. Such behaviour cannot be described by a power-law model. 

The simplest type of behaviour for a fluid exhibiting a yield stress is known as Bingham-plastic. The shear rale is directly proportional to the amount by which the stress exceeds the yield stress. 

The boundary between the two regions and the radius rc of the core is determined by the position in the cross-section at which the shear stress is exactly equal to the yield stress Ry of the fluid. Since the shear stress is linearly related to the radial position ... 

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