Absolute or Dynamic Viscosity

For an actual fluid there always exists a relationship between shear stress and shear rate as follows  

The form of the function J is characteristic of the fluid s rheological behavior. In the particular case of so-called, Newtonian fluids, we have a linear equation  

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The absolute or dynamic viscosity is defined as the ratio of shear resistance to the shear velocity gradient. This ratio is constant for Newtonian fluids. 

Kinematic viscosity is the ratio of absolute or dynamic viscosity to density—a quantity in which no force is involved. Kinematic viscosity can be obtained by dividing the absolute viscosity of a fluid by its mass density, as shown in Equation 18.3. 

The momentum, which is a certain amount of mass moving at a certain velocity (v), takes into account the fluid s density (p) and the diameter of the tube (Df). The momentum of the fluid can be increased by increasing the velocity or the diameter of the tube or both. The resistance to flow is expressed as the absolute or dynamic viscosity of the fluid (rj), which is in units of grams per centimeter-second, or centipoise (cP). The transition from laminar to turbulent-flow occurs as Re increases past a critical value between 2000 and 3000 in a straight tube having a smooth internal surface. 

Speed of pump in radians per second absolute or dynamic viscosity... 

The quantity n is the absolute or dynamic viscosity of the fluid. As derived here, viscosity is an adjustment to the hydrodynamic equations relating stress and flow in a fluid to make them fit a postulated mode of behavior. But, as shown in Chapter 4, viscosity can also be defined... 

The sliding plate viscometer, also known as sliding plate micro-viscometer (Figure 4.4a), measures absolute or dynamic viscosity. The apparatus comprises a loading system that applies a shear stress and a recording system of flow as a function of time. The bitumen sample is placed between two plates so as to create a very thin film of 5-50 pm. The apparatus can measure the viscosity only in the range of 10 to 10 Pa s thus, it is not suitable for low-viscosity measurements. 

The viscosity of gases is purely Newtonian, that is, dependent solely on pressure and temperature. Absolute or dynamic viscosity is defined as the shear stress between adjacent layers of different velocities in a flowing medium. 

Slurry is essentially a mixture of solids and liquids. Its physical characteristics are dependent on many factors such as size and distribution of particles, concentration of solids in the liquid phase, size of the conduit, level of turbulence, temperature, and absolute (or dynamic) viscosity of the carrier. Nature offers examples of slurry flows such as seasonal floods that carry sUt and gravel. Every year during the flood season, the Nile transports massive amounts of silt over thousands of miles to the Saharan desert. To rephrase Herodotus, who once said Egypt is the gift of the NUe, one may consider that one of the most ancient civilizations was dependent on natural slurry flows for its survival. 

The flow of slurry in a pipeline is much different from the flow of a single-phase liquid. Theoretically, a single-phase liquid of low absolute (or dynamic) viscosity can be allowed to flow at slow speeds from a laminar flow to a turbulent flow. However, a two-phase mixture, such as slurry, must overcome a deposition critical velocity or a viscous transition critical velocity. The analogy can be made here in terms of an airplane if the speed drops excessively, the airplane stalls and stops flying. If the slurry s speed of flow is not sufficiently high, the particles will not be maintained in suspension. On the other hand, in the case of highly viscous mixtures, if the shear rate in the pipeline is excessively low, the mixture will be too viscous and will resist flow. 

The presence of clays in certain circuits must not be ignored. If clay is not separated, the slurry can be quite viscous. Pumps and pipes must be sized properly to handle the re sultant absolute (or dynamic) viscosity. Certain mines in Peru contain material called soft high clay, which can increase the absolute (or dynamic) viscosity of the slurry up to 400 mPa at weight concentrations in excess of 45%. Dilution to lower concentration and changes to recycling load are solutions to such a problem. 

A mixture of an emulsion and solids such as fine coal could be used to produce a fluid with a high calorific value. Coal must be very fine to burn readily in combustion furnaces. The flow is similar to a homogeneous flow with a high absolute (or dynamic) viscosity component. 

When absolute (or dynamic) viscosity is an important factor, such as in clayish slurries or homogeneous flows, another parameter, the viscous transition critical velocity Kj-must be determined. There are two regimes for flow of homogeneous mixtures. Flow at speeds less than Fj-is associated with laminar flows, whereas flows above Vj-are characteristic of turbulent flows. 

Although density is essentially a static property, absolute (or dynamic) viscosity is a dynamic property and tends to reduce in magnitude as the shear rate in a pipeline increases. Thus, engineers have had to define different forms of viscosity over the years, everything from dynamic viscosity, to kinematic viscosity, to effective pipeline viscosity. The effective pipeline viscosity will be discussed in detail in Chapters 3, 4, and 5. In this chapter, the reader is introduced to basic concepts of the mixture of slurry in a stationary state. This is effectively what the pump, or a mixer, might see at the start-up of a plant. As is often the case, when the driver cannot deliver enough torque to overcome the absolute (or dynamic) viscosity, the operator is forced to dilute the slurry mixture. 

Plasticity as defined in Section 1-1-4 is an important parameter in determining overall absolute (or dynamic) viscosity of a mixture of clay and water. There are, however, numerous soik in nature, such as sand and water or gravel and water, in which the solids contribute little to the overall absolute (or dynamic) viscosity, except in terms of their concentration by volume. 

Absolute (or Dynamic) Viscosity of Mixtures with Volume Concentration Smaller Than 1%... 

For such solid-liquid mixtures in diluted form, Einstein developed the following formula for a linear relationship between absolute (or dynamic) viscosity and volume concentration ... 

The kinematic viscosity is the absolute (or dynamic viscosity) divided by the density. Its unit of measurement are, strictly speaking, m /s or ft /sec. Another unit used is the centistokes, which is obtained by dividing the absolute viscosity in centipoises by the specific gravity of the fluid. A centipoise is equivalent to one miUi-Pascal-second. 

Carrier liquid absolute or dynamic viscosity (usually expressed in Pascal-seconds or poise)... 

The Absolute or Dynamic viscosity is the tangential force per unit area required to move one horizontal plane of the fluid at unit velocity with respect to another maintained at a unit distance apart by the fluid. When the force is 1 dyne/an, the distance between the layers or planes 1 cm and the velocity gradient 1 cm/sec, the viscosity is 1 poise. This being a large unit, absolute viscosity is more commonly... 

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